Light processing system and method

[0001] The instant application is a 371 U.S. national stage of PCT/US10/62111, filed on Dec. 24, 2010, which claims benefit of priority from U.S. Provisional Patent Application Ser. No. 61/290,004, filed on Dec. 24, 2009, and is a CIP of PCT/US10/43801, filed Jul. 29, 2010, which claims benefit of priority from U.S. Provisional Patent Application No. 61/229,608 filed Jul. 29, 2009, and claims benefit of priority from U.S. Provisional Patent Application No. 61/266,916, filed Dec. 4, 2009, and claims benefit of priority from U.S. Provisional Patent Application No. 61/290,004, filed on Dec. 24, 2009, and is a CIP of PCT/US10/31965, filed Apr. 21, 2010, which claims benefit of priority from U.S. Provisional Patent Application No. 61/171,080, filed on Apr. 21, 2009, and claims benefit of priority from U.S. Provisional Patent Application No. 61/178,550, filed on May 15, 2009, and claims benefit of priority from U.S. Provisional Patent Application No. 61/290,004, filed on Dec. 24, 2009, all of which are incorporated herein by reference.

[0002] FIG. 1 illustrates a side view of a wind farm in association with an atmospheric measurement system;

[0003] FIG. 2 illustrates a top view of the wind farm and associated atmospheric measurement system illustrated in FIG. 1;

[0004] FIG. 3 illustrates a LIDAR sensor of an atmospheric measurement system, and an associated measurement volume;

[0005] FIG. 4 illustrates a plurality of LIDAR sensors of an atmospheric measurement system, and a plurality of associated measurement volumes in common therewith;

[0006] FIG. 5 illustrates a planetary boundary layer containing turbulent eddies generated either by associated surface roughness or by thermal gradients;

[0007] FIG. 6a illustrates a first set of embodiments of a first aspect of a range-imaging LIDAR system incorporated in a first aspect of an atmospheric measurement system;

[0008] FIG. 6b illustrates a transverse cross-section of a first embodiment of a beam of light;

[0009] FIG. 6c illustrates a transverse cross-section of a second embodiment of a beam of light;

[0010] FIG. 6d illustrates a second aspect of a Fabry-Pérot interferometer of a range-imaging LIDAR system;

[0011] FIG. 7 illustrates a half-tone image of fringes from a fully illuminated Fabry-Pérot etalon;

[0012] FIG. 8 illustrates an example of a composite of an image of scattered light from an interaction region and an associated reference beam, as input to a Fabry-Pérot interferometer of the first aspect of the range-imaging LIDAR system illustrated in FIG. 6a;

[0013] FIG. 9 illustrates an example of an image of a fringe pattern output from the Fabry-Pérot interferometer, and the input to an associated detection system, of the first aspect of the range-imaging LIDAR system illustrated in FIG. 6a, processing the image illustrated in FIG. 8;

[0014] FIG. 10a illustrates a plot of signal intensity as a function of image distance of the fringe pattern illustrated in FIG. 9;

[0015] FIG. 10b illustrates a plot of signal intensity as a function of range from the LIDAR system to the interaction region, corresponding to the plot illustrated in FIG. 10a;

[0016] FIG. 11 illustrates a third aspect of a Fabry-Pérot interferometer of a range-imaging LIDAR system;

[0017] FIGS. 12a and 12b illustrate a circular image compression process operating on a fringe pattern from a Fabry-Pérot interferometer;

[0018] FIG. 13 illustrates an image of a set of circular fringe patterns and regions of interest associated with a circular binning process;

[0019] FIG. 14a illustrates a flow chart of a first aspect of a circular binning process;

[0020] FIG. 14b illustrates an alternate decision block of the first aspect of a circular binning process illustrated in FIG. 14a;

[0021] FIG. 15 illustrates a flow chart of a second aspect of a circular binning process;

[0022] FIG. 16a illustrates a radial cross-section of an intensity distribution of a set of fringes from a Fabry-Pérot interferometer;

[0023] FIG. 16b illustrates fringes from the Fabry-Pérot interferometer from two scattered signals associated with different velocities;

[0024] FIG. 16c illustrates a fringe associated with a scatter signal channel processed by the Fabry-Pérot etalon, wherein the fringe comprises aerosol (Mie), molecular (Rayleigh) and background signal components;

[0025] FIG. 17 illustrates a block diagram of a data analysis process used to determine atmospheric measurements from signals from a Fabry-Pérot interferometer;

[0026] FIG. 18 illustrates a periodic transmission function of a Fabry-Pérot interferometer;

[0027] FIG. 19 illustrates a block diagram of various aspects of a range-imaging LIDAR system;

[0028] FIG. 20 illustrates an exploded view of thermal chamber assembly enclosing a Fabry-Pérot etalon;

[0029] FIG. 21 illustrates a first exploded view of a core assembly incorporated in the thermal chamber assembly illustrated in FIG. 20;

[0030] FIG. 22 illustrates a second exploded view of the core assembly incorporated in the thermal chamber assembly illustrated in FIG. 20;

[0031] FIG. 23 illustrates a third exploded view of the core assembly incorporated in the thermal chamber assembly illustrated in FIG. 20;

[0032] FIG. 24 illustrates a flow chart of a process for determining measured air data products with a range-imaging LIDAR system;

[0033] FIG. 25 illustrates a flow chart of a process for determining derived air data products with a range-imaging LIDAR system;

[0034] FIG. 26 illustrates a flow chart of a process for determining atmospheric measurements using a range-imaging LIDAR system;

[0035] FIG. 27 illustrates a second embodiment of the first aspect of the range-imaging LIDAR system, incorporating a Fabry-Pérot interferometer without an associated collimating lens;

[0036] FIG. 28 illustrates an embodiment of a second aspect of range-imaging LIDAR system incorporating a second aspect of an associated detection system, suitable for determining atmospheric measurements that are not dependent upon relative wind velocity;

[0037] FIG. 29a illustrates a first embodiment of a third aspect of an associated detection system of a range-imaging LIDAR system;

[0038] FIG. 29b illustrates a plan view of a digital micromirror device (DVD) used in the embodiments illustrated in FIG. 29a.

[0039] FIG. 30 illustrates a pixel element of a digital micromirror device;

[0040] FIG. 31 illustrates two adjacent pixel elements of a digital micromirror device, each in a different pixel mirror rotational state;

[0041] FIG. 32 illustrates a partial derivative with respect to velocity of the intensity distribution of FIG. 16a;

[0042] FIG. 33 illustrates a partial derivative with respect to temperature of the intensity distribution of FIG. 16a;

[0043] FIG. 34 illustrates a set of complementary reflection patterns of a digital micromirror device programmed to gather associated complementary aerosol signal components;

[0044] FIG. 35 illustrates a set of complementary reflection patterns of a digital micromirror device programmed to gather associated complementary molecular signal components;

[0045] FIG. 36 illustrates a set of complementary reflection patterns of a digital micromirror device programmed to gather associated complementary velocity signal components;

[0046] FIG. 37 illustrates a set of complementary reflection patterns of a digital micromirror device programmed to gather associated complementary temperature signal components;

[0047] FIG. 38 illustrates a set of complementary reflection patterns of a digital micromirror device programmed to gather associated complementary background signal components;

[0048] FIGS. 39a-e illustrate radial cross-sections through the complementary reflection patterns illustrated in FIGS. 34-38, respectively;

[0049] FIG. 40 illustrates a partial derivative with respect to velocity of the intensity distribution of FIG. 16a as in FIG. 32, upon which is superimposed a corresponding radial cross-section of a first set of associated complementary reflection patterns of a digital micromirror device programmed to gather associated complementary velocity signal components, for a first value of a velocity threshold that distinguishes the complementary components of the associated complementary reflection patterns;

[0050] FIG. 41 illustrates a partial derivative with respect to velocity of the intensity distribution of FIG. 16a as in FIG. 32, upon which is superimposed a corresponding radial cross-section of a second set of associated complementary reflection patterns of a digital micromirror device programmed to gather associated complementary velocity signal components, for a second value of a velocity threshold that distinguishes the complementary components of the associated complementary reflection patterns;

[0051] FIG. 42 illustrates a flowchart of a Monte Carlo simulation process;

[0052] FIG. 43 illustrates the results from a Monte Carlo simulation used to optimize parameters associated with the complementary reflection patterns used to program a digital micromirror device for gathering signals used to determine atmospheric measurements from a fringe pattern output from a Fabry-Pérot interferometer;

[0053] FIG. 44 illustrates a flowchart of a Genetic Algorithm process;

[0054] FIG. 45 illustrates a composite of radial cross-sections through a first alternative set of complementary reflection patterns;

[0055] FIG. 46 illustrates a composite of radial cross-sections through a second alternative set of complementary reflection patterns;

[0056] FIG. 47 illustrates a second embodiment of the third aspect of an associated detection system of a range-imaging LIDAR system;

[0057] FIG. 48 illustrates an embodiment of a third aspect of a range-imaging LIDAR system;

[0058] FIG. 49 illustrates and embodiment of a fourth aspect of a range-imaging LIDAR system;

[0059] FIG. 50 illustrates an embodiment of a fifth aspect of a range-imaging LIDAR system;

[0060] FIG. 51 illustrates an embodiment of a sixth aspect of a range-imaging LIDAR system;

[0061] FIG. 52 illustrates an embodiment of a seventh aspect of a range-imaging LIDAR system;

[0062] FIG. 53 illustrates a first aspect of plural fringe patterns generated by the sixth aspect of a range-imaging LIDAR system illustrated in FIG. 51;

[0063] FIG. 54 illustrates a second aspect of plural fringe patterns generated by the sixth aspect of a range-imaging LIDAR system illustrated in FIG. 51;

[0064] FIG. 55a illustrates a first embodiment of an eighth aspect of a range-imaging LIDAR system incorporating a first aspect of the associated mask system and the first aspect of an associated detection system;

[0065] FIG. 55b illustrates a transverse cross-section of an expanded reference beam of light associated with the range-imaging LIDAR system illustrated in FIG. 55a;

[0066] FIG. 55c illustrates a transverse cross-section of the expanded reference beam of light after passing through a mask associated with the range-imaging LIDAR system illustrated in FIG. 55a;

[0067] FIG. 55d illustrates an image that would be produced by a Fabry-Pérot interferometer of the range-imaging LIDAR system illustrated in FIG. 55a if the associated Fabry-Pérot etalon were removed therefrom, corresponding to an image of the light signals entering the Fabry-Pérot interferometer;

[0068] FIG. 55e illustrates an image from the Fabry-Pérot interferometer of the range-imaging LIDAR system illustrated in FIG. 55a;

[0069] FIG. 56a illustrates a transverse cross-section of an expanded reference beam of light after passing through a mask associated with a first aspect of plural fringe patterns generated by a first variation of the eighth aspect of a range-imaging LIDAR system used to process light signals from plurality of associated regions of interest;

[0070] FIG. 56b illustrates an image from the Fabry-Pérot interferometer of the range-imaging LIDAR system associated with the image illustrated in FIG. 56a;

[0071] FIG. 57a illustrates a transverse cross-section of an expanded reference beam of light after passing through a mask associated with a second aspect of plural fringe patterns generated by a second variation of the eighth aspect of a range-imaging LIDAR system used to process light signals from plurality of associated regions of interest;

[0072] FIG. 57b illustrates an image from the Fabry-Pérot interferometer of the range-imaging LIDAR system associated with the image illustrated in FIG. 57a;

[0073] FIG. 58a illustrates a transverse cross-section of an expanded reference beam of light after passing through a mask associated with a third aspect of plural fringe patterns generated by a third variation of the eighth aspect of a range-imaging LIDAR system used to process light signals from plurality of associated regions of interest;

[0074] FIG. 58b illustrates an image from the Fabry-Pérot interferometer of the range-imaging LIDAR system associated with the image illustrated in FIG. 58a;

[0075] FIG. 59a illustrates a second embodiment of the eighth aspect of a range-imaging LIDAR system incorporating the first aspect of the associated mask system and the third aspect of an associated detection system;

[0076] FIG. 59b-e illustrate various images associated with the second embodiment of the eighth aspect of a range-imaging LIDAR system corresponding to corresponding images of FIG. 55d-g for the first embodiment of the eighth aspect;

[0077] FIG. 60a-e illustrates a third embodiment of the eighth aspect of a range-imaging LIDAR system incorporating a second aspect of the associated mask system and the third aspect of an associated detection system;

[0078] FIG. 61 illustrates various applications of a range-imaging LIDAR system;

[0079] FIG. 62 illustrates a first embodiment a range-imaging LIDAR system in cooperation with a wind turbine;

[0080] FIG. 63 illustrates a first embodiment a range-imaging LIDAR system in cooperation with a wind turbine;

[0081] FIG. 64 illustrates a schematic block diagram of a ninth aspect of a LIDAR system incorporated in a second aspect of an atmospheric measurement system;

[0082] FIG. 65a illustrates several opto-mechanical elements of an optical air data system;

[0083] FIG. 65b illustrates a geometry of an embodiment of an optical head of a LIDAR system;

[0084] FIG. 66 illustrates an optical head of a biaxial system;

[0085] FIG. 67 illustrates an optical head of a coaxial system;

[0086] FIG. 68 illustrates an isometric view of a Fabry-Pérot interferometer;

[0087] FIG. 69a illustrates fringes from a fully-illuminated Fabry-Pérot etalon;

[0088] FIG. 69b illustrates fringes from a Fabry-Pérot etalon illuminated with four fiber input channels;

[0089] FIG. 70 illustrates four channels of fringes being collapsed by a quad circle-to-line interferometer optic (quad-CLIO) to four lines in the shape of a cross-pattern on an opto-electric detector;

[0090] FIG. 71 illustrates a prior art circle-to-line interferometer optic (CLIO);

[0091] FIG. 72 illustrates the operation of a circle-to-line interferometer optic (CLIO);

[0092] FIG. 73 illustrates a side view of a quad-CLIO element and an associated detector;

[0093] FIG. 74 illustrates a plan view of the quad-CLIO element illustrated in FIG. 73, viewed from the side of an associated first pyramidal shaped optic element;

[0094] FIG. 75 illustrates a plan view of the quad-CLIO element illustrated in FIG. 73, viewed from the side of an associated second pyramidal shaped optic element;

[0095] FIG. 76 illustrates a fragmentary end view of a concave conical reflector on a face of the first pyramidal shaped optic element illustrated in FIGS. 73 and 74, wherein the direction of the end view is substantially parallel to the face of the first pyramidal shaped optic element;

[0096] FIGS. 77a and 77b illustrate a cross-binning process operating on a cross-pattern from a quad-CLIO element;

[0097] FIGS. 78a and 78b illustrate a circular process operating on a fringe pattern from a Fabry-Pérot interferometer;

[0098] FIG. 79 illustrates an image of a set of circular fringe patterns and regions of interest associated with a circular binning process;

[0099] FIG. 80 illustrates a physical layout of various LIDAR system embodiments;

[0100] FIG. 81 illustrates an end view of a fiber-optic assembly connected to the input of the Fabry-Pérot interferometer illustrated in FIG. 80;

[0101] FIG. 82 illustrates a view of a set of circular fringe patterns imaged onto the detector of the optical air data system illustrated in FIG. 80 for an embodiment that does not incorporate a quad-CLIO;

[0102] FIG. 83 illustrates a view of a set of substantially linear fringe patterns imaged onto the detector of the optical air data system illustrated in FIG. 80 for an embodiment that incorporates a quad-CLIO;

[0103] FIG. 84 illustrates a side-view of a signal processor of an optical air data system, including a bi-CLIO element, adapted to provide for measuring wavelength as a function of range;

[0104] FIG. 85 illustrates a plan view of the bi-CLIO element illustrated in FIG. 84, viewed from the perspective of an associated first pyramidal shaped optic element;

[0105] FIG. 86 illustrates a fragmentary end view of a concave conical reflector on a face of the first pyramidal shaped optic element of the bi-CLIO element illustrated in FIGS. 84 and 36, wherein the direction of the end view is substantially parallel to the face of the first pyramidal shaped optic element;

[0106] FIG. 87 illustrates a plan view of the bi-CLIO element illustrated in FIG. 84, viewed from the perspective of an associated second pyramidal shaped optic element;

[0107] FIG. 88 illustrates a fragmentary end view of a reflective surface on a face of the first second shaped optic element of the bi-CLIO element illustrated in FIGS. 84 and 87, wherein the direction of the end view is substantially parallel to the face of the second pyramidal shaped optic element;

[0108] FIG. 89 illustrates a plan view of a CCD detector illustrated in FIG. 84, and an associated imaging process;

[0109] FIG. 90 illustrates an image from the CCD detector illustrated in FIG. 89;

[0110] FIG. 91 illustrates a flow chart of a first imaging process for generating range-resolved images;

[0111] FIG. 92a illustrates a plan view of a CCD detector in an initial state;

[0112] FIG. 92b illustrates a plan view of the CCD detector at the beginning stage of an image recording cycle;

[0113] FIG. 92c illustrates a plan view of the CCD detector at an intermediate stage of the image recording cycle;

[0114] FIG. 92d illustrates a plan view of the CCD detector at a final stage of the image recording cycle;

[0115] FIG. 92e illustrates an image transferred from the CCD detector;

[0116] FIG. 93 illustrates a flow chart of a second imaging process for generating range-resolved images;

[0117] FIG. 94 illustrates various embodiments for multiplexing reference and signal channels for a range-resolved optical air data system;

[0118] FIG. 95 illustrates various interaction regions associated with a common line-of-sight of a second laser beam;

[0119] FIG. 96 illustrates an alternative to the various embodiments illustrated in FIG. 95, suitable for determining air data products that are not dependent upon relative wind velocity;

[0120] FIG. 97 illustrates a laser coupled with a fiber optic to an associated harmonic generator, the output of which is then propagated in free space;

[0121] FIG. 98a illustrates a first embodiment of a laser coupled with a fiber optic to a plurality of harmonic generators in series for generating a fourth harmonic;

[0122] FIG. 98b illustrates a second embodiment of a laser coupled with a fiber optic to a plurality of harmonic generators in series for generating a third harmonic;

[0123] FIG. 98c illustrates a third embodiment of a laser coupled with a first fiber optic to a first harmonic generator, the latter of which is connected to a second harmonic generator with a second fiber optic;

[0124] FIG. 98d illustrates a fourth embodiment of a laser coupled to a first harmonic generator, the latter of which is connected to a second harmonic generator with a fiber optic;

[0125] FIG. 99 illustrates a gimbal mechanism operatively associated with an optical air data system;

[0126] FIG. 100 illustrates a schematic block diagram of a tenth aspect of a LIDAR system;

[0127] FIG. 101 illustrates a schematic block diagram of an eleventh aspect of a LIDAR system;

[0128] FIG. 102a illustrates a schematic block diagram of a twelfth aspect of a LIDAR system;

[0129] FIG. 102b illustrates an image in the output focal plane of the Fabry-Pérot interferometer incorporated in the twelfth aspect of the LIDAR system illustrated in FIG. 102a, absent the associated Fabry-Pérot etalon;

[0130] FIG. 102c illustrates an image in the output focal plane of the Fabry-Pérot interferometer incorporated in the twelfth aspect of the LIDAR system illustrated in FIG. 102a, with the associated Fabry-Pérot etalon in place;

[0131] FIG. 103a illustrates a schematic block diagram of a thirteenth aspect of a LIDAR system;

[0132] FIG. 103b illustrates an image in the output focal plane of the Fabry-Pérot interferometer incorporated in the thirteenth aspect of the LIDAR system illustrated in FIG. 103a, absent the associated Fabry-Pérot etalon;

[0133] FIG. 103c illustrates an image in the output focal plane of the Fabry-Pérot interferometer incorporated in the thirteenth aspect of the LIDAR system illustrated in FIG. 103a, with the associated Fabry-Pérot etalon in place;

[0134] FIG. 104 illustrates a generalized embodiment a direct detection LIDAR system in accordance with a fourteenth aspect of a LIDAR system incorporated in a third aspect of an atmospheric measurement system;

[0135] FIG. 105a illustrates a first embodiment of an analog phase detector;

[0136] FIG. 105b illustrates an operating characteristic of the first embodiment of the analog phase detector illustrated in FIG. 105a;

[0137] FIG. 106a illustrates a second embodiment of an analog phase detector;

[0138] FIG. 106b illustrates an operating characteristic of the second embodiment of the analog phase detector illustrated in FIG. 106a;

[0139] FIG. 107 illustrates an operating characteristic of a digital phase detector;

[0140] FIG. 108 illustrates a fourth aspect of an atmospheric measurement system;

[0141] FIG. 109 illustrates a fifth aspect of an atmospheric measurement system;

[0142] FIG. 110a illustrates a first embodiment of a fifteenth aspect of a LIDAR system incorporated in the second aspect of an atmospheric measurement system that provides for processing backscattered light from a single range cell using a LIDAR system incorporating a second aspect of an associated mask system, a first aspect of an associated collimation system and a first aspect of an associated detection system;

[0143] FIG. 110b illustrates a transverse cross-section of an expanded reference beam of light associated with the atmospheric measurement system illustrated in FIG. 110a;

[0144] FIG. 110c illustrates a transverse cross-section of the expanded reference beam of light after passing through a mask associated with the atmospheric measurement system illustrated in FIG. 110a;

[0145] FIG. 110d illustrates an image that would be produced by a Fabry-Pérot interferometer of the LIDAR system illustrated in FIG. 110a if the associated Fabry-Pérot were removed therefrom, corresponding to an image of the light signals entering the Fabry-Pérot interferometer;

[0146] FIG. 110e illustrates an image from the Fabry-Pérot interferometer of the LIDAR system illustrated in FIG. 110a;

[0147] FIGS. 111a-111e illustrate a second embodiment of the fifteenth aspect of a LIDAR system incorporated in the second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the first embodiment illustrated in FIGS. 110a-110e except that the second embodiment incorporates a second embodiment of an associated collimation system;

[0148] FIGS. 112a-112e illustrate a first embodiment of a sixteenth aspect of a LIDAR system incorporated in the second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the second embodiment of the fifteenth aspect illustrated in FIGS. 111a-111e except that the first embodiment the sixteenth aspect provides for processing a plurality of associated range cells, wherein the associated backscatter light signals are not all radially aligned with a common set of fringes of the associated Fabry-Pérot interferometer;

[0149] FIGS. 113a-113e illustrate a second embodiment of the sixteenth aspect of a LIDAR system incorporated in the second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the first embodiment illustrated in FIGS. 112a-112e except that the associated backscatter light signals are all radially aligned with a common set of fringes of the associated Fabry-Pérot interferometer;

[0150] FIGS. 114a-114f illustrate a seventeenth aspect of a LIDAR system incorporated in the second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the second embodiment of the fifteenth aspect illustrated in FIGS. 111a-111e except that the seventeenth aspect incorporates a second embodiment of an associated detection system;

[0151] FIGS. 115a-115e illustrate an eighteenth aspect of a LIDAR system incorporated in the second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the seventeenth aspect illustrated in FIGS. 114a-114f except that the eighteenth aspect provides for processing a plurality of associated range cells; and

[0152] FIGS. 116a-116e illustrate a nineteenth aspect of a LIDAR system incorporated in the second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the eighteenth aspect illustrated in FIGS. 115a-115e except that the nineteenth aspect incorporates the second aspect of an associated mask system.

[0153] FIG. 117 illustrates a second aspect of an interferometer comprising a Michelson interferometer configured as Fourier Transform Spectrometer, used in cooperation with a fourth aspect of an associated detection system;

[0154] FIG. 118a illustrates a third aspect of an interferometer comprising a Spatial Heterodyne Spectrometer (SHS) used in cooperation with a fifth aspect of an associated detection system;

[0155] FIG. 118b illustrates the operation of each diffraction grating that is incorporated in the Spatial Heterodyne Spectrometer illustrated in FIG. 118a;

[0156] FIG. 119 illustrates a fourth aspect of an interferometer comprising a Doppler Asymmetric Spatial Heterodyne (DASH) Spectrometer used in cooperation with the fifth aspect of an associated detection system;

[0157] FIG. 120 illustrates output images of the fourth aspect of the interferometer illustrated in FIG. 119, for corresponding inputs comprising two light signals, one substantially monochromatic, and the other slightly Doppler-shifted with respect thereto;

[0158] FIG. 121 illustrates the output image of the fourth aspect of the interferometer illustrated in FIG. 119, for corresponding inputs comprising two light signals, one a temperature-broadened scattered light signal, the other slightly Doppler-shifted with respect thereto, together with a plot of the difference therebetween;

[0159] FIG. 122a illustrates a top view of an embodiment of the fourth aspect of the interferometer, portions of which are otherwise shown schematically in FIG. 119;

[0160] FIG. 122b illustrates a side view of the embodiment of the fourth aspect of the interferometer illustrated in FIG. 122a;

[0161] FIG. 122c illustrates a magnified view of the formation of the image illustrated in FIG. 122b;

[0162] FIGS. 123a and 123b illustrate a twentieth aspect of a LIDAR system incorporated in a second aspect of an atmospheric measurement system and an image associated therewith;

[0163] FIGS. 124a and 124b illustrate a first embodiment of a twenty-first aspect of a LIDAR system incorporated in a second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the ninth aspect of the LIDAR system illustrated in FIG. 64 but with either a third or fourth aspect of the associated interferometer;

[0164] FIGS. 125a-125d illustrates a first embodiment of a twenty-second aspect of a LIDAR system incorporated in a second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the fifteenth aspect of the LIDAR system illustrated in FIGS. 110a-110c and 110e but with either a third or fourth aspect of the associated interferometer;

[0165] FIGS. 126a and 126b illustrate a second embodiment of the twenty-first aspect of a LIDAR system incorporated in a second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the thirteenth aspect of the LIDAR system illustrated in FIGS. 103a and 103c but with either a third or fourth aspect of the associated interferometer;

[0166] FIGS. 127a-127d illustrate a second embodiment of the twenty-second aspect of a LIDAR system incorporated in a second aspect of an atmospheric measurement system and various images associated therewith, corresponding to the sixteenth aspect of the LIDAR system illustrated in FIGS. 112a-112c and 112e and 113a-113c and 113e but with either a third or fourth aspect of the associated interferometer;

[0167] FIGS. 128a-128d illustrate a twenty-third aspect of a range-imaging LIDAR system incorporated in a first aspect of an atmospheric measurement system and various images associated therewith, corresponding to the eighth aspect of the LIDAR system illustrated in FIGS. 55a-55c and 55e but with either a third or fourth aspect of the associated interferometer; and

[0168] FIGS. 129a and 129b illustrate a twenty-forth aspect of a range-imaging LIDAR system incorporated in a first aspect of an atmospheric measurement system and an image associated therewith, corresponding to the seventh aspect of the LIDAR system illustrated in FIG. 52 but with either a third or fourth aspect of the associated interferometer.

[0169] Referring to FIGS. 1 and 2, an atmospheric measurement system 10 is illustrated in association with a wind farm 12 comprising a plurality of wind turbines 14 that are used to generate power, e.g. electrical power, from the wind 16.

[0170] For each wind turbine 14, the theoretical upper limit to the amount of wind power P* available for conversion to mechanical or electrical power is given by Bentz Law, i.e.
P*=0.5*ρ*v³*A  (1)
wherein the wind power P* is the power in units of watts of the wind 16 flowing at an effective wind speed v through the area A swept by the rotor 18 of the wind turbine 14, ρ is the density of the atmosphere 20 in units of [kg m⁻³], the effective wind speed v of the wind 16 is in units of [m s⁻¹], and the swept area A of the rotor 18 is in units of [m²], with the wind 16 flowing in a direction normal to the swept area A.

[0171] More generally, for an arbitrary direction of wind 16 relative to the swept area A, the corresponding upper limit of wind power P flowing through the area A swept by the rotor 18 of the wind turbine 14 is given by the dot product of the wind power flux density ψ and the area vector Ā of the swept area A of the rotor 18 of the wind turbine 14, or
P*= ψ*Ā  (2)
wherein the wind power flux density ψ is a vector pointing in the direction of the wind 16, having a magnitude of:
∥ ψ∥=0.5*ρ*v³  (3)
with units of [watt m⁻²], and the area vector Ā is a vector pointing in a direction that is normal to, and having a magnitude equal to, the swept area A of the rotor 18, wherein the associated wind power flux propagates in the direction of the wind power flux density ψ vector.

[0172] The direction and magnitude of wind power flux density ψ are a function of spatial coordinates, which can be expressed with respect to any suitable coordinate system, for example, Cartesian coordinates, i.e. ψ(x, y, z); spherical coordinates centered about the Earth i.e. ψ(r, φ, θ) with r being the distance from the center of the earth, φ being the angle of longitude, and θ being the angle of latitude; or ellipsoidal or oblate spheroidal coordinates that might better account for the shape of Earth's surface.

[0173] The atmospheric measurement system 10 provides for generating a measure of wind power flux density ψ over the geographic area of the wind farm 12, which can be used to predict an upper bound on power generating capability of each of the wind turbines 14 thereof, and which can accordingly be used for controlling the wind turbines 14 responsive thereto. More particularly, the atmospheric measurement system 10 comprises a network 22 of LIDAR systems 24, each of which provide for remotely sensing atmospheric data including wind speed v and atmospheric density ρ at one or more different range bins 26 along one or more associated beams of light 28 projected into the atmosphere 20, from scattered light 30 scattered by the atmosphere 20 from within the range bins 26 and received by associated receive optics 32, e.g. one or more telescopes 32′, of each LIDAR system 24 that cooperate with one or more associated detection systems 34. For example, each LIDAR system 24 may be constructed and operated in accordance with the teachings of any of the following: U.S. patent application Ser. No. 11/460,603 filed on 27 Jul. 2006 that issued as U.S. Pat. No. 7,495,774 on 24 Feb. 2009, entitled Optical Air Data System; International Application Serial No. PCT/US10/31965 filed on 21 Apr. 2010, entitled Atmospheric measurement system; U.S. application Ser. No. 12/780,895 filed on 15 May 2010, entitled Range imaging LIDAR U.S. Provisional Patent Application Ser. No. 61/266,916, filed on Dec. 4, 2009, entitled Direct Detection LIDAR; and U.S. Provisional Patent Application Ser. No. 61/290,004, filed on Dec. 24, 2009, entitled LIDAR Signal Processing System and Method, all of which above-identified patents and patent applications are incorporated herein by reference in their entirety.

[0174] For each beam of light 28, and within each associated range bin 26 thereof, the associated LIDAR system 24 provides for measuring corresponding atmospheric data 36, including a component of wind speed v in a direction along the beam of light 28 responsive to a Doppler shift in the frequency of the scattered light 30 by either or both molecular or aerosol components of the atmosphere 20, and including associated atmospheric data scalars of atmospheric temperature T, atmospheric density ρ, molecular counts N_M, aerosol counts N_A and background counts N_B at a given sampling times, wherein the particular sampling times t_i are also measured, for example, using an associated GPS receiver 38 that provides a corresponding universal time reference, so as to provide for accounting for the dynamic behavior of the associated atmospheric data. Accordingly, in an atmospheric measurement system 10 adapted to generate a measure of wind power flux density ψ over a geographic area, each associated LIDAR system 24 provides for generating an atmospheric measurement record 40 for each range bin 26 at each sampling time t_i that includes at least an identification or nominal location of the associated range bin 26, the extent, e.g. length, of the range bin 26, the sampling time t_i, the magnitude and direction of the component of wind speed v in the direction along the beam of light 28, the local density ρ of the atmosphere 20, and may also include measurements of the other atmospheric data scalars identified herein, for example, temperature. As another example, in some embodiments, water vapor is also measured and the measurement of water vapor is also included in the atmospheric measurement record 40.

[0175] In the example of the atmospheric measurement system 10 and wind farm 12 illustrated in FIGS. 1 and 2, two of the wind turbines 14.1, 14.2 are illustrated with associated LIDAR systems 24.1, 24.2 incorporating corresponding beams of light 28ⁱ, 28ⁱⁱ that emanate from a central region of the rotors 18 of the associated wind turbines 14.1, 14.2—for example, from the hubs 19 thereof—and that rotate therewith so that the respective associated beams of light 28 sweep out corresponding conical surfaces of revolution 42.1, 42.2, wherein different wind turbines 14.1, 14.2 are illustrated pointing in different directions, for example, responsive to spatial variations of the associated wind field 16′, with the associated conical surfaces of revolution 42.1, 42.2 aligned with the associated rotors 18.1, 18.2 pointing in the corresponding different directions. The LIDAR system 24 can also be decoupled from the hub, providing fixed beams of light 28 pointing in different directions. Anywhere from one to six beams of light 28 would be typical. In one embodiment, a single beam of light 28 is aligned with the axis of rotation of the wind turbine. The beam of light 28 can be either aligned with and along the axis of rotation or transversely offset relative thereto. A third wind turbine 14.3 is illustrated with an associated LIDAR system 24.3 relatively fixed to the nacelle 44 thereof and incorporating three associated fixed beams of light 28.1ⁱⁱⁱ, 28.2ⁱⁱⁱ, 28.3ⁱⁱⁱ directed in three corresponding different directions 46.1ⁱⁱⁱ, 46.2ⁱⁱⁱ, 46.3ⁱⁱⁱ, wherein the beams of light 28.1ⁱⁱⁱ, 28.2ⁱⁱⁱ, 28.3ⁱⁱⁱ along the associated directions 46.1ⁱⁱⁱ, 46.2ⁱⁱⁱ, 46.3ⁱⁱⁱ turn with the nacelle 44 as the direction 48ⁱⁱⁱ of the nacelle 44 is changed to accommodate changes in the local direction 50 of the wind 16. The atmospheric measurement system 10 is also illustrated with additional LIDAR systems 24.4, 24.5 that are separate from the wind farm 12, for example, upstream thereof in the associated wind field 16′ so as to provide associated atmospheric data 36 of wind 16 in advance of the interaction thereof with the wind turbines 14.1, 14.2, 14.3 located downstream thereof. For example, a fourth LIDAR system 24.4 is illustrated incorporating two associated beams of light 28.1^iv, 28.2^iv in two corresponding different directions 46.1^iv, 46.2^iv, and a fifth LIDAR system 24.5 is illustrated also incorporating two associated beams of light 28.1^v, 28.2^v in two corresponding different directions 46.1^v, 46.2^v.

[0176] Generally, the determination of wind direction and the total magnitude of wind speed v requires at least three measures of associated wind speed v in three linearly independent directions. This can be provided either by a single LIDAR system 24 with an associated beam or beams of light 28 and associated receive optics 32 looking in at least three linearly independent directions, or a plurality of different LIDAR system 24 that collectively incorporate associated beams of light 28 and associated receive optics 32 collectively looking in at least three linearly independent directions, such that the wind field 16′ being measured by the LIDAR system or systems 24 is assumed to be relatively uniform for each group of separate associated measurements, for example, each group of three measurements in three associated linearly independent directions.

[0177] For example, in accordance with a first aspect, referring to FIGS. 1, 2 and 3, for a single LIDAR system 24 with either a single beam of light 28 projected into the atmosphere 20 at three different times in three different linearly independent directions 46, or three separate beams of light 28′, 28″, 28′″ projected into the atmosphere 20 substantially simultaneously in three different linearly independent directions 46.1, 46.2, 46.3, the resulting three measurements of wind speed v for the associated range bin 26 can be combined to provide a vector measure of wind velocity v for the associated measurement volume 52 if the wind field 16′ is relatively uniform within measurement volume 52 during the period of time over which the associated measurements are made with the LIDAR system 24. For example, the first aspect illustrated in FIG. 3 is representative of the measurement volumes 52ⁱ, 52ⁱⁱ, 52ⁱⁱⁱ associated with the first 24.1, second 24.2 and third 24.3 LIDAR systems illustrated in FIGS. 1 and 2, wherein for the first 24.1 and second 24.2 LIDAR systems the three separate beams of light 28′, 28″, 28′″ illustrated in FIG. 3 correspond to the respective single beams of light 28ⁱ, 28ⁱⁱ illustrated in FIGS. 1 and 2 at three distinct points in time corresponding to three distinct rotational angles of the corresponding rotors 18 of the corresponding wind turbines 14.1, 14.2; and for the third LIDAR system 24.3, the three separate beams of light 28′, 28″, 28′″ illustrated in FIG. 3 correspond to the respective associated three separate beams of light 28.1ⁱⁱⁱ, 28.2ⁱⁱⁱ, 28.3ⁱⁱⁱ illustrated in FIGS. 1 and 2 at a substantially common point in time. The resolution and accuracy of the resulting measure of wind velocity v will depend upon the relative separation and independence of the associated directions 46.1, 46.2, 46.3 of the beams of light 28′, 28″, 28′″ from which the measurement is derived. For example, to be independent, the three beams of light 28′, 28″, 28′″ cannot all lie in the same plane. The resulting measure of wind velocity v is improved with increasing mutual angles of separation of the associated beams of light 28′, 28″, 28″. The resolution and accuracy of the resulting measure of wind velocity v will also depend upon the variation of actual wind velocity v within the measurement volume 52 during the associated measurement interval. For example, for the first 24.1 and second 24.2 LIDAR sensors, this is dependent both upon the spatial extent of the associated conical surfaces of revolution 42.1; 42.2, and the temporal extent between the first and last rotational positions of the associated rotors 18 and associated respective beams of light 28ⁱ, 28ⁱⁱ associated with the corresponding beams of light 28′, 28″, 28′″ for which the measurements of wind speed v are made, and upon the associated change in wind velocity v over both these associated spatial and temporal extents.

[0178] With three separate beams of light 28′, 28″, 28′″ emanating from a common LIDAR system 24, the spatial extent of the measurement volume 52 and the associated separation between wind speed v measurements grows with range from the LIDAR system 24, thereby increasing the prospects for variation in associated actual wind velocity v within the measurement volume 52 with increasing range, which could thereby reduce the accuracy of a resulting associated measurement of wind velocity v from the associated wind speed v measurements. For example, it is not uncommon to have a substantial variation of actual wind speed v between the top and bottom of the path of the associated rotor 18 during the rotation thereof.

[0179] In accordance with a second aspect, referring to FIGS. 1, 2 and 4, the LIDAR systems 24 may be used in cooperation with one another so as to provide for a plurality of different beams of light 28′, 28″, 28′″ in different directions from different LIDAR systems 24.1, 24.2, 24.3 directed through a common measurement volume 52, and with associated receive optics 32 of the different LIDAR systems 24.1, 24.2, 24.3 having associated different fields-of-view 54.1, 54.2, 54.3 (with different superscripts ′, ″ and ′″ associated with different beams of light 28′, 28″, 28′″ from each of the LIDAR systems 24.1, 24.2, 24.3) that each intersect one another within the common measurement volume 52 so as to receive scattered light 30 therefrom, and thereby collectively provide for generating three different corresponding measures of wind speed v₁, v₂, v₃ from three different associated directions 46.1, 46.2, 46.3 for the common measurement volume 52, from which an associated wind velocity v can be determined that is substantially unaffected by either spatial or temporal variations in actual wind velocity v if the measures of wind speed v₁, v₂, v₃ are sufficiently simultaneous relative to any temporal variation of the wind field 16′ within the measurement volume 52. The size of the common measurement volume 52, and therefore the spatial resolution of the resulting measurement of wind velocity v, depends upon the extent to which the different beams of light 28′, 28″, 28′″ and the associated different fields-of-view 54.1, 54.2, 54.3 of the associated receive optics 32 intersect one another, and the relative angles thereof, within the common measurement volume 52.

[0180] To the extent that the different beams of light 28′, 28″, 28′″ or the associated different fields-of-view 54.1, 54.2, 54.3 of the associated receive optics 32 do not all intersect one another within the common measurement volume 52, or to the extent that all of the associated measures of wind speed v₁, v₂, v₃ are not generated simultaneously, then the accuracy of the resulting measure of wind velocity v as determined from the measures of wind speed v₁, V₂, v₃ will be affected by both the spatial and temporal variation of actual wind velocity v from an assumed uniform common actual wind velocity v that is otherwise assumed to be associated with the measures of wind speed v₁, v₂, v₃.

[0181] Referring in particular to FIG. 4, there is illustrated a group of three LIDAR systems 24.1, 24.2, 24.3 in cooperation with one another so as to provide for generating three different measures of wind velocity v₁, v₂, v₃ from three corresponding different measurement volumes 52.1, 52.2, 52.3, substantially independent of spatial and temporal variations of the associated wind field 16′. More particularly, each of the LIDAR systems 24.1, 24.2, 24.3 respectively projects a corresponding respective first beam of light 28.1′, 28.2′, 28.3′ into the respective corresponding measurement volume 52.1, 52.2, 52.3 substantially in front of the corresponding respective LIDAR system 24.1, 24.2, 24.3, and each LIDAR system 24.1, 24.2, 24.3 incorporates a respective corresponding first set of receive optics 32.1ⁱ, 32.2ⁱ, 32.3ⁱ, each having a respective corresponding associated fields-of-view 54.1′, 54.2′, 54.3′ that intersect the respective corresponding first beam of light 28.1′, 28.2′, 28.3′ within the respective corresponding measurement volume 52.1, 52.2, 52.3 so as to provide for measuring a respective corresponding first component of wind speed v_1.1, v_1.2, v_1.3 therewithin along a respective corresponding first direction 46.1′, 46.2′, 46.3′. The first LIDAR system 24.1 also projects a second beam of light 28.1″ through the second 52.2 and third 52.3 measurement volumes, and incorporates a second set of receive optics 32.1ⁱⁱ having associated fields-of-view 54.1″ that intersect the second beam of light 28.1″ within the second 52.2 and third 52.3 measurement volumes so as to provide for measuring respective corresponding second components of wind speed v_2.2, v_2.3 therewithin along a corresponding second direction 46.1″. The second LIDAR system 24.2 also projects a second beam of light 28.2″ through the first measurement volume 52.1 and incorporates a second set of receive optics 32.2ⁱⁱ having an associated field-of-view 54.2″ that intersects the second beam of light 28.2″ within the first measurement volume 52.1 so as to provide for measuring a corresponding second component of wind speed v_2.1 therewithin along a corresponding second direction 46.2″. Furthermore, the second LIDAR system 24.2 also projects a third beam of light 28.2″ through the third measurement volume 52.3, and incorporates a third set of receive optics 32.2ⁱⁱⁱ having an associated field-of-view 54.2′″ that intersects the third beam of light 28.2′″ within the third measurement volume 52.3 so as to provide for measuring a corresponding third component of wind speed v_3.3 therewithin along a corresponding third direction 46.2′″. The third LIDAR system 24.3 also projects a second beam of light 28.3″ through the second 52.2 and first 52.1 measurement volumes, and incorporates a second set of receive optics 32.3ⁱⁱ having associated fields-of-view 54.3″ that intersect the second beam of light 28.3″ within the second 52.2 and first 52.1 measurement volumes so as to provide for measuring respective corresponding third components of wind speed v_3.2, v_3.1 therewithin along a corresponding second direction 46.3″. The associated beams of light 28.1′, 28.2″, 28.2′, 28.2″, 28.3′″, 28.3′, 28.3″ are configured so that the associated directions 46.1′, 46.2″ and 46.3″ are linearly independent (i.e. not all in the same plane) within the first measurement volume 52.1, the associated directions 46.2′, 46.1″ and 46.3″ are linearly independent (i.e. not all in the same plane) within the second measurement volume 52.2, and the associated directions 46.3′, 46.1″ and 46.2′″ are linearly independent (i.e. not all in the same plane) within the third measurement volume 52.3, so as to provide for determining a first measure of wind velocity v₁ from the first v_1.1, second v_2.1 and third v_3.1 components of wind speed within the first measurement volume 52.1, determining a second measure of wind velocity v₂ from the first v_1.2, second v_2.2 and third v_3.2 components of wind speed within the second measurement volume 52.2, and determining a third measure of wind velocity v₃ from the first v_1.3, second v_2.3 and third v_3.3 components of wind speed within the third measurement volume 52.3. For example, the second aspect illustrated in FIG. 4 is representative of the measurement volumes 52^iv, 52^v associated with the third 24.3, fourth 24.4 and fifth 24.5 LIDAR sensors illustrated in FIGS. 1 and 2.

[0182] Generally, each LIDAR system 24 may provide for one or more beams of light 28 and associated fields-of-view 54, and any number of distinct beams of light 28 and associated fields-of-view 54 from different LIDAR systems 24 may be associated with each measurement volume 52. The configurations illustrated in FIGS. 1-4 are not intended to be limiting. For example, the a particular LIDAR systems 24.3, 24.4, 24.5 illustrated in FIGS. 1 and 2, or the LIDAR systems 24.1, 24.2, 24.3 illustrated in FIG. 4, with associated distinct beams of light 28 could each incorporated more than three distinct fields-of-view 54, for example, using the same number of fixed beams of light 28 or a fewer number of beams of light 28 whose position or direction is varied over time. Furthermore, there could be more than three associated fields-of-view 54 associated with any of the associated measurement volumes 52ⁱⁱⁱ, 52^iv, 52^v, 52.1, 52.2, 52.3. As a further example, for either the first 14.1 or second 14.2 wind turbine illustrated in FIGS. 1 and 2, the beams of light 28 associated therewith could be adapted to sweep out a plurality of conical surfaces of revolution 42, or a more general pattern, by varying the angle of the beam of light 28 relative to the axis of rotation of the associated wind turbine 14. Furthermore, the associated LIDAR systems 24 of the atmospheric measurement system 10 may incorporate, or be incorporated in, a variety of platforms, including, but not limited to fixed, portable, or mobile platforms, the latter of which include land vehicles, aircraft, balloons and satellites, wherein for each platform, the associated one or more beams of light 28 of the associated LIDAR system 24 may be either fixed or positionable relative to the associated platform, the latter of which includes either positioning at discrete orientations or continuous scanning.

[0183] The location of a particular measurement volume 52 and the value of the associated measure of wind velocity v collectively depend upon the locations of the associated LIDAR systems 24 and the associated directions 46.1, 46.2, 46.3 of the associated beams of light 28 and the directions of the fields-of-view 54 of the associated receive optics 32. Accordingly, the accuracy to which the locations of the associated LIDAR systems 24, the directions 46.1, 46.2, 46.3 of the associated beams of light 28, and the directions of the fields-of-view of the 54 of the associated receive optics 32 are known or measured, and the variability thereof, will affect the accuracy and variability of the resulting calculated location of the associated measurement volume 52 and the resulting calculated measure of wind velocity associated therewith. When a plurality of different LIDAR systems 24 are associated with a particular measurement volume 52, then the resulting accuracy and variability of the associated calculated location of the associated measurement volume 52 and the calculated measure of wind velocity v associated therewith will depend upon the collective accuracy and variability of the underlying locations and directions of the associated plural LIDAR systems 24, wherein for a given level of accuracy and variability, the resulting level of accuracy needed for each associated LIDAR system 24 decreases as the number of associated LIDAR systems 24 is increased.

[0184] Depending upon the underlying structure to which the LIDAR system 24 is mounted, the location of the LIDAR system 24 can be influenced by the local winds. For example, although commercial wind turbines 14 can be impressive structures, they should not necessarily be considered to be stationary. Large wind loads can cause the associated towers to bend and sway, thereby changing the associated LIDAR look angles and location, respectively, of an associated LIDAR system 24 mounted thereon. Changes in the LIDAR look angle(s) will produce errors in reporting the measurement vector resulting in relatively larger altitude errors at relatively longer ranges. Sway of the LIDAR system 24 causes an error in the resulting measure of wind velocity v.

[0185] However, these errors may be accounted for by measuring the motion of each LIDAR system 24 with associated sensors responsive to bending and swaying of the underlying platform. The selection of the sensors will depend upon the dynamics of the particular platform. For example, for a mobile platform, an Inertial Measurement Unit, IMU, might be required to provide the necessary platform orientation, location and velocity information. In other situations, such as a portable or stationary scenario, a simple tilt sensor coupled with a compass or some other method of determining an azimuth might be sufficient. There are entire suites of sensors and techniques that may be used depending upon the platform dynamics and the required measurement accuracy. The associated measurements from each LIDAR system 24 can then be corrected to account the underlying movement thereof, for example, by transforming the locations of the associated measurements to locations in either an absolute coordinate system or an earth-fixed coordinate system responsive to measurements of the motion of the underlying platform.

[0186] Given a measure of three independent wind speed v₁, v₂, v₃ components of a common wind velocity v within a particular measurement volume 52 along respective directions 46.1, 46.2, 46.3 represented by associated respective unit vectors ê₁, ê₂, ê₃, the corresponding wind velocity v is given by:

[0187] $\begin{array}{cc}\stackrel{\_}{v}={\left[\begin{array}{c}{\hat{e}}_1\\ {\hat{e}}_2\\ {\hat{e}}_3\end{array}\right]}^{-1}·\left[\begin{array}{c}{v}_1\\ v_2\\ v_3\end{array}\right]& \left(4\right)\end{array}$

[0188] If more than three wind speed v measurements are available for a particular measurement volume 52—for at least three linearly independent directions 46, i.e. not all in the same plane—then the corresponding wind velocity v can be solved therefrom, for example, using linear regression.

[0189] The LIDAR systems 24 provide for determining wind velocity v at each of the associated measurement volumes 52 from a combination of measurements along separate directions 46; and for determining a measure of atmospheric density ρ associated with each measurement within each measurement volume 52, which can be averaged to provide for a single associated averaged measure of atmospheric density ρ for each measurement volume 52. Accordingly, the LIDAR systems 24 provide for determining the associated wind power flux density ψ, the magnitude of which is given by Equation (3), the direction of which is given by that of the associated wind velocity v, i.e.:
ψ=0.5*ρ*v²· v  (5)
where:
v=∥ v∥  (6)

[0190] In addition to vector measures of wind velocity v and wind power flux density ψ, and the associated scalar magnitudes thereof, and the atmospheric data scalar atmospheric density ρ, the associated LIDAR systems 24 provide for generating measures of atmospheric data scalars of atmospheric temperature T, molecular counts N_M, aerosol counts N_A and background counts N_B, which, together with a measure of the associated sampling times for example, using an associated GPS receiver 38, can be stored for each measurement volume 52 so as to provide for a map of atmospheric data over space and time, which can be used for anticipatory control of the associated wind farm 12 and the associated power grid 56 supplied therefrom, or for other applications, such as weather forecasting. Depending upon the location, size and number of measurement volumes 52, the associated atmospheric measurement system 10 can provide for detecting associated atmospheric turbulence so as to provide for warning if turbulence—for example, as a from an approaching boundary layer interface 58—exceeds or is expected to exceed acceptable associated turbine-dependent threshold levels for the wind turbines 14 of the wind farm 12, so as to prevent turbulence-induced damage to the wind turbines 14.

[0191] Referring to FIG. 5, from Robert A. Brown, Fluid Mechanics of the Atmosphere, Academic Press, Inc., New York, 1991, which is incorporated herein by reference, turbulence is a random velocity fluctuation from the mean wind speed and direction, wherein associated turbulent elements are vortex elements of variable size and strength and associated turbulent eddies 59 provide for transporting fluid properties in random motion and associated properties are exchanged by rapid mixing.

[0192] In general, wind turbines 14 are pointed in a direction 48 to receive the main flow of wind 16 from the associated wind field 16′, so that an associated LIDAR system 24 mounted on a wind turbine 14 and looking towards incoming the wind 16 is positioned optimally to measure the wind speed v directed at the wind turbine 14. However, turbulence or a velocity component that is perpendicular to the main flow could potentially damage the wind turbine 14, but might not be detectable by a LIDAR system 24 mounted on a wind turbine 14 and looking towards incoming the wind 16. The atmospheric measurement system 10 can incorporate additional LIDAR systems 24 that provide for detecting this turbulence so as to provide for protecting the associated wind turbines 14 from turbulence-induced damage. More particularly, with a sufficient number and density of associated measurement volumes 52, the atmospheric measurement system 10 can provide sufficient resolution to detect turbulent eddies 59, vortices and billows within the atmosphere 20, and to provide an indication when changes in wind velocity v or wind power flux density ψ are sufficiently large to possibly damage one or more wind turbines 14.

[0193] More particularly, the atmospheric measurement system 10 can provide for measuring the uniformity or non-uniformity of the wind field 16′ from spatially-distributed measurements of the wind velocity v field from the spatially-distributed LIDAR systems 24 so as to provide for characterizing either turbulence or wind shear. These measurements can include approximations of the vorticity on several different length scales that are important to wind turbines 14.

[0194] Measurements of an associated temperature structure parameter C_T² can also be used to identify areas where significant turbulence is occurring. A time series of temperature T may be used to compute its power spectral density for the C_T².

[0195] Kolmogorov theory provides the tools necessary to convert the series of temperature measurements into the power spectral density. Recall that each temperature measurement is the temperature of the air mass that was moving through the LIDAR field-of-view (FOV) during the measurement interval. The LIDAR system 24 provides the velocity (speed and direction) so that measurements made at particular times represent different samples in space.

[0196] Simplifying the power spectral density, S_T(K), for a single dimension is given by the following:

[0197] $\begin{array}{cc}{S}_T\left(K\right)=0.25C_T^2{K}^{-\frac{5}{3}}& \left(7\right)\end{array}$

[0198] The power spectral density may be obtained by taking the Fourier transform of the temperature differences as illustrated in the following equation.
S_T(K)=F{T(t)}(K)  (8)

[0199] where F{ } is the Fourier transform of the Temperature data, T, collected at time T, but presented in spatial terms via the time samples and the measured velocity.

[0200] The level at which the power spectrum becomes an issue depends upon the scenario. In the case of a wind turbine, power spectral density for spatial wave numbers on the order of the turbine blade diameter or larger are of interest. Changes at higher frequencies are not as damaging as they don't contain the same energy as the larger structures.

[0201] Another potential indicator of turbulence is the boundary layer interface 58. Turbulence usually occurs at the boundary layer interface 58, so that the location of that interface can be used to predict impending turbulence. The boundary layer starts out low and may reach only a few tens of meters in the morning. As solar heating warms the terrain, the boundary layer will rise and may reach altitudes of 1 km to 2 km. In the evening, the boundary layer will decrease and can fall to the point where the associated turbulence will interact with wind turbines.

[0202] In accordance with a first method, the derivative of the rate of change of atmospheric temperature T as a function of altitude—based upon measurements of temperature T at different altitudes from the LIDAR systems 24—can be used to measure the extent of the boundary layer interface 58. For example, the partial derivative of temperature T with respect to time can be given by:

[0203] $\begin{array}{cc}\frac{\partial T\left(z,t\right)}{\partial t}=\sum a_i{\vartheta }_i\left(z,t\right)& \left(9\right)\end{array}$

[0204] and partial derivative with respect to altitude of this time rate of change of temperature T is then given by:

[0205] $\begin{array}{cc}\frac{{\partial }^{2}T\left(z,t\right)}{\partial z\partial t}=\sum a_i\frac{\partial {\vartheta }_i\left(z,t\right)}{\partial z}& \left(10\right)\end{array}$

[0206] Wherein in equations (9) and (10), (z, t) are interpolation functions for example B-spline and a is a weight determined by fitting the data.

[0207] In accordance with a second method, because aerosol concentration is significantly reduced above the boundary layer interface 58, a change in aerosol content detected by the LIDAR systems 24 responsive to a measures of aerosol counts N_A and molecular counts N_M, can be used to estimate the location of the boundary layer interface 58.

[0208] The atmospheric measurement system 10 can further provide for generating a measure of wind shear from measurements of wind speed v at different ranges and at different pointing angles. For example, in one embodiment, wind shear is characterized by a wind shear exponent a given from the following power law equation:

[0209] $\begin{array}{cc}\frac{v\left(z\right)}{v_0\left(z_0\right)}={\left(\frac{z}{z_0}\right)}^{\alpha }\mathrm{or},& \left(11\right)\\ \alpha =\frac{\ln \left(v\right)-\ln \left(v_0\right)}{\ln \left(z\right)-\ln \left(z_0\right)}& \left(12\right)\end{array}$

[0210] where v(z) is the total wind speed at altitude z, and v₀(z₀) is the total wind speed at altitude z₀, wherein the altitudes z, z₀ are measured above ground level.

[0211] The above measures of turbulence and wind shear are based upon measurements along the associated beams of light 28 that are generally angled with respect to horizontal and vertical, with associated distances being with respect to the associated light source 11. These distances may be either transformed to corresponding altitudes for purposes of determining the above measures of turbulence and wind shear. Alternatively, the above measures of turbulence and wind shear may be made with respect to an associated slant range. Generally, at least three different beams of light 28 would be used, with at least two of those beams of light 28 at an angle with respect to horizontal. Generally the aerosol to molecular ratio could be measured along each beam that has an angle with respect to the horizontal.

[0212] There are no absolute requirements on the spacing of measurements in either space or time. One could determine turbulence with a single measurement, or one could use a time series of measurements to determine turbulence. If the aerosol to molecular ratio changes suddenly with respect to altitude within a single measurement, that could be an indicator of turbulence. Similarly, turbulence could be determined by using a time series for each altitude.

[0213] The threshold values can be determined based on the measurement precision and the characteristics of the wind turbine, with different wind turbines having different thresholds. The measurement precision defines a lower bound based on probability. Generally, the false alarm rate would also be considered along with the probability of detection.

[0214] Referring to FIG. 2, the atmospheric measurement system 10 provides for either communication between the LIDAR systems 24 and a central, network or cloud processor 60, or for communication amongst the associated LIDAR systems 24, so as to provide for exchanging pertinent data as necessary to construct a map, model or database 62 of the associated atmospheric data with respect to space and time. For example, the communication can be by either a wire or fiber-optic communication channel 64 or by a wireless communication channel 66, using either direct or networked interconnections. For example, among other techniques, data may be communicated wirelessly via either a satellite or ground-based transponder, and networked communications may use an Ethernet protocol.

[0215] For example, in a centralized, hierarchical system 68, the separate LIDAR systems 24 provide their measurements to the central, network or cloud processor 60 which then calculates the associated wind velocity v and wind power flux density ψ for the various measurement volume 52, possibly using measurements from separate associated LIDAR systems 24, and combines these calculated vector measures with the associated atmospheric data scalars in the map, model or database 62 that can then be distributed to the various wind turbines 14 for control thereof. The centralized, hierarchical system 68 can include various sub-processors 70 that interface with subsets of associated LIDAR systems 24 and communicate the information therefrom to the central, network or cloud processor 60 while also possible combining measurements from the associated LIDAR systems 24 in communication therewith so as to provide for determining the necessary local set of atmospheric data needed for local control of the associated wind turbines 14.

[0216] As another example, in a decentralized system 72, each particular LIDAR system 24 provides for communicating with other LIDAR systems 24 so as to acquire the data therefrom as necessary to determine the corresponding atmospheric data for the measurement volume 52 or measurement volumes 52 associated with that particular LIDAR system 24. For example, referring to FIG. 2, the third LIDAR system 24.3 could communicate with the fourth 24.4 and fifth 24.5 LIDAR sensors so as to obtain the associated measures of wind speed v as necessary to determine the associated wind velocity v for the measurement volumes 52^iv, 52^v associated therewith. Generally, the measurement volumes 52 of different LIDAR systems 24 may overlap, in which case the LIDAR systems 24 associated with the overlapping measurement volumes 52 could each generate their own associated localized map, model or database 62 as the associated atmospheric data that can be used by the wind turbine 14 or wind turbines 14 associated with each LIDAR system 24. For example, similar to the third LIDAR system 24.3, the fourth LIDAR system 24.4 could communicate with the third 24.3 and fifth 24.5 LIDAR systems, and the fifth LIDAR system 24.5 could communicate with the third 24.3 and fourth 24.4 LIDAR systems, so as to obtain the associated measures of wind speed v as necessary to determine the associated wind velocity v for the same measurement volumes 52^iv, 52^v.

[0217] A decentralized system 72 can be operated in either a request mode or a broadcast mode, depending upon the nature of the communication between LIDAR systems 24. In accordance with the request mode of operation, a particular LIDAR system 24 sends out a request for atmospheric measurement records 40 for information associated with particular measurement volumes 52, or within a particular geographic regions, and other LIDAR systems 24 in communication therewith that can provide atmospheric data for the specified location or geographic criteria then return the requested atmospheric measurement records 40. In a broadcast mode, each particular LIDAR system 24 broadcasts its atmospheric measurement records 40 to the associated communication network 74, from which other LIDAR systems 24 can then select and use those atmospheric measurement records 40, for example, to calculate a composite atmospheric measurement record 40′ for one or more common measurement volumes 52, or for compiling a local map, model or database 62. A decentralized system 72 can provide for improved fault tolerance, reliability and robustness by distributing information and associated decision processes amongst a group of associated, or all, LIDAR systems 24, thereby avoiding the prospect of single-point failure that might otherwise be possible with some embodiments of a centralized, hierarchical system 68.

[0218] Generally, each LIDAR system 24 could have a pre-assigned measurement volume 52 over which to perform associated data analysis, wherein external data that is within that measurement volume 52 is incorporated in the generation of a local atmospheric map, model or database 62, for example of wind power flux density ψ, wind velocity v, atmospheric density ρ, atmospheric temperature T, and the ratio of molecular counts N_M to aerosol counts N_A. Each atmospheric measurement record 40 could first be filtered to determine if it is within the assigned measurement volume 52. Atmospheric measurement records 40 from measurements located within the assigned measurement volume 52 could then be processed further to determine the relative proximity thereof by computing the relative distances between the locations associated therewith. For a given set of measurements of wind speed v₁, v₂, v₃ for a given associated measurement volume 52, the associated measurement direction vectors, for example, the associated unit vectors ê₁, ê₂, ê₃, are examined to insure that the look directions provide the diversity necessary to produce reasonable orthogonal measurement components, for example, so that resulting wind velocity v calculated therefrom is sufficiently accurate. For example, in one embodiment, the following metric η, having a value between zero and unity, may be used to evaluate the diversity or relative orthogonality of the associated measurement direction vectors:
η=ê₁×ê₂·ê₃  (13)

[0219] Atmospheric measurement records 40 that are deemed to be sufficiently close in space and time and are associated with sufficient diversity in pointing angle are combined into a single composite atmospheric measurement record 40′ that includes the associated averaged values of location and sampling time t_i, averaged values of the associated atmospheric data scalars, and the calculated values of associated wind velocity v and wind power flux density ψ and the associated magnitudes thereof.

[0220] The vector measures of wind velocity v and wind power flux density ψ from each LIDAR system 24, and the locations of the associated measurement volumes 52, are referenced to a particular coordinate system, and these measures can be transformed as necessary so that the corresponding measures in the map, model or database 62 are referenced to a common coordinate system. For example, for the first 24.1, second 24.2 and third 24.3 LIDAR sensors, the wind velocity v and wind power flux density ψ might be based on measurements of wind speed v₁, v₂, v₃ along corresponding directions 46.1, 46.2, 46.3 with respect to a first local spherical coordinate system referenced to the nacelle 44 of the associated wind turbines 14.1, 14.2, 14.3 oriented in a second local cylindrical coordinate system aligned with the corresponding vertical axes of rotation 76 about which the nacelle 44 can rotate with respect to the associated towers 78 so as to provide for aligning the associated rotors 18.1, 18.2, 18.3 with the local direction 50 of the wind field 16′, wherein the towers 78 of the wind turbines 14.1, 14.2, 14.3 can be located on the Earth with respect to a central Earth-referenced spherical, oblate-spherical or ellipsoidal coordinate system. Accordingly, if the vector measures in the map, model or database 62 are expressed with respect to this central Earth-referenced coordinate system, then the wind velocity v and wind power flux density ψ from each LIDAR system 24, and the locations of the associated measurement volumes 52, could be transformed from the associated local coordinate systems to coordinate system of the map, model or database 62 before inclusion therein.

[0221] Atmospheric data from the atmospheric measurement system 10 can be used for controlling the wind turbines 14 of an associated wind farm 12—or of a plurality of wind farms 12 within the geographic extent of the associated map, model or database 62 compiled by the atmospheric measurement system 10—or the power grid 56 supplied therefrom. The associated LIDAR systems 24 need not be located exclusively at wind sites or with overlapping fields-of-view 54 in order to provide useful information to the wind farm 12. Furthermore, as illustrated in FIGS. 1 and 2, The LIDAR systems 24 need not necessarily be mounted on associated wind turbines 14. For example, LIDAR systems 24 located kilometers away from the wind farm 12 can make atmospheric measurements that can be combined with measurements from other LIDAR systems 24 within the region of the wind farm 12 so as to provide a larger scale estimation of wind energy potential in an approaching air mass. At longer ranges, small scale turbulences are not necessarily as important because they may dissipate by the time they reach the wind farm 12. Although a map, model or database 62 of atmospheric data for the wind field 16′ local to a particular wind turbine 14 can be useful for immediate control of the particular wind turbine 14, a map, model or database 62 of atmospheric data for the wind field 16′ over and upstream of the entire wind farm 12 provide for a coordinated control of the associated wind turbines 14 and the associated power grid 56 so as to provide for extracting as much power as either possible or necessary from the wind field 16′ while protecting the associated wind turbines 14 from damage, for example, as a result of excessive wind speed v or turbulence. A regional or global map, model or database 62 of atmospheric data could be provided by a centralized, hierarchical system 68, or could be compiled from separate maps, models or databases 62 that are separately generated by the separate LIDAR systems 24 of a decentralized system 72. Atmospheric data from adjacent and/or up-wind LIDAR systems 24 can improve measurement resolution, measurement accuracy, and turbulence or wind shear estimation of other LIDAR systems 24, perhaps in conjunction with weather modeling or forecasting software, or in conjunction with other sources of weather data. In a decentralized system 72, in addition to the individual map, model or database 62 local to a particular wind turbine 14, atmospheric data from the entire wind farm 12 can be compiled and a detailed large scale three dimensional wind power density, wind velocity, turbulence, density, molecular to aerosol scattering ratio and temperature maps can be generated. These maps can be maintained for historical purposes and for sale to others such as weather forecasters who could find the data beneficial in their enterprises. In addition to the information mentioned above, the LIDAR systems 24 are able to measure the extinction coefficient at their operational wavelength and the aerosol-to-molecular scattering ratio which could be used to locate the boundary layer interface 58 and estimate visibility.

[0222] As each new measurement is added to the map, model or database 62, it is compared to previous measurements to determine if the new measurement indicates significant changes in the current conditions. New measurements are compared to the mean and standard deviation that are calculated on a window of time history data. Deviations between the measured value and the expected value are indicative of changes, and if the deviation exceeds established limits, appropriate warnings are issued. In one example if the wind speed v suddenly decreases, one might want to prepare to tap stored energy to take up the slack. In another example, if the temperature data indicates thermal turbulence, then one might expect turbulence to strike the wind farm 12 or wind turbine 14 in the near future.

[0223] For example, referring to FIG. 2, each wind turbine 14 could incorporate an associated controller 80 for controlling the associated generator 82 and rotor 18 of the wind turbine 14, and for controlling the orientation of the rotor 18 relative to the local direction 50 of the wind 16, wherein the generators 82 are connected to the power grid 56 so as to provide for supplying electrical power thereto. In one mode of operation, the wind turbines 14 are controlled so as to generate the maximum amount of electrical power available from the wind, and atmospheric data from the atmospheric measurement system 10 is used to anticipate atmospheric conditions that could be potentially damaging to the wind turbine 14 so that the controller 80 can control the wind turbine 14—for example, by feathering the rotor 18 or turning the wind turbine 14 out of the wind—so as to prevent damage to the elements thereof. In another mode of operation, the controller 80 can use the information of the wind power flux density ψ to anticipate the amount of electrical power that can be generated by the wind turbine 14, and responsive to a demand signal 84 from the power grid 56, possibly in cooperation or coordination with signals from other controllers 80 of the wind farm 12, then the controller 80 controls the elements of the wind turbine 14 so as to generate and supply the appropriate amount of electrical power to the power grid 56. Atmospheric data from the atmospheric measurement system 10, i.e. the associated map, model or database 62, can be provided to the power grid 56 so that the power grid 56 can anticipate the amount of electrical power that could potentially be available from the wind farm 12, for example, for peaking power if necessary.

[0224] Wind velocity v provides the information necessary to generate extended maps showing the location of a particular air mass with its temperature T, density ρ, and molecular-to-aerosol ratio. A spatial rather than the temporal view provides another independent method for examining data and projecting when the wind power will interact with the wind turbine 14. Knowing that a neighboring wind farm 12 or wind turbine 14 has just detected a wind change event is a strong indicator that the current wind farm 12 or wind turbine 14 might also experience that same event in the near future. It is highly unlikely that a wind gust could hit all the wind turbines 14 in an installation at the same time. It is more likely that some wind turbines 14 could be subjected to the disturbance before others.

[0225] Atmospheric data from the atmospheric measurement system 10 can be made commercially available to operators of wind farms 12, or for other purposes. For example, the atmospheric data, continuously gathered from various altitudes, can be used for weather forecasting. Instead of obtaining atmospheric profiles twice a day at sixty-nine sites throughout the continental United States under current practice, atmospheric data from the atmospheric measurement system 10 could be streamed continuously from thousands of LIDAR systems 24 distributed across the country, or across other countries or regions, which can lead to more accurate weather forecasts. For example, for an atmospheric measurement system 10 primarily developed for use by wind farms 12, available atmospheric data from associated LIDAR systems 24 that is not of direct use or need for operation of a wind farm 12, but which could have value for meteorological forecasts, could be included in the associated map, model or database 62. This additional data such as molecular to aerosol scattering ratio and extinction coefficient could be made commercially available to other interested parties. Furthermore, the atmospheric data may be further processed to establish visibility or other metrics that might be peculiar to weather forecasting.

[0226] Global trend monitoring, for example, via cloud-based computing, can also be applied to analyzing climate change, pollution (dust, aerosols), weather patterns and volcanic events (particulates) Predictive analytics and other learning-based software paradigms can be applied on an individual turbine, wind farm, or grid level to provide learning-based optimization through a learning module. The learning module consists of a processor, for example quad core computer combined with GPUS, that runs the predictive analytics software. On an individual turbine, the learning module collects data from the LIDAR as well as the turbine. As new data is collected, the predictive analytics software optimizes the control inputs to the turbine to minimize the effects of wind loading and maximize turbine health and lifetime. Over time, the learning module produces an optimal set of control system commands in response to the LIDAR atmospheric measurements, customized for the performance of each individual turbine. Effects such as turbulence and shear may differ for individual turbines and require different responses, depending on the type, size, and age of the turbine. Those effects are incorporated automatically into the learning module without the need for direct supervisory control. On a wind farm SCADA level, a learning module identifies trends in the overall health of each individual turbine that can be used to predict problems and optimize performance or maintenance schedules of other turbines within the farm.

[0227] The networking of LIDAR systems 24 allows the lifetime of each sensor to be extended. This is accomplished by turning off some sensors or placing them in a standby mode that minimizes the operational state or duty cycles of the components, thereby extending the sensor lifetime and reducing maintenance and repair requirements. One or more LIDAR systems 24 would remain in full operation and provide data to the other sensors in the atmospheric measurement system 10, thereby acting as sentries to warn of changing weather conditions. In one embodiment, most LIDAR systems 24 in the atmospheric measurement system 10 are placed in standby mode, with wind speeds averaging less than a certain value, for example one meter per second, over a period of time; one or more LIDAR systems 24 in a atmospheric measurement system 10 of sensors remain in full operation, monitoring wind speeds; when average wind speeds over a period of time exceed a certain value, for example two meters per second, some or all of the other sensors in the atmospheric measurement system 10 are placed in full operational mode again.

[0228] Using the same approach, the reliability of the entire atmospheric measurement system 10 is increased since a failure with one of the LIDAR systems 24 can be mitigated by sending data from other sensors in the atmospheric measurement system 10 to that node, essentially introducing multiple levels of redundancy and backup into the atmospheric measurement system 10. In one embodiment, a LIDAR system 24 being used for turbine control fails, but within a short time period, data from the other sensors in the atmospheric measurement system 10 is used to replace the function of the failed sensor, ensuring the continual safe operation of the turbine.

[0229] A measurement of water vapor—for example, using a Raman-based receiver incorporated with the LIDAR system 24—alone or in combination with other atmospheric measurements can provide for predicting and monitoring conditions that may cause or lead to the formation of ice on the blades of the wind turbine. In one embodiment, a Raman-based receiver incorporated with the LIDAR system 24.

[0230] The aforementioned U.S. application Ser. No. 12/780,895 filed on 15 May 2010, entitled Range imaging LIDAR illustrate various embodiments of LIDAR systems 24 and associated platforms that may be incorporated in the atmospheric measurement system 10.

[0231] Referring to FIG. 6a, in accordance with a first aspect, a range-imaging LIDAR system 24′, 24ⁱ incorporated in a first aspect of an atmospheric measurement system 10ⁱ incorporates a light source 11 that provides for generating at least substantially monochromatic light 13, which is projected into the atmosphere 20 as a beam of light 28 through and by associated source optics 15. For example, the source optics 15 may comprise a lens assembly 15′ that provides for the width and divergence of the beam of light 28, and a suitable location of the associated beam waist thereof, so as to illuminate an interaction region 17 within the atmosphere 20 that is detectable by the range-imaging LIDAR system 24′, 24ⁱ, wherein the beam width within the interaction region 17 establishes the associated transverse spatial resolution limit of the range-imaging LIDAR system 24′, 24ⁱ. For example, referring to FIG. 6b, the source optics 15 may be configured so as to provide for a pencil-like beam of light 28^P having a limited width w and depth d, for example, of circular or elliptical cross-section, so as to limit the associated width w and depth d of the associated interaction region 17. As another example, referring to FIG. 6c, the source optics 15 may be configured so as to provide for a sheet-like beam of light 28^S—for example, using source optics 15 comprising cylindrical optics—having a limited depth d but an extended width w, for example, so as provide for an associated interaction region 17 with a corresponding extended width w, so as to provide for probing extending regions of the atmosphere 20.

[0232] A set of receive optics 32, for example, a telescope 32′, laterally offset from the beam of light 28, provides for imaging a portion of the beam of light 28 onto an intermediate image plane 19, so as to provide for a one-to-one mapping of measurement volumes 52 within the beam of light 28 and corresponding associated regions or points 21 in the intermediate image plane 19. More particularly, the beam of light 28 illuminates molecules 20′ or aerosols 20″ of the atmosphere 20, or a combination thereof, within the interaction region 17, which in turn scatter the monochromatic light 13 of the beam of light 28. The resulting scattered light 30 within the field-of-view 54 of the receive optics 32 is collected thereby and imaged onto the intermediate image plane 19. The receive optics 32 is laterally offset from and points towards the beam of light 28, so that the optic axis 23 of the receive optics 32 is inclined relative to the optic axis 25 of the beam of light 28 at an associated parallax angle θ. Accordingly, each measurement volume 52 of the beam of light 28 imaged onto a corresponding region or point 21 on the intermediate image plane 19 corresponds to a different nominal range R from the intermediate image plane 19 to a point 27 on the optic axis 25 of the beam of light 28 associated with the corresponding measurement volume 52. Accordingly, each region or point 21 on the intermediate image plane 19, corresponding to the measurement volume 52 of the beam of light 28 within the field-of-view 54 of the receive optics 32, corresponds to a different nominal range R. Accordingly, different regions or points 21 of the intermediate image 29 in the intermediate image plane 19 correspond to different nominal ranges R to the beam of light 28, and therefore correspond to different nominal ranges R to the associated measurement volumes 52 thereof within the interaction region 17. For example, as illustrated in FIG. 6a, a closest measurement volume 52.1 of the beam of light 28 within the field-of-view 54 of the receive optics 32 located at a closest nominal range R_MIN from the intermediate image plane 19 is imaged as a corresponding first region or point 21.1 on the intermediate image plane 19, and a farthest measurement volume 52.2 of the beam of light 28 within the field-of-view 54 of the receive optics 32 located at a farthest nominal range R_MAX from the intermediate image plane 19 is imaged as a corresponding second region or point 21.2 on the intermediate image plane 19. Furthermore, scattered light 30 from different measurement volumes 52 is imaged onto the intermediate image plane 19 at corresponding different angles of incidence relative thereto. The range R to the interaction region 17 is defined by the geometry of the associated beam of light 28 and the corresponding receive optics 32. The receive optics 32 can be in focus for one of a plurality of different ranges to the beam of light 28, so that for measurement volumes 52 of the beam of light 28 not in focus, the corresponding images thereof in the intermediate image plane 19, i.e. the corresponding regions or points 21 thereon, will be unfocused and therefore blurred. The range R within the interaction region 17 can optionally be further resolved with associated temporal range gating, or range-resolved imaging, of the associated scattered light 30 if desired or necessary for a particular application.

[0233] The range-imaging LIDAR system 24′, 24ⁱ further comprises an interferometer 31, for example, in accordance with a first aspect, a Fabry-Pérot interferometer 31′ having an input focal plane 31.1′ and an output focal plane 31.2′. The input focal plane 31.1′ is collocated with the intermediate image plane 19 so as to receive scattered light 30 therefrom, which is then processed by the Fabry-Pérot interferometer 31′ and imaged onto a detection system 34 located at the output focal plane 31.2′. Between the input 31.1′ and output 31.2′ focal planes, the Fabry-Pérot interferometer 31′ comprises a collimating lens 33, a Fabry-Pérot etalon 35, and imaging optics 37 spaced along an associated common optic axis 39, wherein the input focal plane 31.1′ is a focal plane of the collimating lens 33, the output focal plane 31.2′ is a focal plane of the imaging optics 37, and scattered light 30 at the input focal plane 31.1′ entering the collimating lens 33 is substantially collimated thereby, then processed by the Fabry-Pérot etalon 35, and finally imaged onto the detection system 34 by the imaging optics 37. The Fabry-Pérot etalon 35 of the Fabry-Pérot interferometer 31′ comprises first 41 and second 43 partially-reflective surfaces that are parallel to one another and separated by a fixed gap 45. The angles at which the scattered light 30 is passed through the Fabry-Pérot etalon 35 is dependent upon the optical frequency of the scattered light 30 and the length of the gap 45, resulting in an associated scatter fringe pattern 47 comprising a plurality of concentric arcuate fringes 49′—also known as Haidinger fringes—in the output focal plane 31.2′ of the Fabry-Pérot interferometer 31′, for example, as illustrated in FIG. 7 for a fully illuminated Fabry-Pérot interferometer 31′. The scatter fringe pattern 47 is imaged onto the detection system 34 that generates a scatter electronic image signal 51 responsive thereto which is then processed as described hereinbelow by an associated data processor 53 so as to generate a corresponding set of atmospheric data 36 from information in the scatter fringe pattern 47.

[0234] For example, in one embodiment, the Fabry-Pérot etalon 35 comprises a pair of planar optical windows 55—for example, constructed of either optical glass or fused quartz—aligned parallel to and facing one another, and spaced apart from one another by the gap 45, wherein, for example, the first 41 and second 43 partially-reflective surfaces—e.g. partially-silvered surfaces or other partially-reflective surfaces—are on separate facing surfaces of the planar optical windows 55. Alternatively, the first 41 and second 43 partially-reflective surfaces could be on the outside opposing faces of the planar optical windows 55, or one of the first 41 and second 43 partially-reflective surfaces could be on a inner facing surface of one of the planar optical windows 55, and the other of the first 41 and second 43 partially-reflective surfaces could be on a outer facing surface of the other of the planar optical windows 55. In one embodiment, the gap 45 is substantially fixed, whereas in other embodiments, the gap 45 is moveable, e.g. adjustable, for example, using an etalon control actuator 57 responsive to a controller 71 operatively associated with or a part of the data processor 53, so as to provide for a tunable Fabry-Pérot etalon 35.

[0235] Referring to FIG. 6d, alternatively, the Fabry-Pérot etalon 35 could comprise a solid optical element 61—for example, constructed of either optical glass or fused quartz—with planar parallel faces 63 comprising first 41 and second 43 partially-reflective surfaces separated by a gap 45.1 constituting the length of the solid optical element 61.

[0236] Referring to FIG. 7, for a fully-illuminated Fabry-Pérot etalon 35, the resulting associated circular fringe pattern 65 is in the form of closed concentric circular fringes 65′ centered about the optic axis 39 of the imaging optics 37. For example, a typical circular fringe pattern 65 is illustrated in FIG. 7 for an associated scattered light signal 30′ that has been source thermally broadened by a medium comprising both aerosols and molecules. The light scattered from the molecules is spread over the shaded regions of the circular fringe pattern 65 in FIG. 7, and the light scattered from the heavy, slow moving aerosols is contained in the narrow white rings. The associated atmospheric state variables affect the circular fringe pattern 65 in different ways. Wind induced Doppler shifts change the diameter of the rings, and the constant that determines Doppler shift is dependent upon temperature. Atmospheric (molecular) temperature affects the width of molecular rings. Aerosol density controls the intensity of the narrow white rings and molecular density increases the brightness of the shaded regions in FIG. 7. Accordingly, wind velocity, density, and temperature can be determined directly from the circular fringe pattern 65.

[0237] For example, referring to FIG. 8, a simulated image in the intermediate image plane 19 is illustrated for a beam of light 28 having a beam radius of 0.1 centimeters (cm) and a half-angle of divergence of 0.05 milliradians, and for receive optics 32 having an aperture radius of 2.5 centimeter and a focal length of 15 cm, separated from the beam of light 28 by 35 cm, for which the range R to beam of light 28 within the field-of-view 54 of the receive optics 32 ranged from R_MIN=8 meters to the closest measurement volume 52.1 to R_MAX=500 meters to the farthest measurement volume 52.2, respectively, with the receive optics 32 focused at the farthest measurement volume 52.2. Accordingly, as illustrated in. FIG. 8, the second region or point 21.2 in the intermediate image plane 19 corresponding to the farthest measurement volume 52.2 is most sharply focused, and the first region or point 21.1 in the intermediate image plane 19 corresponding to the closest measurement volume 52.1 is the most blurred, with the amount of blurring and therefore the associated size of regions or points 21 in the intermediate image plane 19 therebetween increasing with decreasing corresponding associated nominal range R from the second region or point 21.2 to the first region or point 21.1, thereby giving the associated intermediate image 29 of the interaction region 17 of the beam of light 28 a wedge-shaped profile.

[0238] Absent the Fabry-Pérot etalon 35, the associated collimating lens 33 and imaging optics 37 provide for imaging the intermediate image plane 19 onto the output focal plane 31.2′ that is detected by the detection system 34. Accordingly, the first 21.1 and second 21.2 regions or points on the intermediate image plane 19—corresponding to the closest 52.1 and farthest 52.2 measurement volumes of the beam of light 28 within the field-of-view 54 of the receive optics 32—are imaged as corresponding first 67.1 and second 67.2 regions or points on the output focal plane 31.2′. More generally, there is a one-to-one correspondence between regions or points 67 on the output focal plane 31.2′ and corresponding measurement volumes 52 of the beam of light 28, and therefore, there is a one-to-one correspondence between regions or points 67 on the output focal plane 31.2′ and the corresponding nominal range R thereto, given the parallax angle θ between the optic axes 23, 25 of the receive optics 32 and the beam of light 28, respectively, so that the nominal range R associated with any region or point 67 on the output focal plane 31.2′—or in the associated corresponding scatter electronic image signal 51 detected by the detection system 34—can be inferred from the location of that region or point 67 on the output focal plane 31.2′. With the Fabry-Pérot etalon 35 present, the arcuate fringes 49′ of the scatter fringe pattern 47 are present for those regions or points 67 for which the associated frequency or wavelength of the associated scattered light 30 in cooperation with the gap 45 of the Fabry-Pérot etalon 35 provide for constructive interference, whereas arcuate nulls 69 in the scatter fringe pattern 47 are present for those regions or points 67 for which the associated frequency or wavelength of the associated scattered light 30 in cooperation with the gap 45 of the Fabry-Pérot etalon 35 provide for destructive interference. Locations of the arcuate fringes 49′ are determined by the frequency or wavelength of the associated scattered light 30, the gap 45 of the Fabry-Pérot etalon 35 and the angle of incidence in the Fabry-Pérot etalon 35.

[0239] For example, for the conditions described hereinabove for FIG. 8, FIG. 9 illustrates a simulation of a resulting scatter fringe pattern 47 for a solid Fabry-Pérot etalon 35 having a thickness, or gap 45.1, of 0.7 cm and an associated reflectivity of 0.85. As with the associated intermediate image 29, with the receive optics 32 in focus at the farthest nominal range R_MAX, the arcuate fringes 49′ associated with relatively closer measurement volumes 52 of the beam of light 28 are transversely broadened relative to those associated with relatively farther measurement volumes 52, so that the scatter fringe pattern 47 exhibits a wedge-shaped profile similar to that of the intermediate image 29, wherein the radial size of the associated arcuate nulls 69 decreases with increasing fringe order relative to the optic axis 39 of the Fabry-Pérot interferometer 31′. FIG. 10a illustrates a plot of the intensity of the scatter fringe pattern 47 along a section thereof through the optic axis 39 as a function of distance in the output focal plane 31.2′, which is transformed in FIG. 10b to a plot of the intensity of the scatter fringe pattern 47 as a function of nominal range R. The nominal range R for which the intermediate image 29 and the associated scatter fringe pattern 47 are in focus can be set to improve the sharpness of the associated range resolution at any particular nominal range R, for example, either using an associated fixed focal setting, or using a focus control actuator 86 responsive to a signal from the controller 71.

[0240] The locations of the arcuate fringes 49′ and associated arcuate nulls 69 can be changed by either changing the gap 45 of the Fabry-Pérot etalon 35, for example, by the etalon control actuator 57 responsive to a signal from the controller 71, or by tilting the Fabry-Pérot etalon 35. For example, the gap 45 of the Fabry-Pérot etalon 35 could be repeatedly scanned by the etalon control actuator 57 responsive to a signal from the controller 71 so as to repeatedly generate associated sets of scatter fringe pattern 47 collectively having arcuate fringes 49′ associated with all nominal ranges R to the beam of light 28 within the field-of-view 54 of the receive optics 32, so as to directly provide for associated atmospheric data 36 at any particular nominal range R within the range of associated nominal ranges R from R_MIN to R_MAX.

[0241] The range-imaging LIDAR system 24′, 24ⁱ provides for directly detecting light scattered off of either molecules 20′ of the atmosphere, aerosols 20″ in the atmosphere, or a combination of the two, and provides for directly measuring the density and temperature of the atmosphere 20, and the velocity thereof in the direction of the optic axis 23 of the receive optics 32. For example, relatively short wavelength light is scattered by molecules 20′ of the atmosphere in accordance with Rayleigh scattering. Light can also be scattered by aerosols 20″ in the atmosphere in accordance with Mie scattering. Rayleigh scattering generally refers to the scattering of light by either molecules or particles having a size less than about 1/10^th the wavelength of the light, whereas Mie scattering generally refers to scattering of light by particles greater than 1/10^th the wavelength of the light. Being responsive to Rayleigh scattering, the range-imaging LIDAR system 24′, 24ⁱ is therefore responsive to the properties—e.g. velocity, density and temperature—of those molecules 20′ in the atmosphere giving rise to the associated scattering of the light detected by the range-imaging LIDAR system 24′, 24ⁱ. Furthermore, the range-imaging LIDAR system 24′, 24ⁱ can provide for operation in clean air, i.e. in an atmosphere with no more than a negligible amount of aerosols 20″, depending substantially upon only molecular scatter. If scattered from a moving molecule 20′ or aerosol 20″, the frequency scattered light 30 is Doppler shifted, which for a given gap 45 in the associated Fabry-Pérot etalon 35 thereby causes the associated arcuate fringes 49′ of the scatter fringe pattern 47 from the Fabry-Pérot interferometer 31′ to be shifted to a location for which an associated constructive interference condition is satisfied for the corresponding rays of scattered light 30 entering the Fabry-Pérot interferometer 31′ at a given angle from a corresponding given nominal range R. Accordingly, the Doppler shift in the frequency of the scattered light 30 will depend upon the local velocity of the atmosphere 20 within the interaction region 17 interacting with the beam of light 28, and for different amounts of Doppler shift, arcuate fringes 49′ associated with corresponding different nominal ranges R will be generated by the Fabry-Pérot interferometer 31′, thereby causing the arcuate fringes 49′ to shift within the scatter fringe pattern 47—possibly relative to one another depending upon the distribution of velocity of the atmosphere 20 within the interaction region 17.

[0242] The range-imaging LIDAR system 24′, 24ⁱ further incorporates a filter system 88 to filter the scattered light 30 received by the receive optics 32 so as to prevent background light from being detected by the detection system 34. For example, referring to FIGS. 6a, 6d and 11, in one set of embodiments, the filter system 88 is located within the Fabry-Pérot interferometer 31′ between the collimating lens 33 and the Fabry-Pérot etalon 35. For example, referring to FIG. 11, in one embodiment, the filter system 88 incorporates eight bandpass filter mirrors 88′ having associated filter pass bands centered about the operating frequency of the light source 11 The filter system 88 exhibits high out-of-band rejection, as well as low in-band attenuation, and the bandwidth of the filter system 88 is sufficiently narrow so as to substantially filter or remove components of solar radiation or stray light in the collected scattered light 30, yet sufficiently broad so as to be substantially larger than the bandwidth of the thermally-broadened spectrum in combination with the largest expected associated Doppler shift. For example, in one embodiment, the filter system 88 is adapted so as to provide for maximum filtering of light frequencies that are outside the frequency band of interest, e.g. greater than about 2 nanometers (nm) above or below the nominal center frequency of the light source 11.

[0243] The Fabry-Pérot interferometer 31′ is subject to mechanical defects and thermally induced drift that can be compensated through calibration using a reference beam portion 90 of the substantially monochromatic light 13 extracted from the light source 11 with a beam splitter optic 92 and then input to the Fabry-Pérot interferometer 31′ at the intermediate image plane 19 as a reference source 94. For example, referring to FIG. 6a, in accordance with a first embodiment, the reference source 94 from the beam splitter optic 92 is directed into the Fabry-Pérot interferometer 31′ with a mirror 96. Referring to FIG. 11, in accordance with a second embodiment, the reference beam portion 90 of the monochromatic light 13 extracted from the light source 11 with a beam splitter optic 92 as the reference source 94 is input to fiber optic 98, for example, using a graded index (GRIN) lens 100, the output of which is located at the intermediate image plane 19 so as to illuminate the collimating lens 33 of the Fabry-Pérot interferometer 31′ therefrom. Accordingly, for either embodiment, the reference source 94 is input to the Fabry-Pérot interferometer 31′ from a location 102 on the intermediate image plane 19/input focal plane 31.1′ that is distinct from the intermediate image 29 of the scattered light 30, and is processed by the Fabry-Pérot interferometer 31′ so as to generate a corresponding reference fringe pattern 104 comprising one or more associated arcuate fringes 49″ at a corresponding location on the output focal plane 31.2′, which is then detected by the detection system 34 so as to generate a corresponding reference electronic image signal 106 responsive thereto, which is then processed as described hereinbelow by the associated data processor 53 together with the scatter electronic image signal 51 associated with the scatter fringe pattern 47 from the scattered light 30.

[0244] The light source 11 provides for generating a sufficient amount of sufficiently narrow-band monochromatic light 13 so as to provide for a sufficient amount of scattered light 30 so that the resulting scatter fringe pattern 47 is detectable by the detection system 34 with a sufficient signal-to-noise ratio (SNR) so that the resulting atmospheric data 36 determined therefrom is accurate within a given accuracy threshold and provides for an information temporal bandwidth that is within a given temporal bandwidth threshold. For example, the light source 11 could comprise one or more lasers, light emitting diodes (LEDs), flash lamps, for example, xenon flash lamps, sodium lamps or mercury lamps. The light source 11 may be either continuous or pulsed, and need not necessarily be coherent. If the spectral bandwidth of the light source 11 is not inherently substantially less than the expected minimum Doppler shifts to be measured, then the output of the light source 11 may be filtered with a filter 108 so as to provide for generating sufficiently monochromatic light 13 so as to enable Doppler shifts in the scattered light 30 to be measured sufficiently accurately so as to provide for resolving velocity sufficiently accurately, i.e. less than a given threshold. The particular operating wavelength of the range-imaging LIDAR system 24′, 24ⁱ is not limiting. For example, any optical wavelength that interacts with that which is being sensed in the associated interaction region 17 may be used.

[0245] For example, in one embodiment, the substantially monochromatic light 13 comprises ultraviolet (UV) laser light at a wavelength of about 266 nm that is generated using a laser light source 11. A wavelength of about 266 nm, being invisible to the human eye and substantially absorbed by the atmosphere, is beneficial for its stealth, eye safety and molecular scattering properties. There is relatively little natural background light at this frequency due to absorption of most natural 266 nm light by ozone and molecular oxygen. Ultraviolet light at about 266 nm is readily absorbed by glass and plastic, such as used in aircraft wind screens, which provides for improved eye safety. The particular operating wavelength of the range-imaging LIDAR system 24′ is not limiting, and it should be understood that any optical wavelength that interacts with that which is being sensed in the associated interaction region 17 may be used.

[0246] For example, a Nd:YAG laser 11.1′ can operate at relatively high power levels so as to provide sufficiently intense illumination so as to provide for relatively long range atmospheric sensing applications. An Nd:YAG laser 11.1′ has a fundamental wavelength of 1064 nm, from which shorter wavelengths/higher frequencies may be generated using one or more harmonic generators operatively associated with or a part of the Nd:YAG laser 11.1′. For example, a second-harmonic generator could be used to convert the fundamental 1064 nm light to second-harmonic 532 nm light which could then be transformed with either a third- or fourth-harmonic generator to generate associated 355 nm or 266 nm light respectively. For example, these second-, third- and/or fourth-harmonic generators may be either incorporated in, free-space coupled to, or coupled with a fiber optic to the Nd:YAG laser 11.1′. Accordingly, alternative embodiments of the range-imaging LIDAR system 24′, 24ⁱ incorporating a Nd:YAG laser 11.1′ may be operated at frequencies other than 266 nm, for example, at either the second or third harmonics, respectively, for example, as described more fully hereinbelow.

[0247] The arcuate fringes 49′, 49″ of the scatter 47 and reference 104 fringe patterns are circumferentially (φ) or transversely (Y) integrated either optically prior to detection, or electronically or by software during or following detection by the detection system 34, so as to provide for corresponding detected image signals I(X) and I₀(X), respectively, that representing the total radiometric counts as a function of radial distance through the corresponding scatter 47 and reference 104 fringe patterns. The resulting detected image signals I(X) and I₀(X) are then processed by the data processor 53 as described hereinbelow so as to generate one or more measures of the atmosphere 20 as a function of nominal range R, or at a particular nominal range R, within the interaction region 17.

[0248] Generally, depending upon how the resulting scatter 51 and reference 106 electronic image signals are processed, in accordance with a first aspect, the detection system 34 may comprise either one- or two-dimensional photodetector arrays, for example, either charge-coupled devices (CCDs) or charge injection devices (CIDs); or corresponding arrays of individual photodetectors, for example, photo-conductive, photo-voltaic, photo-emissive, bolometer, or thermopile photodetectors, i.e. generally any device that converts photons to a corresponding electrical signal. The particular detection system 34 may be adapted in cooperation with the associated light source 11 so as to provide for increasing the associated signal-to-noise ratio (SNR). For example, in cooperation with a continuous light source 11, a relatively high-sensitivity, low-noise, low-bandwidth detectors can be used, so as to provide for a higher signal-to-noise ratio (SNR) than possible with corresponding relatively higher-bandwidth detectors, so as to provide for relatively more precise associated measurements. Alternatively, the detection system 34 could comprise a camera with at least one array of concentric circular-segment photodetectors for each of the images being processed.

[0249] For example, in one embodiment, to process the scatter fringe pattern 47, the range-imaging LIDAR system 24′, 24ⁱ incorporates a linear photodetector array or a linear array of photodetectors, wherein, referring to FIG. 9, each photodetector or photodetector element of the array is sufficiently broad in the Y-direction 110 of the output focal plane 31.2′ so as to provide for accumulating all of the photons at a given associated X-position, and the each photodetector or photodetector element of the array is sufficiently narrow in the X-direction 112 of the output focal plane 31.2′ so as to provide for generating a corresponding one-dimensional scatter electronic image signal 51 with sufficient resolution with respect to X to solve for the associated measurements with sufficient accuracy, i.e. accuracy within a given threshold, wherein the X dimension corresponds to nominal range R to the associated measurement volumes 52 of the atmosphere 20 being measured within the beam of light 28. Similarly, one embodiment adapted to process the reference fringe pattern 104, the range-imaging LIDAR system 24′, 24ⁱ incorporates a similar linear photodetector array or a linear array of photodetectors, wherein each photodetector or photodetector element of the array is sufficiently broad in the Y′-direction 110 of the output focal plane 31.2′ so as to provide for accumulating all of the photons at a given associated X′-position, and the each photodetector or photodetector element of the array is sufficiently narrow in the X′-direction 112 of the output focal plane 31.2′ so as to provide for generating a corresponding one-dimensional reference electronic image signal 106 with sufficient resolution with respect to X′ to characterize the Fabry-Pérot etalon 35 sufficiently accurately so as to provide for solving for the associated measurements with sufficient accuracy, i.e. accuracy within a given threshold.

[0250] As another example, in another embodiment, to process both the scatter 47 and reference 104 fringe patterns, the range-imaging LIDAR system 24′, 24ⁱ incorporates a two-dimensional photodetector array or a two-dimensional array of photodetectors that provide for generating associated two-dimensional scatter 51 and reference 106 electronic image signals that, for example, can then be integrated either electronically; or by a process in the data processor 53, for example, as described hereinbelow.

[0251] Scattered light signal 30′ from each of the associated interaction regions 17 are substantially simultaneously processed together with a reference light signal 105 from the reference fringe pattern 104 so as to provide for calibrating, and maintaining the calibration of, the range-imaging LIDAR system 24′, and so as to provide for determining the associated air data products such as the speed, temperature and density of the atmosphere 20. This provides for an inherent self-calibration of the associated measurements or quantities derived therefrom. If wavelength drift of the light source 11 is not otherwise accounted for in the data, then errors can arise when making a measurement of the Doppler shift and resulting wavelength shift of the scattered light signal 30′. The range-imaging LIDAR system 24′ provides for automatically compensating for wavelength drift of the light source 11 from the data because each measurement from a scattered light signal 30′ is corrected using a corresponding measurement from the reference light signal 105 associated with the reference source 94.

[0252] In accordance with a first aspect, the associated detection system 34.1 provides for capturing an image 114 of the scatter 47 and reference 104 fringe patterns in the output focal plane 31.2′ of the Fabry-Pérot interferometer 31′. For example, in one embodiment, the detection system 34.1 comprises an electronic camera, for example, a CCD detection system 34.1′.

[0253] Referring to FIGS. 12a and 12b, this image 114 is then processed to azimuthally compress the associated scatter 47 and reference 104 fringe patterns into corresponding associated linear scatter 47^L and reference 104^L fringe patterns by an associated binning process to give corresponding linear sets of binned pixels 116 from which the corresponding atmospheric data 36 associated with each of the scattered light signals 30′ is then determined by the data processor 53. For example, this process is illustrated in FIGS. 12a and 12b for a range-imaging LIDAR system 24′, 24^viii in accordance with an eighth aspect described hereinbelow, comprising four separate scatter fringe patterns 47, 47.1, 47.2, 47.3, 47.4 from four separate corresponding interaction regions 17, interleaved with a reference fringe pattern 104. In one embodiment, this is accomplished with a circular binning algorithm implemented in software on the associated data processor 53 operatively coupled to the associated CCD detection system 34.1′ that provides for summing all pixels 118 at a particular radius 120 from the common center 122 of the associated circular fringe patterns 65 respectively corresponding to the first 47.1, second 47.2, third 47.3, and fourth 47.4 scatter fringe patterns and the reference fringe pattern 104 interleaved therewith divided into four separate corresponding reference fringe pattern portions 104.1, 104.2, 104.3, 104.4.

[0254] Each pixel 118 is read from the CCD detection system 34.1′ and converted by an A/D conversion process. The ratio of signal to read noise can be enhanced by increasing the exposure time of the CCD detection system 34.1′ between read cycles, although at the cost of reduced dynamic frequency response of the associated resulting air data products. After identifying the center 122 of the associated circular fringe patterns 65, the circular binning algorithm sums up the CCD charges (i.e. pixel values) for each pixel 118 at a particular radius from the center 122, for a particular circular fringe pattern 65, for each of the circular portions of the scatter fringe patterns 47.1, 47.2, 47.3, 47.4 and reference fringe pattern portions 104.1, 104.2, 104.3, 104.4, so as to provide a respective associated linear set of binned pixels 116 for each of the respective scatter fringe patterns 47.1, 47.2, 47.3, 47.4 and reference fringe pattern portions 104.1, 104.2, 104.3, 104.4. Referring to FIG. 13, the image 114 of the set of scatter fringe patterns 47.1, 47.2, 47.3, 47.4 and reference fringe pattern portions 104.1, 104.2, 104.3, 104.4 comprises an array of N rows by M columns of pixels 118, each of which is captured by the CCD detection system 34.1′ and stored in a memory 124 of the associated data processor 53 of the range-imaging LIDAR system 24′. The image 114 comprises eight regions of interest (ROI) 126.1-126.8, each comprising one of the corresponding scatter fringe patterns 47.1, 47.2, 47.3, 47.4 and reference fringe pattern portions 104.1, 104.2, 104.3, 104.4, and located about the common center 122 of associated circular fringe patterns 65, wherein the center 122 of the associated circular fringe patterns 65 is determined upon initial calibration or subsequent recalibration of the associated range-imaging LIDAR system 24′, and is assumed to be stationary during the operation thereof. For example, the center 122 may be determined by recording a substantial number, e.g. thousands, of circular fringe patterns 65 and determining the location of the center 122—by either iteration starting with an initial guess, or least squares or correlation with the coordinates of the center 122 as unknowns to be determined—that provides for a best fit of the recorded circular fringe patterns 65 with a corresponding circular model thereof centered at the center 122 of the circular fringe patterns 65.

[0255] Referring to FIG. 14a, in accordance with a first embodiment of a circular binning process 1400, in step (1402) a K×NROI bin array BIN(*, *) is defined with storage for NROI vectors of K elements each to hold the circumferentially-binned values for each of the NROI=8 portions of associated circular fringe patterns 65, and each value thereof is initialized to zero. Then, in steps (1404) and (1406), for each row i of the N rows, and for each column j of the M columns, of the pixels 118 in the image 114, the value Pixel(i,j) of the pixel 118 is read from the image 114 in step (1408), and in step (1410), the corresponding X and Y locations thereof are calculated respectively as follows:
x_j=j·α_x−x₀
y_i=i·α_y−y₀  (14)
wherein α_X and α_Y are the distances per pixel in the X and Y directions, respectively, and x₀ and y₀ are the coordinates of the center 122 relative to Pixel(1,1) at the lower left corner of the image 114. Then, in step (1412), the Cartesian coordinates (x_j, y_j) from step (1410) are transformed to cylindrical coordinates (R, θ), as follows:

[0256] $\begin{array}{cc}R=\sqrt{x_j^2+y_i^2}\theta ={\mathrm{Tan}}^{-1}\left(\frac{y_i}{x_j}\right)& \left(15\right)\end{array}$

[0257] Then, in step (1414), if the angle θ is within a region of interest (ROI) 126.1-126.8, the associated region of interest ROI 126 is identified, and in step (1416), the radial bin index k is given by:

[0258] $\begin{array}{cc}k=\frac{R}{\beta }-k_0& \left(16\right)\end{array}$
where β is the distance per pixel in the radial direction, and k₀ is the number of pixels 118 between the center 122 and the closest portion of the circular fringe pattern 65 closest thereto. Then, in step (1418), the associated value Pixel(i,j) of the associated pixel 118 is added to the bin element BIN(k,ROI) of the bin array BIN(*,NROI) as follows:
BIN(k,ROI)=BIN(k,ROI)+Pixel(i,j)  (17)

[0259] Then, or otherwise from step (1414), in step (1420), if all of the pixels 118 have been circumferentially binned, then, in step (1422), the circumferentially-binned values for each portion of the associated circular fringe patterns 65 are returned in the associated bin array BIN(*,NROI). Otherwise, the process repeats with steps (1404) and (1406) for each of the rows and columns of pixels 118 until all of the portions of the associated circular fringe patterns 65 are binned.

[0260] Referring to FIGS. 13 and 14b, alternatively, regions of interest (ROI) 126.1′-126.8′ may be defined by the corresponding respective boundaries of the respective portions of the associated circular fringe patterns 65, in which case, step (1414) of the circular binning process 1400 would be replaced by step (1414′), whereby the test as to whether a particular pixel 118 was in a particular regions of interest (ROI) 126.1′-126.8′ would depend upon both cylindrical coordinates (R, θ) of the particular pixel 118.

[0261] Referring to FIG. 15, in accordance with a second embodiment of a circular binning process 1500, rather than processing every pixel 118 of the image 114, only those pixels 118 in predefined regions of interest (ROI) 126.1′-126.8′ are processed, wherein, for example, the regions of interest (ROI) 126.1′-126.8′ are defined by the corresponding respective circular boundaries of the respective portions of the associated circular fringe patterns 65. Beginning with step (1502), for each region of interest (ROI) 126.1′-126.8′, in step (1504) the associated bin elements BIN(*,ROI) are initialized to zero. Then, in step (1506), the number of pixels 118 in the particular region of interest (ROI) 126.1′-126.8′ is given by the predetermined value of N(ROI). Then in step (1508), for pixel m of the N(ROI) pixels 118 in the particular region of interest (ROI) 126.1′-126.8′, the corresponding column j and row i indexes for the particular pixel 118, corresponding to the associated X and Y locations thereof, are given in step (1510) by predetermined values from predetermined index arrays j(m,ROI) and i(in,ROI) respectively, and the corresponding element k of the associated bin array BIN(*,ROI) into which the particular pixel 118 is to be binned is given by the predetermined index array k(m,ROI). Accordingly, in step (1512), the m^th pixel 118 is binned into the k^th element of the bin array BIN(*,ROI) as follows:
BIN(k(m,ROI),ROI)=BIN(k(m,ROI),ROI)+Pixel(i(m,ROI),j(m,ROI))  (18)

[0262] Then, in step (1514), if all of the pixels in in the particular region of interest (ROI) 126.1′-126.8′ have not been binned, then the process continues with step (1508). Otherwise, in step (1516), if all of the regions of interest (ROI) 126.1′-126.8′ have not been binned, then the process continues with step (1502). Otherwise, in step (1518), the circumferentially-binned values for each of the portions of the associated circular fringe patterns 65 are returned in the associated bin array BIN(*,NROI).

[0263] In one embodiment, the scatter fringe patterns 104.1, 104.2, 104.3, 104.4 associated with the reference fringe pattern 104 are binned into a single common linear reference fringe pattern 104^L, whereas in other embodiments the scatter fringe patterns 104.1, 104.2, 104.3, 104.4 associated with the reference fringe pattern 104 are either binned into separate associated linear reference fringe pattern 104^L, 104.1^L, 104.2^L, 104.3^L, 104.4^L, or partially combined into a fewer number of associated linear reference fringe patterns 104^L.

[0264] As yet another example, in yet another embodiment, the range-imaging LIDAR system 24′, 24ⁱ incorporates a plurality of circle-to-line interferometer optic (CLIO) elements 128 that provide for optically integrating the scatter 47 and reference 104 fringe patterns so as to generate corresponding linearly distributed associated fringe patterns that can then be detected with corresponding linear photodetector arrays or linear arrays of photodetectors, for example, as described hereinabove. For example, a separate circle-to-line interferometer optic (CLIO) element 128 would be used for each scatter fringe pattern 47.1, 47.2, 47.3, 47.4 and reference fringe pattern portion 104.1, 104.2, 104.3, 104.4 on diametrically opposing portions of the Fabry-Pérot interferometer 31′ relative to the optic axis 39, wherein each circle-to-line interferometer optic (CLIO) element 128 may be constructed and operated in accordance with the teachings of U.S. Pat. No. 4,893,003, which is incorporated herein by reference in its entirety, and in accordance with the teachings of U.S. Pat. No. 7,495,774, from line 22 at column 8 through line 50 at column 10 with reference to FIGS. 8 through 15b inclusive therein, and line 54 at column 29 through line 41 at column 30 with reference to FIGS. 35 through 39 inclusive therein, all of which is incorporated by reference.

[0265] As yet another example, in yet another embodiment, the range-imaging LIDAR system 24′, 24ⁱ incorporates a holographic optical element 128′ adapted to transform the arcuate fringes 49′, 49″ into corresponding linear distributions of light, for example, in accordance with the teachings of U.S. Pat. No. 6,313,908, which is incorporated herein by reference in its entirety, but adapted so that the arcuate fringes 49′ associated with the scatter fringe pattern 47 are transformed to a first linear distribution of light and the arcuate fringes 49″ associated with the reference fringe pattern 104 are transformed to a second linear distribution of light, wherein the first and second linear distributions are distinct, and detected by corresponding first and second linear photodetector arrays or linear arrays of photodetectors of the associated detection system 34, for example, as described hereinabove.

[0266] The reference 106 and scatter 51 electronic image signals are transmitted to the data processor 53, which processes the reference electronic image signal 106 to characterize the Fabry-Pérot etalon 35, and which then determines one or more range-dependent measures of the atmosphere 20—at one or more given ranges, or as a function of range—from the scatter electronic image signal 51 associated with arcuate fringes 49′, wherein each arcuate fringes 49′ corresponds to a different associated nominal range R and is analyzed separately. More particularly, the scatter electronic image signal 51 provides the information sufficient to determine the following measures of the atmosphere 20: aerosol counts A, molecular counts M, velocity u, temperature t, and background counts B, wherein molecular counts M provides for generating a measure of atmospheric density. As described more fully hereinbelow, data from each arcuate fringe 49′ is analyzed separately, so as to determine one or more of the measures: aerosol counts A, molecular counts M, velocity u, temperature t, and background counts B either at a given nominal range R or set of nominal ranges R, or as a function of nominal range R. The measures are determined by non-linearly fitting the measured reference electronic image signal 106 with a parameterized model of the Fabry-Pérot etalon 35, parameterized with respect to the measures so as to characterize the Fabry-Pérot etalon 35, and then non-linearly fitting the measured scatter electronic image signal 51 associated with different arcuate fringes 49′ to the parameterized model of the Fabry-Pérot etalon 35, parameterized with respect to the measures to be determined, i.e. with respect to aerosol counts A, molecular counts M, velocity u, temperature t, and background counts B, so as to determine values for those measures at the nominal range R associated with that particular arcuate fringe 49′.

[0267] A radial plot of the intensity of the circular fringe pattern 65 is illustrated in FIG. 16a. Referring to FIG. 16b, illustrating an expanded view of a radial cross-section of the intensity of a single circular fringe 65′ of the circular fringe pattern 65, a first fringe 130 corresponds to a zero-wind, i.e. zero-velocity condition, and a second fringe 132 corresponds to a non-zero wind condition, wherein both the first 130 and second 132 fringes are illustrated as exhibiting both an aerosol signal component 130.1, 132.1 and a molecular signal component 130.2, 132.2 respectively. The reference light signal 105 also provides for a zero wind condition, but does not contain either molecular or background components, and accordingly would exhibit only the aerosol signal component 130.1 illustrated in FIG. 16b.

[0268] The spectral shape of the scattered light signal 30′ processed by the Fabry-Pérot etalon 35, for a single associated fringe to be modeled, has a qualitative form illustrated in FIG. 16c, wherein the molecular scattered light, i.e. the molecular signal component 132.2, exhibits a broadened spectral shape, while the aerosol scattered light, i.e. the aerosol signal component 132.1, produces a sharp peak which is nearly identical to the shape of the transmitted laser light. Underlying these two components is a background signal from scattered sunlight, which at the scale of FIG. 16c forms a relatively flat continuum. By way of comparison, the corresponding spectral shape of the light of the reference light signal 105 processed by the Fabry-Pérot etalon 35 is substantially the same as that of the aerosol signal component 132.1.

[0269] The range-imaging LIDAR system 24′ provides for directly detecting laser energy scattered off of either molecules 20′ of the atmosphere, aerosols 20″ in the atmosphere, or a combination of the two, provides for directly measuring the associated velocity and direction, density, and temperature of the atmosphere, and provides for deriving other measurements therefrom, for example, a set of air data products. For example, relatively short wavelength laser energy is scattered by molecules of the atmosphere in accordance with Rayleigh scattering. Laser energy can also be scattered by aerosols in the atmosphere in accordance with Mie scattering. Rayleigh scattering generally refers to the scattering of light by either molecules or particles having a size less than about 1/10^th the wavelength of the light, whereas Mie scattering generally refers to scattering of light by particles greater than 1/10^th the wavelength of the light. Being responsive to Rayleigh scattering, the range-imaging LIDAR system 24′ is therefore responsive to the properties—e.g. velocity, density and temperature—of those molecules in the atmosphere giving rise to the associated scattering of the light detected by the range-imaging LIDAR system 24′. Accordingly, the range-imaging LIDAR system 24′ provides for operation in clean air, i.e. in an atmosphere with no more than a negligible amount of aerosols 20″, depending substantially only upon molecular scatter.

[0270] Referring to FIG. 17, the image 114 of the scatter fringe pattern 47 generated by the range-imaging LIDAR system 24′ is modeled use non-linear least square techniques. The distribution of the stray light and background radiation is provided by measurements of a scatter fringe pattern 47 either with an associated laser seeder 208 turned off when used in cooperation with a Nd:YAG laser 11.1′ so as to enable the Nd:YAG laser 11.1′ to lase over a relatively wider range of wavelengths that provides for simulating background radiation, or with the Fabry-Pérot etalon 35 removed from the Fabry-Pérot interferometer 31′. The scatter fringe patterns 47 are otherwise measured with the laser seeder 208 turned on if used in cooperation with a Nd:YAG laser 11.1′ so as to provide for substantially single-frequency operation. The instrument functions and derivatives used in the algorithm are formed from analytic representations of the Fabry-Pérot interferometer 31′ and include the necessary broadening functions to account for defects of the Fabry-Pérot etalon 35, e.g. the associated solid optical element 61, as well as temperature-dependent line shape broadening from molecular scatter. Empirical data for the illumination pattern is also used so that the correct light distribution of the fringes is accurately represented in the models.

[0271] The transmission T, of a perfect Fabry-Pérot etalon 35 is given by the Airy function as follows, and as described in Hernandez, G., Fabry-Pérot interferometers, Cambridge: Cambridge University Press, 1986, and Vaughan, J. M., The Fabry-Pérot Interferometer: History, Theory, Practice and Applications, Bristol, England: A. Hilger, 1989, both of which documents are incorporated herein by reference:

[0272] $\begin{array}{cc}T\left(M\right)=\frac{{\left(1-\frac{L}{1-R}\right)}^2{\left(1-R\right)}^2}{1-2R\cos 2\pi M+R^2}& \left(19\right)\end{array}$
where L is the loss per plate (absorption and scattering), R is the plate reflectivity, and M is the order of interference. Equation (19) describes a periodic transmission function, which is illustrated in FIG. 18. The separation between peaks is known as the free spectral range and depends inversely on the gap 45, 45.1 between the first 41 and second 43 partially-reflective surfaces, so that a relatively large spacing results in a relatively small free spectral range. The resolution of a Fabry-Pérot interferometer 31′ is determined by the full width at half height (FWHH) of a fringe, which in turn determines the Rayleigh resolving power of the Fabry-Pérot interferometer 31′. The finesse of the Fabry-Pérot interferometer 31′ is a unitless quantity that is defined as the ratio of the Free Spectral Range(FSR) to the FWHH. Finesse defines the number of resolvable elements that can fit in between two resonance peaks, and represents the sensitivity of the Fabry-Pérot interferometer 31′. In the absence of any defects, the finesse is related primarily to the reflectivity. For example, a reflectivity of 0.80 gives a finesse of 14, and a reflectivity of 0.90 gives a finesse of 30. In the presence of defects, both the finesse and the peak transmittance are reduced. Unless careful attention is given to defects when a Fabry-Pérot system is designed, the finesse and throughput can be substantially less than anticipated and can adversely bias the measured results. In order to incorporate defects into the instrument model equation (19) can be written in the equivalent series form, as follows:

[0273] $\begin{array}{cc}T\left(M\right)={\left(1-\frac{L}{1-R}\right)}^2{\left(\frac{1-R}{1+R}\right)}^2\left(1+2\sum _{n=1}^{\infty }{R}^n\cos 2\pi M\right)& \left(20\right)\end{array}$
Equation (20) is a useful form of the Airy function since it provides for relatively easy convolutions with broadening functions.

[0274] The order of interference M is given by:
M=2μtv cos θ  (21)
where μ is the index of refraction of the material between the first 41 and second 43 partially-reflective surfaces, t is the effective gap 45, 45.1, v is the wavenumber of light, and θ is the angle of incidence in the Fabry-Pérot etalon 35 which is responsive to the focal length of the imaging optics 37 and the size of the detection system 34. Perturbations of t, v and θ from a set of standard conditions and normal incidence, can be modeled as follows:
t=t₀+Δt  (22)
v=v₀+Δv  (23)

[0275] $\begin{array}{cc}\cos \theta =1-\frac{{\theta }^2}{2}& \left(24\right)\end{array}$
The order of interference can then be written as follows:

[0276] $\begin{array}{cc}M=2\mu t_0{v}_0+2\mu t_0\Delta v+2\mu v_0\Delta t-2\mu t_0{v}_0\frac{{\theta }^2}{2}& \left(25\right)\end{array}$
where only the first order terms have been retained, and can be further expressed as follows:
M=M_o+ΔM  (26)
where
M₀=2μt₀v₀  (27)

[0277] And

[0278] $\begin{array}{cc}\Delta M=2\mu t_0\Delta v+2\mu v_0\Delta t-2\mu t_0{v}_0\frac{{\theta }^2}{2}& \left(28\right)\end{array}$

[0279] The quantity ½μt₀ it is the change in wavenumber required to change the order of interference by one, and is defined as the free spectral range, Δv_FSR, which results in:

[0280] $\begin{array}{cc}\Delta M=\frac{\Delta v}{\Delta v_{\mathrm{FSR}}}-\frac{v_0{\theta }^2}{\Delta v_{\mathrm{FSR}}2}+2\mu v_0\Delta t& \left(29\right)\end{array}$

[0281] Without loss of generality M₀ can be an integer and therefore T(M)=T(ΔM).

[0282] Real instruments have defects which influence the behavior thereof and can be accounted for by broadening functions in the models used to characterize the device. These broadening functions are well known and are represented by a set of probability functions which can be convolved with the basic Fabry-Pérot Airy function to give the general result:

[0283] $\begin{array}{cc}T\left(\Delta v,\theta \right)={\left(1-\frac{L}{1-R}\right)}^2\left(\frac{1-R}{1+R}\right)\left[1+2\sum _{n=1}^{\infty }{R}^n{D}_n\cos 2\pi n\left(\frac{\Delta v}{\Delta v_{\mathrm{FSR}}}-\frac{v_0}{\Delta v_{\mathrm{FSR}}}\frac{{\theta }^2}{2}\right)\right]& \left(30\right)\end{array}$
wherein the broadening function D_n filters the transmission T depending upon the magnitude of the defect or broadening process, and is calculated from the following product:

[0284] $\begin{array}{cc}{D}_n=\prod _{q=1}^{N_q}{d}_n^q& \left(31\right)\end{array}$
wherein d_n^q is the n^th element of the convolution of the q^th broadening function G_q—described hereinbelow—with the instrument model of equation (20). The convolution integral is defined as follows:
d_n^q=∫_−∞^∞G_q(δ′)*T(M(n)−δ′)dδ′  (32)
where T(M(n)−δ′) is the Fabry-Pérot infinite series term.

[0285] A simplified notation can be used to provide for a more compact representation, wherein

[0286] $\begin{array}{cc}\begin{array}{c}{A}_n={\left(1-\frac{L}{1-R}\right)}^2\left(\frac{1-R}{1+R}\right)\mathrm{for}n=0\\ =2{\left(1-\frac{L}{L-R}\right)}^2\left(\frac{1-R}{1+R}\right)R^n{D}_n\mathrm{for}n>0\end{array}& \left(33\right)\end{array}$
so that the Airy function can be written as follows:

[0287] $\begin{array}{cc}T\left(\Delta v,\theta \right)=\sum _{n=0}^{\infty }{A}_n\cos 2\pi n\left(\frac{\Delta v}{\Delta v_{\mathrm{FSR}}}-\frac{v_0}{\Delta v_{\mathrm{FSR}}}\frac{{\theta }^2}{2}\right)& \left(34\right)\end{array}$

[0288] The broadening functions G_q account for broadening resulting from each of Doppler shift, laser width, scattering broadening, and turbulent motion, respectively, as given hereinbelow, for N_q=3 in equation (31).

[0289] Doppler Broadening:

[0290] The Doppler shift due to the mean air motion is given by:

[0291] $\begin{array}{cc}\Delta v=v_1\frac{2U_h\sin \varphi }{c}& \left(35\right)\end{array}$
where Δv is the Doppler shift, v₁ is the laser wavenumber, U_h is the horizontal wind speed in the direction of viewing, and φ is the angle from the zenith made by the beam of light 28 as it passes through the atmosphere 20, wherein U_h sin φ is the line-of-sight relative wind velocity U. Accordingly, equation (35) provides the relationship between line-of-sight relative wind velocity U and the Doppler shift Δv.

[0292] Laser Spectral Width Broadening:

[0293] The spectral shape of the laser is assumed to be of Gaussian form, as follows:

[0294] $\begin{array}{cc}{G}_{\mathrm{laser}}\left(\Delta v,\Delta v_1\right)=\frac{1}{\sqrt{\pi }\Delta v_1}{e}^{-\frac{\Delta v^2}{\Delta v_1^2}}& \left(36\right)\end{array}$
where Δv₁ is the 1/e width of the laser, wherein the shorter the duration a laser pulse, the broader the associated broadening function, which results in lowered finesse for the Fabry-Pérot etalon 35.

[0295] Scattering Broadening:

[0296] The affect on the transmission T of a Fabry-Pérot interferometer 31′ due to broadening induced by molecular scattering is different from that induced by aerosol scattering. Accordingly, different broadening functions G_q are used to account for molecular and aerosol scattering, respectively, in respective corresponding models for the molecular T_Mol and aerosol T_Aero components of transmission T of the Fabry-Pérot interferometer 31′.

[0297] The molecular scattering media broadens the signal due to associated random motions. The molecules have a Gaussian broadening function, as follows:

[0298] $\begin{array}{cc}{G}_{\mathrm{molecules}}\left(\Delta v,\Delta v_G\right)=\frac{1}{\sqrt{\pi }\Delta v_G}{e}^{-\frac{\Delta v^2}{\Delta v_G^2}}& \left(37\right)\end{array}$
where ΔV_G is the 1/e width and is given by:

[0299] $\begin{array}{cc}\Delta v_G=\frac{v_l}{c}{\left(\frac{2k·\mathrm{Temp}}{m}\right)}^{\frac{1}{2}}& \left(38\right)\\ \Delta v_G=4.30\times {10}^{-7}{v_l\left(\frac{\mathrm{Temp}}{\stackrel{\_}{M}}\right)}^{\frac{1}{2}}& \left(39\right)\end{array}$
where k is Boltzmann's constant, in is the mean mass of a molecule in the atmosphere, Temp is the static absolute temperature in degrees Kelvin, and M is the mean molecular weight ( M=28.964).

[0300] The aerosol broadening function has a Lorentzian form as follows, for example, as described in Fiocco, G., and DeWolf, J. B., “Frequency spectrum of laser echoes from atmospheric constituents and determination of aerosol content of air,” Journal of Atmospheric Sciences, v. 25, n3, May 1968, pp. 488-496; and Benedetti-Michelangeli, G., Congeduti, F., and Fiocco, G., “Measurement of aerosol motion and wind velocity in the lower troposphere by Doppler optical radar,” Journal of the Atmospheric Sciences, v. 29, n5, July 1972, pp. 906-910, both of which references are incorporated herein by reference:

[0301] $\begin{array}{cc}{L}_{\mathrm{aerosol}}\left(\Delta v,{\alpha }_A\right)=\frac{1}{\pi }\frac{{\alpha }_A}{{\alpha }_A^2+\Delta v^2}& \left(40\right)\end{array}$
where the half width α_A is given by:

[0302] $\begin{array}{cc}{\alpha }_A=\frac{2\pi v^{2}D}{c}& \left(41\right)\end{array}$
The spectral width of the aerosol-induced broadening component is extremely narrow compared to the molecular-induced broadening component, and in most cases are much narrower than the laser pulse, so that aerosol scattering essentially acts as a delta function and is not dependent on temperature.

[0303] Turbulent Motion Broadening:

[0304] In addition to random motions of molecules and aerosols, the model allows for random motions of bulk parcels, i.e. turbulence, wherein this broadening is represented by a relatively simple Gaussian shape, as follows:

[0305] $\begin{array}{cc}{G}_{\mathrm{turbulence}}\left(\Delta v,\Delta v_T\right)=\frac{1}{\sqrt{\pi }\Delta v_T}{e}^{-\frac{\Delta v^2}{\Delta v_T^2}},\mathrm{where}& \left(42\right)\\ \Delta v_T=\frac{v_1}{c}{U}_T,& \left(43\right)\end{array}$
and U_T is a characteristic turbulent velocity, which is a predefined constant that is independent of the line-of-sight relative wind velocity U. In some embodiments, this term is ignored because it is indistinguishable from temperature, so that the affects of equations (37) and (42) are indistinguishable from one another.

[0306] Other broadening functions G_q can also be utilized in addition to those described hereinabove, for example, so as to account for a defocus of the imaging optics 37.

[0307] The values of the linear sets of binned pixels 116 for the reference light signal 105 and scattered light signals 30′, respectively, provide a corresponding transmission measure T′ of the Fabry-Pérot interferometer 31′ for the corresponding reference light signal 105 and scattered light signals 30′, respectively. Each transmission measure T′ is an N-element vector, wherein each element n of the vector corresponds to a different wavelength or corresponding order of interference. The element values are in units of measurement counts; for example, with one measurement count being equal to one photo-electron captured by the detection system 34. The transmission measure T′ is a measure of data from the Fabry-Pérot interferometer 31′ that can be modeled as described hereinabove in accordance with equations (19) through (43), as represented by FIGS. 16c and 18, wherein FIG. 16c illustrates a finer scale of detail of each fringe illustrated in FIG. 18. Accordingly, the transmission measure T′, in units of total counts of binned values from the detection system 34, can be modeled as the sum of associated molecular, aerosol and background counts, as follows:
T=T_Mol(Temp,U)·MolCounts+T_Aero(U)·AeroCounts+T_Back·BackCounts  (44)
where T_Mol(Temp,U)·MolCounts is the component of transmission T of the Fabry-Pérot interferometer 31′ resulting from molecular scatter, which is a function of temperature and line-of-sight relative wind velocity U; T_Aero(U)·AeroCounts is the component of transmission T of the Fabry-Pérot interferometer 31′ resulting from aerosol scatter, which is not affected by temperature but is dependent upon the line-of-sight relative wind velocity U; and T_Back·BackCounts is the component of transmission T of the Fabry-Pérot interferometer 31′ resulting from stray light and background wherein T_Back is the continuum distribution or illumination profile through the instrument that is measured during calibration of the instrument from the response of the Fabry-Pérot interferometer 31′ with the laser seeder 208 turned off, which is representative of the associated spectral distribution from the Fabry-Pérot interferometer 31′ that would result from background illumination. During operation of the range-imaging LIDAR system 24′, the continuum distribution T_Back is obtained from pre-measured values that are stored in memory, and the components T_Mol and T_Aero are calculated from equation (34) using the appropriate associated broadening terms. Each of the above-described components of transmission T of the Fabry-Pérot interferometer 31′ is in units of counts resulting from the charge collected by the elements of the detection system 34. The distributions T_Mol(Temp,U), T_Aero (U) are evaluated with equation (34) using broadening functions that are appropriate for the molecular and aerosol components of scatter, respectively. In practice, when evaluating equation (34), the associated infinite series is truncated to ignore higher-order terms of relatively insignificant value, wherein the level of truncation is either predetermined, or determined during the accumulation of the elements of the series.

[0308] Accordingly, the transmission T of the Fabry-Pérot interferometer 31′ is modeled with a non-linear model of equation (44) that is parameterized by a first set (or vector) of parameters P that characterize a particular measurement, i.e. which characterize a particular transmission measure T′; and a second set of parameters Q which are assumed constant during operation of the Fabry-Pérot interferometer 31′, the values of which are determined during calibration. Referring to FIG. 17, the first set of parameters P, referred to as observables P, include the following elements: line-of-sight relative wind velocity U, static temperature Temp, molecular counts MolCounts, aerosol counts AeroCounts, and scatter counts BackCounts. The second set of parameters Q includes the gap 45, 45.1 (t), index of refraction μ (1 for an air gap) and reflectivity R of the Fabry-Pérot etalon 35, the nominal wavenumber v (or wavelength λ) of the monochromatic light 13 from the light source 11, the focal properties of the imaging optics 37 (i.e. θ in equation (21)), and the continuum distribution T_Back.

[0309] The observables P can be determined as the values of the parameters P that minimize the following χ² merit function:

[0310] $\begin{array}{cc}{\chi }^2\left(P,Q\right)=\sum _{n=1}^N\frac{{\left[T^{\prime }\left(n\right)-T\left(M\left(n\right);P,Q\right)\right]}^2}{{\sigma }^2\left(n\right)}& \left(45\right)\end{array}$
using, for example, a Levenberg-Marquardt method of a non-linear least square process which provides for varying smoothly between an inverse-Hessian method and a steepest descent method, as described, along with other suitable non-linear methods, by W. H. Press, S. A. Teukolsky, W. T Veterling, and B. P. Flannery in Numerical Recipes in C, The Art of Scientific Computing, Second Edition, Cambridge University Press, 1992, pp. 656-661 and 681-706 which is incorporated herein by reference. In equation (45), T′(n) is the value of the n^th binned pixel 116′, and T(M(n),P,Q) is the value of the transmission model T from equation (44).

[0311] Accordingly, for the range-imaging LIDAR system 24′, the transmission model T is overdetermined in the sense that the number of elements N of the detection system 34, i.e. the number of binned pixels per channel, is of a higher dimension than the number of observables P. For the range-imaging LIDAR system 24′ embodiment described herein, there are 5 observables P.

[0312] In the inverse Hessian method, the gradient of χ² is given by:

[0313] $\begin{array}{cc}{\beta }_k=\frac{\partial {\chi }^2}{\partial P_k}=-2\sum _{n=1}^N\frac{\left[T^{\prime }\left(n\right)-T\left(M\left(n\right);P,Q\right)\right]}{{\sigma }^2\left(n\right)}\frac{\partial T\left(M\left(n\right);P,Q\right)}{\partial P_k}& \left(46\right)\end{array}$
and the Hessian is approximated by:

[0314] $\begin{array}{cc}{\alpha }_{\mathrm{kl}}=\frac{{\partial }^2{\chi }^2}{\partial P_k\partial P_l}=2\sum _{n=1}^N\frac{\partial T\left(M\left(n\right);P,Q\right)}{\partial P_k}\frac{\partial T\left(M\left(n\right);P,Q\right)}{\partial P_l}& \left(47\right)\end{array}$
where k=1 to 5 for the 5 observables P.

[0315] The observables P are then solved by solving the set of linear equations:

[0316] $\begin{array}{cc}\sum _{l=1}^5{\alpha }_{\mathrm{kl}}\delta P_l={\beta }_k& \left(48\right)\end{array}$
where δP_l is an vector increment that is to be added to a current approximation for the observable vector P_l. This system of equations can be represented as:
A·δP=B  (49)
where A is the Hessian matrix, δP is a vector of increments to the observables P that are to be added to a current approximation for the observable P, and B is the gradient vector. This system of equations can be solved as follows:
δP=A⁻¹·B  (50)
where A⁻¹ is the inverse Hessian matrix.

[0317] The inverse Hessian method is suitable when the χ² merit function can be locally approximated by a quadratic form. If a quadratic form is a relatively poor local approximation, then the steepest descent formula can be used to find the increment δP of the observable P as follows:
δ·P_l=constant×β_k  (51)

[0318] The Levenberg-Marquardt method provides for a combination of the inverse Hessian and steepest descent methods, wherein the Hessian matrix in equation (48) is replaced with:
α′_kk=α_kk(1+λ)α′_jk=α_jk
(j≠k)  (52)
and both equations (48) and (51) are replaced with the following:

[0319] $\begin{array}{cc}\sum _{l=1}^5{\alpha }_{\mathrm{kl}}^{\prime }\delta P_l={\beta }_k& \left(53\right)\end{array}$
the solution of which is given by:
δP=A′⁻¹·B  (54)
where the elements of A′ are given by a′_jk.

[0320] The Levenberg-Marquardt method commences with an initial guess for the observable vector P, after which χ²(P,Q) is calculated, and an initial value of λ is chosen (e.g. λ=0.001). An iterative process then commences with the solution for δP of equation (44), and the evaluation of χ²(P+δP,Q). If χ²(P+δP,Q)≧χ²(P,Q), then λ is increased, e.g. by a factor of 10, and the iteration is repeated. Otherwise, if χ²(P+δP,Q)<χ²(P,Q), then λ is decreased, e.g. by a factor of 10, and the iteration is repeated. The iterations on the observable vector P are continued until a stopping criteria is satisfied, for example, on the first or second occasion when χ² decreases by a negligible amount, and with the final solution, the method converses towards the inverse Hessian method.

[0321] The components of the gradient of the transmission model T used in calculating the gradient of χ² and the Hessian matrix are given as follows, and are calculated numerically:

[0322] $\begin{array}{cc}\frac{\partial T\left(U,\mathrm{MolCounts},\mathrm{AeroCounts},\mathrm{Temp},\mathrm{BackCounts}\right)}{\partial U}=\frac{\partial }{\partial U}\left(T_{\mathrm{Mol}}\left(\mathrm{Temp},U\right)·\mathrm{MolCounts}+T_{\mathrm{Aero}}\left(U\right)·\mathrm{AeroCounts}\right)& \left(55\right)\\ \frac{\partial T\left(U,\mathrm{MolCounts},\mathrm{AeroCounts},\mathrm{Temp},\mathrm{BackCounts}\right)}{\partial \mathrm{MolCounts}}=T_{\mathrm{Mol}}\left(\mathrm{Temp},U\right)& \left(56\right)\\ \frac{\partial T\left(U,\mathrm{MolCounts},\mathrm{AeroCounts},\mathrm{Temp},\mathrm{BackCounts}\right)}{\partial \mathrm{AeroCounts}}=T_{\mathrm{Aero}}& \left(57\right)\\ \frac{\partial T\left(U,\mathrm{MolCounts},\mathrm{AeroCounts},\mathrm{Temp},\mathrm{BackCounts}\right)}{\partial \mathrm{Temp}}=\frac{\partial }{\partial \mathrm{Temp}}{T}_{\mathrm{Mol}}\left(\mathrm{Temp},U\right)& \left(58\right)\\ \frac{\partial T\left(U,\mathrm{Mol},\mathrm{Aero},\mathrm{Temp},\mathrm{BackCounts}\right)}{\partial \mathrm{BackCounts}}=T_{\mathrm{back}}& \left(59\right)\end{array}$

[0323] When processing the reference light signal 105, the observables MolCounts and BackCounts are assumed to be zero valued, and the partial derivatives with respect to MolCounts, BackCounts and Temp of equations (46), (59) and (58), respectively, are also assumed to be zero.

[0324] The σ²(n) weighing term in the χ² merit function is the associated variance of the n^th measurement channel (i.e. interference order or wavelength), which includes variance of the collected signal in combination with the variance associated with the noise from the detection system 34. The collected photons exhibit Poisson noise statistics. Accordingly, for Signal(n) photons/counts/photo-electrons collected on a single channel, the associated variance is equal to the signal level, as follows:
σ_Signal²(n)=Signal(n)  (60)
wherein Signal(n) is the sum of the molecular, aerosol and background components, i.e.:
Signal(n)=Molecular(n)+Aerosol(n)+Background(n)  (61)
so that Signal(n) is the predicted value from equation (44). The total variance is the combination of the signal variance and the variance of the detector, as follows:
σ²(n)=Signal(n)+Noise_Detector(n)²  (62)
wherein, for a CCD detection system 34.1, the detector noise is the associated read noise on each detector channel.

[0325] Alternatively, the observables P could be estimated using other non-linear modeling or non-linear programming techniques, or other techniques such as non-linear estimation or Kalman filtering.

[0326] Referring to FIG. 19, in accordance with other embodiments, the range-imaging LIDAR system 24′ comprises a laser 11′ as the light source 11, for example, in one embodiment, a Nd:YAG laser 11.1′, which operates in a pulsed mode, and which is operatively associated with a laser seeder 208, for example, a laser diode that provides for seeding the cavity of the pulsed Nd:YAG laser 11.1′ with photons via an associated light coupling system, wherein the photons are injected from the laser seeder 208 into the cavity of the Nd:YAG laser 11.1′ prior to the build-up of the laser pulse associated of the light source 11, causing the frequency thereof to substantially match that of the laser seeder 208, so as to provide for substantially single-frequency operation. For example, in one embodiment, the laser seeder 208 is adapted in cooperation with the Nd:YAG laser 11.1′ so that the bandwidth of the light source 11 is as narrow or narrower than the bandwidth of the associated Fabry-Pérot interferometer 31′, wherein the bandwidth of the Fabry-Pérot interferometer 31′ is related to the finesse thereof.

[0327] The substantially monochromatic light 13 from the laser 11′ is divided by a beam splitter optic 92 into a reference source 94 and the beam of light 28, the latter of which in some embodiments may be further divided into a plurality of beams of light 28 by beam steering optics 210, for example, incorporating beam splitting mirrors, prisms, a combination thereof, or some other type of beam splitter, each different beam of light 28 directed in a different direction into the atmosphere 20. The scattered light signals 30′ and reference source 94 are each first collimated by a collimator 212, e.g. a collimating lens 33, then filtered by a filter system 88 as described hereinabove, and then processed by an associated Fabry-Pérot etalon 35, the output of which is imaged by associated imaging optics 37 as portions of associated circular fringe patterns 65 onto the associated detection system 34. The associated optical components are adapted for the frequency and power levels of operation. For example, for a range-imaging LIDAR system 24′ incorporating a Nd:YAG laser 11.1′ operating at 355 nanometers, the optical elements would incorporate UV-grade fused silica substrates and standard anti-reflection coatings tuned for 355 nanometers.

[0328] The geometry of the circular fringe patterns 65 from the Fabry-Pérot etalon 35 is responsive to the operative gap 45, 45.1 thereof, which would vary with temperature if the associated material or materials controlling the length of the gap 45, 45.1 were to exhibit a non-zero coefficient of thermal expansion. Although the reference source 94 simultaneously processed by the Fabry-Pérot etalon 35 provides for compensating for thermal drift affecting all portions of the Fabry-Pérot etalon 35 equally, it is beneficial if the temperature of the Fabry-Pérot etalon 35 can be controlled or maintained at a constant level so as to prevent a thermal expansion or contraction thereof during the operation thereof. Accordingly, in accordance with one aspect of the range-imaging LIDAR system 24′, the Fabry-Pérot etalon 35 is thermally stabilized by enclosure in a thermally-controlled enclosure 214 so as to prevent thermally-induced drift of the circular fringe pattern 65.

[0329] In accordance with one aspect, the thermally-controlled enclosure 214 is passive, for example, with the Fabry-Pérot etalon 35 enclosed, i.e. thermally insulated or isolated, using a material or materials with a very low thermal conductance to increase the thermal time constant and to prevent any substantial thermal shock from reaching the Fabry-Pérot etalon 35. In accordance with another embodiment, or in combination therewith, the thermally-controlled enclosure 214 is constructed from a combination of materials adapted so that there is negligible net coefficient of thermal expansion in the portions of the structure surrounding the Fabry-Pérot etalon 35 that affect the length of the gap 45, 45.1.

[0330] Referring to FIGS. 20-23, in accordance with another aspect, a temperature of the thermally-controlled enclosure 214 is actively controlled responsive to at least one associated temperature sensor 216 using a temperature controller 218 incorporating a feedback control system 220 to control a heater, chiller or a combination heater and chiller—depending upon the temperature of the thermally-controlled enclosure 214 in relation to that of its environment. For example, referring to FIGS. 21 and 22, the Fabry-Pérot etalon 35 comprises a solid optical element 61—for example, constructed from high purity UV grade fused silica—enclosed within a etalon mount 222 comprising a cylindrical sleeve constructed from a material with a coefficient of thermal expansion that closely matches that of the solid optical element 61 so as to provide for preventing or substantially eliminating unwanted thermally induced radial stress in the solid optical element 61. The etalon mount 222 in turn is surrounded by a plurality, e.g. three, heat sink segments 224, each having a relatively high thermal conductance—for example, constructed of copper—each comprising an inner cylindrical face 226 that abuts an outside surface 228 of the etalon mount 222, and an outer face 230 incorporating a recess 232 adapted to receive and abut a first surface 234 of a thermo-electric heat pump 236, for example, what is known as a thermoelectric cooler (TEC). Upon assembly, the heat sink segments 224 collectively constitute an inner enclosure 238 that extends around and surrounds the etalon mount 222, the latter of which incorporates a flange 240 that abuts a set of first faces 242 on one side of the heat sink segments 224, and is fastened thereto with a plurality of fasteners 244, e.g. cap screws. The inner enclosure 238 is surrounded by an outer enclosure 246 comprising a plurality, e.g. three, heat conducting outer ring segments 248, e.g. constructed on aluminum, each of which incorporates an inside face 250 with an associated recess 252 that is adapted to receive and abut a second surface 254 of the thermo-electric heat pump 236. Each of the outer ring segments 248 incorporate associated flanges 256 at both ends, one side 258 of which are adapted to cooperate with internal grooves 260 in an outer shell 262 of the thermally-controlled enclosure 214, the other side 264 of which are adapted to cooperate with an outer ring retainer wedge 266 that operates between corresponding sides 264 of adjacent flanges 256 of adjacent outer ring segments 248 when the outer ring segments 248 are assembled to form the outer enclosure 246 surrounding the inner enclosure 238.

[0331] The inner 238 and outer 246 enclosures are assembled together to form a core assembly 268, as follows. The solid optical element 61 Fabry-Pérot etalon 35 is bonded inside a bore 270 of the etalon mount 222 with a thermal epoxy which provides for thermal conduction therebetween, wherein the inside diameter of the bore 270 is adapted so as to provide for a non-interfering fit with the solid optical element 61. The flange 240 of the etalon mount 222 is attached with fasteners 244 to the first faces 242 of the three heat sink segments 224 assembled around the outside surface 228 of the etalon mount 222. Three thermo-electric heat pumps 236 are sandwiched between respective recesses 232, 252 in a corresponding outer face 230 of each heat sink segment 224 and a corresponding inside face 250 of each outer ring segment 248, so that the first 234 and second 254 surfaces of the thermo-electric heat pumps 236 abut and are in thermal communication with the corresponding associated heat sink segment 224 and outer ring segment 248 respectively. The core assembly 268 further comprises a plurality, e.g. three, temperature sensors 216, e.g. thermistors, resistive temperature devices, or thermocouples—each of which is inserted in a corresponding hole 272 in a second face 274 of each heat sink segment 224, so as to provide for monitoring the temperature thereof, and so as to provide in cooperation with the associated temperature controller 218 and the associated thermo-electric heat pump 236, for controlling the temperature thereof.

[0332] The core assembly 268 is inserted in the outer shell 262 so that the flanges 240 of the outer ring segments 248 mate with the corresponding internal grooves 260 of the outer shell 262, and the outer ring retainer wedges 266 are inserted in the gaps 276 between the facing sides 264 of the flanges 240 so as to wedge the opposing sides 258 of the flanges 240 against associated internal grooves 260 of the outer shell 262, thereby providing for retaining the core assembly 268 within the outer shell 262, and providing for thermal communication therebetween. The ends 278 of the outer shell 262 are closed with associated end cap assemblies 280 secured thereto with associated fasteners 282 and sealed therewith associated seals 284, e.g. gaskets or o-rings. The end cap assemblies 280 incorporate associated window assemblies 286 fastened thereto and incorporating optical windows 288, e.g. constructed from UV grade fused silica substrates with standard anti-reflection coatings, which provide for transmission of the associated scattered 30′ and reference 105 light signals. The resulting assembly constitutes a thermally stabilized etalon assembly 290 incorporating a thermally-controlled enclosure 214. The thermally stabilized etalon assembly 290 further comprises a plurality of electrical connectors 292 therein which provide for connecting the thermo-electric heat pumps 236 and the temperature sensors 216 with the associated temperature controller 218. The temperature controller 218 uses the temperature sensors 216 to monitor the temperature of the core assembly 268, and controls the heating or cooling thereof relative to the environment using the associated thermo-electric heat pumps 236 so as to maintain the temperature of the core assembly 268 at a specified set-point. The outer enclosure 246 in thermal communication with the outer shell 262 provides for either supplying heat to or rejecting heat from the inner enclosure 238 responsive to the thermal effort of the thermo-electric heat pumps 236 as needed to maintain a particular set-point temperature. For example, in one embodiment, the set-point temperature is adapted so as to minimize the energy needed to maintain that temperature, while also maintaining a sufficient offset so as to operate the thermo-electric heat pumps 236 most efficiently. For example, for a thermo-electric heat pump 236 that operates most efficiently when heating, the set-point temperature might be 5 to 10 degrees Celsius above the nominal environmental temperature, e.g. 5 to 10 degrees Celsius above room temperature.

[0333] Referring to FIG. 19, in one embodiment, the firing of the Nd:YAG laser 11.1′ is, for example, controlled with an associated Q-switch in cooperation with a synchronizer 294, so as to provide for synchronization with the acquisition of associated images by the detection system 34, thereby precluding the need for an electronic shutter that would otherwise provide for gating scattered 30′ and reference 105 light signals to the detection system 34, although, alternatively, an electronic shutter could also be used or could be used without a synchronizer 294, for example, so as to preclude subsequent imaging during the process of reading image data if using a CCD detection system 34.1′. The synchronizer 294, if used, could be incorporated in a control electronics assembly 296, e.g. which could also incorporate the associated temperature controller 218 and/or the associated data processor 53. The synchronizer 294 could be adapted to either generate a master timing signal for controlling both the laser 11′ and the detection system 34, or could be adapted to relay a timing pulse generated by either one of the laser 11′ and detection system 34 to the other of the detection system 34 and laser 11.

[0334] The range-imaging LIDAR system 24′ can take advantage of aerosols when present, but does not rely upon their presence. The reference light signal 105 and the scattered light signals 30′ of the range-imaging LIDAR system 24′ can be used to directly measure velocity, true airspeed, vertical speed, angle of attack, angle of sideslip, static density, static temperature, and aerosol to total scattering ratio (ASR). From these data products the following quantities can be directly calculated: calibrated airspeed, Mach number, static pressure, total pressure, dynamic pressure, pressure altitude, air density ratio, total temperature, angle of attack, pressure differential, and angle-of-sideslip pressure differential. Wind velocity, density, and temperature are directly calculated using the fringe data from the Fabry-Pérot interferometer 31′. The other air data products are derived from these three basic measurements, in view of the knowledge of the associated geometry of the beam steering optics 210. The molecular signal yields a measure of air density that can be related to pressure. The aerosol to total scattering ratio is also directly derived from the results.

[0335] As used herein, the term relative wind is intended to refer to the relative motion between the atmosphere—included molecules and aerosols—and the range-imaging LIDAR system 24′. In addition to frequency—which, responsive to associated Doppler shift, provides for measuring associated velocity—the algorithm determines the contribution to the fringe pattern from molecular and aerosol scatter, the background radiation, and the temperature of the atmosphere 20 for each particular associated direction associated with each corresponding measurement volume 52 as viewed by the associated receive optics 32.

[0336] For example, referring to FIGS. 16b and 24, in accordance with a first measurement process 2402, the relative wind velocity V_i is determined along a corresponding direction from a difference between the centroids of the associated scatter fringe pattern 47 associated with a corresponding scattered light signal 30′ in comparison with that of the circular fringe pattern 65 associated with the reference light signal 105. The fringe position relative to the optic axis 39 is directly related to wavelength. Accordingly, a difference in wavelength between the circular fringe patterns 65 associated with a scattered light signal 30′ and that of the circular fringe pattern 65 associated with the reference light signal 105 is a direct measure of the molecular/aerosol Doppler shift in the scattered light 30 from the atmosphere 20 responsive to either molecular or aerosol scattering. The relative wind velocity V_i for each associated scattered light signal 30′ is calculated by subtracting the associated line-of-sight velocity U observable from the corresponding “line-of-sight velocity U” observable of the reference light signal 105, similarly so solved, so as to provide an associated calibrated relative wind velocity V_i.

[0337] Referring to FIGS. 16b and 24, in accordance with a second measurement process 2404, the air density, i.e. static density ρ, is determined from an integral of the molecular signal component 130.2, 132.2 of the circular fringes 65′ of the associated circular fringe patterns 65 associated with the scattered light signal 30′. The density of the atmosphere 20 is related to molecular density, not aerosol density. Accordingly, the Rayleigh scatter is separated from the Mie scatter by spectrally resolving the scattered light and de-convolving the spectrum into associated molecular and aerosol contributions, which provides for determining the density of the atmosphere 20 from the associated molecular component responsive to the total number of photons therein, i.e. responsive to an integral of the molecular signal component in accordance with Rayleigh scattering theory. The denser the air is, the more molecules are present to scatter light 30 back to the telescope 32′ for detection by the associated detection system 34. The observables MolCounts and AeroCounts inherently provides for a deconvolution of the spectrum into the associated molecular and aerosol contributions, i.e. MolCounts is responsive to the integral of the molecular contribution, and AeroCounts is responsive to the integral of the aerosol contribution. Accordingly, static density is given by ρ=C·MolCounts, wherein C is an empirically determined constant that depends upon the parameters that define the range-imaging LIDAR system 24′, i.e. the laser power, interaction region, the transmission of the system, the gain of the detectors, the size of the telescope 32′, and the coefficient of scatter from the atmospheric molecules 20′.

[0338] Referring to FIGS. 16b and 24, in accordance with a third measurement process 2406, the absolute temperature, i.e. static temperature T_s, of the atmosphere 20 is determined from a width of the molecular signal component 130.2, 132.2 of the circular fringes 65′ of the associated circular fringe patterns 65 associated with the scattered light signal 30′. The temperature of the atmosphere 20 affects the random thermal motions of the constituent molecules, which causes an associated thermal broadening—referred to as “Doppler broadening” in the field of spectroscopy because of the random velocities in all directions of an ensemble of molecules—of the spectrum of the associated scattered radiation, thereby increasing the associated signal bandwidth which produces correspondingly wider fringes in the associated circular fringe patterns 65 from the Fabry-Pérot interferometer 31′. The absolute temperature of the atmosphere 20 is directly related to this signal bandwidth, and is directly determined as the observable temperature t.

[0339] Referring to FIG. 24, for the example of an air data system in an aircraft 400, various other measured air data products may be calculated as follows: In accordance a fourth measurement process 2408, the relative wind velocities V_i determined by the first measurement process 2402 along corresponding associated directions are first transformed from a line-of-sight frame of reference to a frame of reference (x_m, y_m, and z_m) of the range-imaging LIDAR system 24′, and then to a frame of reference (x, y, z) of the aircraft 400 using known transformations, so as to provide the relative wind velocities V_X, V_Y and V_Z in the frame of reference (x, y, z) of the aircraft 400, from which the true airspeed V_T may be calculated from the relative wind velocities V_X, V_Y and V_Z in accordance with a fifth measurement process 2410. The vertical speed H′_P is given by the Z-component of relative wind velocity V_Z. The sideslip may be calculated from the Y-component of relative wind velocity V_Y and the true airspeed V_T in accordance with a sixth measurement process 2412. The angle of attack may be calculated from the X and Z-components of relative wind velocity V_X and V_Z in accordance with a seventh measurement process 2414. The Aerosol-to-Total Scattering Ratio (ASR) may also be calculated as the ratio of the observable AeroCounts to the sum of the observables MolCounts, AeroCounts and BackCounts. Referring to FIG. 25, the measured values of static density ρ, static temperature T_S, true airspeed V_T, sideslip and angle of attack may then be used to compute the following derived values using associated known relations and processes: air density ratio, static pressure, total pressure, pressure altitude, total temperature, speed of sound, Mach number, dynamic pressure, calibrated airspeed, angle of sideslip pressure differential, and angle of attack pressure differential.

[0340] More particularly, referring to FIG. 26, in accordance with a process 2600 for determining measures of atmosphere from the scatter electronic image signal 51, in step (2602), the Fabry-Pérot etalon 35 is characterized using the reference electronic image signal 106, wherein the velocity u, molecular counts M and background counts B are all assumed to be zero, as are the partial derivatives with respect to molecular counts M, background counts B and temperature t. Then, beginning with step (2604), for each arcuate fringe 49′, I(X_i) of interest, in step (2606), the associated nominal range R_i is given from a pre-determined function or table given the location in the output focal plane 31.2′ of the arcuate fringes 49′, I(X_i) being analyzed. Then, in step (2608), given the measurement vector I(X_i) of the arcuate fringe 49′, one or more of the atmospheric measures: aerosol counts A, molecular counts M, velocity u, temperature t, and background counts B is solved as described hereinabove. Then, in step (2610), if all of the arcuate fringes 49′, I(X_i) of interest have not been analyzed, then the above process repeats with step (2604). Otherwise, in step (2612), vectors U, t, M, A, and/or B of the one or more measures for each of the arcuate fringes 49′, I(X_i) analyzed in step (2608) are returned, together with a nominal range vector R of associated nominal ranges R, wherein the nominal ranges R_i of the nominal range vector will depend upon the associated velocities U_i (responsive to Doppler shift), and the gap 45 of the Fabry-Pérot etalon 35. These vectors can then be used to either determine functions of one or more measures U(r), t(r), M(r), A(r*) or B(r) as a function of nominal range R, as indicated by step (2614), or to interpolate values one or more measures U(r*), t(r*), M(r*), A(r*) or B(r*) at a particular nominal range R*, as indicated by step (2616). Alternatively, the nominal range vector R may be fixed, i.e. associated with a set of predetermined nominal ranges R, by adjusting the gap 45 of the Fabry-Pérot etalon 35 responsive to Doppler shift, for example, with the etalon control actuator 57, so that the associated arcuate fringes 49′ being analyzed remain at substantially fixed locations regardless of the conditions of the atmosphere 20.

[0341] Referring to FIG. 27, in accordance with a second embodiment of the first aspect, the range-imaging LIDAR system 24′, 24ⁱ, may be built without the collimating lens 33 and input telescope 32′. With the detector of the detection system 34 located in the output focal plane 31.2′ of the imaging optics 37—which is where the circular fringes 65′ produced by the Fabry-Pérot etalon 35 are sharpest—when the scattered light signal 30′ is relatively close to the sensor, the resulting image 114 of the scatter fringe pattern 47 will be out of focus, but the pertinent information is still present in the image. The geometry between the source beam of light 28 and the field-of-view 54 of the receive optics 32 is essentially the same as the system with the input telescope 32′ and collimating lens 33.

[0342] A reference beam portion 90 of the substantially monochromatic light 13 from the light source 11 is reflected from a first beam splitter optic 92 so as to generate an associated third embodiment of a reference source 94 which is coupled into an associated fiber optic 98 that routes the signal to where it is needed. The output from the fiber optic 98 is divergent and is subsequently collimated by an associated lens 134 and then combined with the scattered light 30 using a second beam splitter optic 136 that reflects a relatively small portion of the substantially monochromatic light 13 from the reference source 94 into the Fabry-Pérot interferometer 31′ as the associated reference light signal 105 while transmitting a substantial portion of the scattered light 30 therethrough into the Fabry-Pérot interferometer 31′ as the scattered light signal 30′.

[0343] The position of the fiber optic 98 in the image plane of the lens 134 determines where the associated image 114 of the reference light signal 105 will appear on the detection system 34. In one embodiment, the image 114 of the reference light signal 105 is positioned so as to not overlap the associated scattered light signal 30′ in the output focal plane 31.2′ of the Fabry-Pérot interferometer 31′. In another embodiment, in accordance with the eighth aspect of the range-imaging LIDAR system 24′, 24^viii described more fully herein below, the image 114 of the reference light signal 105 is positioned so as to overlap the associated scattered light signal 30′, with the portion of the reference light signal 105 overlapping the scattered light signal 30′ blocked by an associated mask 138 between the lens 134 and the second beam splitter optic 136.

[0344] The associated optics can be designed so that the reference light signal 105 will be sufficient to determine the center of the interference pattern produced by the Fabry-Pérot interferometer 31′ as well as the location of the associated arcuate fringes 49′, 49″.

[0345] Referring to FIG. 28, in accordance with a second aspect, the range-imaging LIDAR system 24′, 24ⁱⁱ may be adapted in accordance with a second aspect of an associated detection system 34.2 to measure the overall intensity of a fourth embodiment of a reference source 94 with a detector 140, rather than processing the reference beam through the Fabry-Pérot interferometer 31′, for example, so as to provide for either reducing the total number of signals processed with the Fabry-Pérot interferometer 31′. Such an arrangement would be suitable when the associated atmospheric data 36 being measured therewith are not dependent upon relative wind velocity, the latter of which measure is calibrated responsive to a measure of frequency shift of the reference light signal 105 using the Fabry-Pérot interferometer 31′. For example, the range-imaging LIDAR system 24′, 24″ illustrated in FIG. 28 would be suitable for measuring either or both of static density ρ and static temperature T_S, or to provide for deriving therefrom one or more of static air pressure total air temperature, speed of sound, air density ratio or pressure altitude.

[0346] Referring to FIGS. 29a and 29b, a first embodiment of a third aspect of an associated detection system 34, 34.3 of a range-imaging LIDAR system 24′ incorporates a digital micromirror device (DMD) 142 comprising an array—for example, a Cartesian array of N rows and M columns—of associated micromirrors 144, each of which constitutes a controllable pixel 146 that is individually addressable and controllable to one of at least three possible associated pixel mirror rotational states 148, 150, 152. The digital micromirror device (DMD) 142 is located in the output focal plane 31.2′ of the imaging optics 37 of the Fabry-Pérot interferometer 31′ so as to receive the scatter 47 and reference 104 fringe patterns processed by the Fabry-Pérot interferometer 31′, portions of which, when processed, are selectively reflected onto a pair of photodetectors 154^A, 154^B, for example, photomultiplier detectors 154^A′, 154^B′, from which complementary signals 156, 158 detected thereby are processed by the data processor 53 so as to provide for determining the associated measures of the atmosphere 20 therefrom as a function of nominal range R.

[0347] The micromirrors 144 of the associated array of micromirrors 144 of the digital micromirror device (DMD) 142 in the first pixel mirror rotational state 148 cause first portions 160′ of either the scatter fringe pattern 47 or the reference fringe pattern 104 from the Fabry-Pérot interferometer 31′ impinging thereupon to be reflected in a first direction 162 to an associated first objective lens 164, and to be directed thereby to the a first photomultiplier detector 154^A′. Similarly, micromirrors 144 of the associated array of micromirrors 144 of the digital micromirror device (DMD) 142 in the second pixel mirror rotational state 150 cause second portions 160″ of either the scatter fringe pattern 47 or the reference fringe pattern 104 from the Fabry-Pérot interferometer 31′ impinging thereupon to be reflected in a second direction 166 to an associated second objective lens 168, and to be directed thereby to the a second photomultiplier detector 154^B′. Finally, micromirrors 144 of the associated array of micromirrors 144 of the digital micromirror device (DMD) 142 in the third pixel mirror rotational state 152 cause third portions 160′″ of either the scatter fringe pattern 47 or the reference fringe pattern 104 from the Fabry-Pérot interferometer 31′ impinging thereupon to be reflected in a third direction 170 to the light block 172 that provides for absorbing light impinging thereupon. For example, in one embodiment, the third pixel mirror rotational state 152 corresponds to a state of substantially no rotation of the associated micromirrors 144, which may be achieved, for example, by, applying a common voltage to the associated micromirror 144 and it associated mirror address electrodes and yoke address electrodes, so as to create an equal state of electrostatic repulsion between all associated pairs of electrodes associated with the micromirror 144, thereby maintaining the micromirror 144 in a substantially unrotated condition.

[0348] The micromirrors 144 of the digital micromirror device (DMD) 142 are relatively efficient, with overall efficiency approaching 90% in one set of embodiments. Accordingly, the digital micromirror device (DMD) 142 provides for digitally isolating light impinging thereupon into two disjoint sets for the portion of the light being analyzed, and for masking a remaining portion of the light. More particularly, the digital micromirror device (DMD) 142 is used to interrogate portions the scatter 47 and reference 104 fringe patterns from the Fabry-Pérot interferometer 31′, and in cooperation with the associated first 154^A′ and second 154^B′ photomultiplier detectors, to provide for generating associated one or more pairs of associated complementary signals 156, 158, each responsive to the number of photons in the associated two disjoint sets of light reflected by the digital micromirror device (DMD) 142 resulting from a particular pattern of pixel mirror rotational states to which the associated array of micromirrors 144 of the digital micromirror device (DMD) 142 are set for a particular set of measurements, wherein the associated first 154^A′ and second 154^B′ photomultiplier detectors provide for counting the corresponding number of photons associated with each of the disjoint sets of light reflected by the digital micromirror device (DMD) 142.

[0349] For example, referring also to FIGS. 30 and 31, in accordance with the teachings of U.S. Pat. No. 5,535,047, and with the publication entitled “The Digital Micromirror Device: A Historic Mechanical Engineering Landmark”, published by Texas Instruments Inc. and the American Society of Mechanical Engineers on 1 May 2008 with 20 pages, both of which references are incorporated herein by reference, one embodiment of the digital micromirror device (DMD) 142 comprises an array of 16 micron square movable micromirrors 144 on 17 micron centers, each micromirror 144 of which is mechanically supported by a yoke 174 suspended from a pair of compliant torsion hinges or flexures 176 operatively coupled to a common CMOS substrate 178. Each micromirror 144 is rotatable into one of two stable pixel mirror rotational states responsive to electrostatic attraction between a corner portion 144.1, 144.2 of the micromirror 144 and one of two associated elevated mirror address electrodes 180.1, 180.2, and responsive to electrostatic attraction between a corresponding on of two opposed portions 174.1, 174.2 of the yoke 174 and one of two associated yoke address electrodes 182.1, 182.2. The micromirror 144 is rotated to one of the two stable pixel mirror rotational states by applying a first voltage to the micromirror 144 and yoke 174 via a bias-reset bus 184 in electrical connection therewith, and applying a second voltage to one of the mirror address electrodes 180.1, 180.2, and a corresponding one of the yoke address electrodes 182.1, 182.2, wherein first corresponding mirror 180.1 and yoke 182.1 address electrodes are electrically connected with one another, second corresponding mirror 180.2 and yoke 182.2 address electrodes are electrically connected with one another, and the first and second voltages are set so as to provide for attraction between the first or second mirror 180.1, 180.2 and yoke 182.1, 182.2 address electrodes and corresponding portions 144.1, 144.2, 174.1, 174.2 of the micromirror 144 and yoke 174.

[0350] For example, referring to FIG. 31, with the first voltage applied to a first micromirror 144¹ and associated yoke 174¹ via the associated bias-reset bus 184¹, a second voltage applied to the associated first mirror address electrode 180.1¹ and to the associate first yoke address electrode 182.1¹, causes the first corner portion 144.1¹ of the first micromirror 144¹ to be electrostatically attracted to the associated first mirror address electrode 180.1¹, and causes the first opposed portion 174.1¹ of the associated yoke 174¹ to be electrostatically attracted to the associated first yoke address electrode 182.1¹, thereby causing the first micromirror 144¹ to rotate to the first pixel mirror rotational state 148, which for example, is illustrated in FIG. 31 as +12 degrees for a particular commercial embodiment, wherein the first and second voltages are adapted to provide for an electrostatically attractive force therebetween. Similarly, with the first voltage applied to a second micromirror 144² and associated yoke 174² via the associated bias-reset bus 184², a third voltage applied to the associated second mirror address electrode 180.2² and to the associate second yoke address electrode 182.2², causes the second corner portion 144.2² of the second micromirror 144² to be electrostatically attracted to the associated second mirror address electrode 180.2², and causes the second opposed portion 174.2² of the associated yoke 174² to be electrostatically attracted to the associated second yoke address electrode 182.2², thereby causing the second micromirror 144² to rotate to the second pixel mirror rotational state 150, which for example, is illustrated in FIG. 31 as −12 degrees for the particular commercial embodiment, wherein the first and third voltages are adapted to provide for an electrostatically attractive force therebetween. The tips 186 of the yoke 174 contact corresponding landing sites 188 on the associated bias-reset bus 184, and the landing sites 188 may be passivated so as to prevent or reduce stiction, so as to provide for reducing the voltage needed to either reset the micromirror 144 to a flat state, or to rotate the micromirror 144 to the other pixel mirror rotational state. Another commercial embodiment, for example, provides for mirror rotational states of +/−10 degrees. In the rest state, the micromirror 144 is flat, but this state is not addressable for individual pixels in one set of commercial embodiments.

[0351] Commercial digital micromirror devices (DMD) 142 comprise arrays of micromirrors 144 ranging from an array of 640×480 micromirrors 144 containing approximately a half million micromirrors 144 in total, to an array of 2048×1080 micromirrors 144 containing over two million micromirrors 144 in total. Each micromirror 144 of the array represents one pixel 146 of a pattern 190 of associated pixel mirror rotational states 148, 150, 152, wherein each pixel is independently controllable or programmable responsive to a signal from the data processor 53.

[0352] The scattered light signal 30′ of the associated scattered light signal 30′ received from the interaction region 17 associated with the field-of-view 54 of the telescope 32′ is processed by the Fabry-Pérot interferometer 31′ to generate an associated scatter fringe pattern 47 that is then separated by the digital micromirror device (DMD) 142 into disjoint portions 47′, 47″ that are then detected by the corresponding associated first 154^A′ and second 154^5′ photomultiplier detectors. The reference light signal 105 is processed by the same Fabry-Pérot interferometer 31′, either simultaneously or sequentially, to generate an associated reference fringe pattern 104 that is then separated by the digital micromirror device (DMD) 142 or a separate corresponding digital micromirror device (DMD) (not illustrated) into disjoint portions 104′, 104″ that are then detected by the corresponding associated first 154^A′ and second 154^B′ photomultiplier detectors, or by a separate set of first and second photomultiplier detectors (not illustrated). The resulting complementary signals 156, 158 associated with the reference light signal 105 are used to provide for calibrating atmospheric measurements associated with the scattered light signal 30′. Accordingly, the range-imaging LIDAR system 24′ uses the Fabry-Pérot interferometer 31′ to directly detect information from the scattered laser energy, wherein the scatter 30′ and reference 105 light signals are each detected separately, and information from the reference light signal 105 can then be used to calibrate the associated scattered light signal 30′. The detection process is responsive to an incoherent Doppler shift of the laser light scattered by molecules and aerosols in the atmosphere 20 responsive to Rayleigh and Mie scattering respectively.

[0353] The response of a Fabry-Pérot interferometer 31′ is well documented in the literature, for example, as described by P. B. Hays and R. G. Roble in “A Technique for Recovering Doppler Line Profiles from Fabry-Pérot Interferometer Fringes of very Low Intensity”, Applied Optics, 10,193-200, 1971, which is incorporated herein by reference. The ideal intensity distribution of a the fringe pattern for a single wavelength transmitted through a Fabry-Pérot interferometer 31′ by a LIDAR system without optical defects is given by

[0354] $\begin{array}{cc}{H}_{\mathrm{ideal}}\left(\phi \right)=\frac{T^2}{1+R^2-2R\cos \left(\phi \right)}\mathrm{where}& \left(63.1\right)\\ \phi =\frac{4\mathrm{\pi \mu }d}{\lambda }\left(1-2\frac{u}{c}\right)\cos \left(\theta \right)& \left(63.2\right)\end{array}$
wherein T is the transmissivity, R is the reflectivity, μ is the refractive index of the Fabry-Pérot etalon 35, d is the thickness of the gap 45, 45.1 of the Fabry-Pérot etalon 35, λ is the wavelength of the source, θ is the angle of transmission through the Fabry-Pérot etalon 35, c is the speed of light, and u is the line-of-sight air velocity. Hence, the Doppler shift is 2u/c. In the presence of a source distribution including many wavelengths and optical defects it is advantageous to use the Fourier cosine series expansion of the response. The distribution of intensity transmitted per molecular weight (of the scattering species) is given by:

[0355] $\begin{array}{cc}H\left(\varphi ,m\right)=\frac{T^2}{1-R^2}\left(1+2\sum _{n=1}^{\infty }{R}^n\exp \left(-\frac{n^2}{4}{G}^2\left(t\right)\right)\prod _k{D}_{n,k}\cos \left(n\varphi \right)\right)\mathrm{where}& \left(64.1\right)\\ G\left(t\right)=\frac{4\mathrm{\pi \mu }d}{\lambda c}\sqrt{\frac{2A_0\mathrm{kt}}{m}}& \left(64.2\right)\end{array}$
where t is the atmospheric temperature, k is the Boltzmann constant, A₀ is Avogadro's number, m is the molecular mass of the scattering species, and the convolution effects of the optical defects are represented by associated defect coefficients D_n,k.

[0356] If there were no optical defects, then each of the defect coefficients D_n,k would be identically equal to one. However, in a system with optical defects, these may be accounted for in various ways. For example, in accordance with a first method, the defect coefficients D_n,k are calibrated using a reference source 94 that does not interact with the atmosphere 20. As long as the range-imaging LIDAR system 24′ stays calibrated then these defect coefficients D_n,k may be used directly in the inversion of data to recover atmospheric state variables. As another example, in accordance with a second method, a signal from the reference light signal 105 is periodically collected together with one or more associated signals from the corresponding one or more scattered light signals 30′, and the effect of the defect coefficients D_n,k is computed by de-convolving the ideal signal, H_ideal,—for example, H_ideal as given by equation (63.1),—from the recovered data using the Fourier transform of the ideal signal, H_ideal, for example, as given by equations (73.1), (73.2) and (74) described hereinbelow. The function G(t) approximates the effect of thermal broadening of a source by a low density gas, which effects are more precisely accounted for by Rayleigh-Brillouin scattering, although that level of detail is not essential to the practice of the range-imaging LIDAR system 24′.

[0357] For an atmosphere 20 containing both aerosols and molecules, and for the range-imaging LIDAR system 24′ adapted to sample the entire circular fringe pattern 65, the associated total response is given by:

[0358] $\begin{array}{cc}I\left(\phi \right)=AH\left(\phi ,m_A\right)+MH\left(\phi ,m_M\right)+\frac{T^2}{1-R^2}B& \left(65\right)\end{array}$
where I is the total number of photons reaching the photodetector 154, A is the number of photons that have been scattered by aerosols, M is the number of photons that have been scattered by molecules, B is the number of background photons transmitted to the range-imaging LIDAR system 24′ by the ambient atmosphere 20, m_A is the molecular mass of an aerosol particle (for example, a very large number on the order of 1.0e5), and m_M is the molecular mass of air (about 28.92). Given this model, the sensitivity of the system to the atmospheric variables A, M, u, t and B is respectively given by respectively taking partial derivatives of equation (65) with respect to each respective variable, as follows:

[0359] $\begin{array}{cc}\frac{\partial I}{\partial A}=H\left(\phi ,m_A\right)& \left(663.1\right)\\ \frac{\partial I}{\partial M}=H\left(\phi ,m_M\right)& \left(66.2\right)\\ \frac{\partial I}{\partial u}=\left(A\frac{\partial }{\partial \phi }H\left(\phi ,m_A\right)+M\frac{\partial }{\partial \phi }H\left(\phi ,m_M\right)\right)\frac{\partial \phi }{\partial u}& \left(66.3\right)\\ \frac{\partial I}{\partial t}\approx M\frac{\partial }{\partial t}H\left(\phi ,m_M\right),\mathrm{and}& \left(66.4\right)\\ \frac{\partial I}{\partial B}=\frac{T^2}{1-R^2}\mathrm{where}& \left(66.5\right)\\ \frac{\partial \phi }{\partial u}=-2\frac{4\mathrm{\pi \mu }d}{\lambda c}\cos \left(\theta \right).& \left(66.6\right)\end{array}$