Optical air data systems and methods

[0001] This application claims benefit of priority to U.S. Provisional Patent Application Ser. No. 60/699,630 filed Jul. 15, 2005. This application is also a continuation-in-part of U.S. application Ser. No. 11/103,020 filed 11 Apr. 2005, which is a continuation of U.S. application Ser. No. 10/632,735 filed Aug. 1, 2003, now U.S. Pat. No. 6,894,768, which claims benefit of priority to U.S. Provisional Patent Application No. 60/400,462 filed Aug. 2, 2002. All of the aforementioned applications are hereby incorporated by reference.

[0002] This invention was made in part with the support of the U.S. Government; the U.S. Government has certain rights in this invention as provided for by the terms of Grant #NAS4-02043 awarded by the NASA Dryden Flight Research Center.

[0003] An Air Data System (“ADS”) provides sensed telemetry informing pilots, navigators or Vehicle Management System computers of air parameter(s) affecting aircraft stability. These air parameters include, for example, air speed, air temperature and air pressure, each being useful for navigation and flight control. The ADS exists in many forms, for example, as mechanical, opto-mechanical or opto-electronic devices.

[0004] An Optical Air Data System (“OADS”) uses light to determine parameters of air speed. The OADS transmits light pulses into the atmosphere and receives light that aerosols reflect or “backscatter” towards the aircraft. Aerosols are fine solids and/or liquid particles suspended in air or other gases. The OADS may also measure the Doppler effect by receiving backscattered light and measuring its return frequency to determine speed. Certain prior art OADSs rely on scattered light that is unpredictable because of aerosol distributions that vary significantly with altitude and cloud content. In addition, some regions of the atmosphere contain too few aerosols to enable reliable air data measurements, and such an OADS cannot determine air temperature or air pressure.

[0005] In an embodiment, a method for remotely sensing air outside a moving aircraft includes generating laser radiation within a swept frequency range. A portion of the laser radiation is projected from the aircraft into the air to induce scattered laser radiation. Filtered scattered laser radiation, filtered laser radiation, and unfiltered laser radiation are detected. At least one actual ratio is determined from data corresponding to the filtered scattered laser radiation and the unfiltered laser radiation. One or more air parameters are determined by correlating the actual ratio to at least one reference ratio.

[0006] In an embodiment, a method for remotely sensing air outside a moving aircraft includes generating laser radiation within a swept frequency range, wherein the swept frequency range includes at least two absorption features of at least one band stop filter. A portion of the laser radiation is projected from the aircraft into the air to induce scattered radiation Filtered scattered laser radiation, filtered laser radiation, and unfiltered laser radiation are detected. A normalized atmospheric return curve is determined from the filtered scattered laser radiation and the unfiltered laser radiation; a normalized filter transmission curve is determined from the filtered laser radiation and the unfiltered laser radiation. At least one actual ratio is determined from the normalized atmospheric return curve. At least one reference ratio is determined from the normalized filter transmission curve and a Rayleigh line shape corresponding to one or more estimated air parameters. One or more air parameters are determined by correlating the at least one actual ratio to the at least one reference ratio.

[0007] In an embodiment, a method for remotely sensing air outside a moving aircraft includes generating laser radiation within a swept frequency range. A portion of the laser radiation is projected from the aircraft into the air to induce scattered radiation. Filtered scattered laser radiation, filtered laser radiation, unfiltered scattered laser radiation, and unfiltered laser radiation are detected. A normalized filter transmission and a normalized atmospheric return are determined from the filtered scattered laser radiation, filtered laser radiation, unfiltered scattered laser radiation, and unfiltered laser radiation. A plurality Doppler line shifts and a plurality of radial wind velocities are determined from a plurality of frequency shifts between the normalized filter transmission and the normalized atmospheric return, wherein each frequency shift corresponds to an absorption feature of at least one band stop filter.

[0008] In an embodiment, a system for sensing of air outside a moving aircraft includes at least one laser for generating laser radiation and at least one transceiver for projecting the laser radiation to the air and for receiving scattered laser radiation from the air. Additionally, the system includes at least one band stop filter selected from the group consisting of a fixed frequency atomic vapor filter, an interference filter, a dichroic filter, a fiber Bragg grating filter, a Rugate filter, and combinations thereof. Furthermore, the system includes a computer for controlling the laser and for processing signals from the transceiver to determine one or more air parameters based on the scattered laser radiation.

[0009] In an embodiment, a software product includes instructions, stored on computer-readable media, wherein the instructions, when executed by a computer, perform steps for remotely sensing air outside a moving aircraft. The software product includes instructions for generating laser radiation within a swept frequency range. The software product also includes instructions for determining a normalized atmospheric return curve from filtered scattered laser radiation and unfiltered laser radiation and instructions for determining a normalized filter transmission curve from filtered laser radiation and the unfiltered laser radiation. Furthermore, the software product includes instructions for determining at least one actual ratio from the normalized atmospheric return curve and instructions for determining at least one reference ratio from the normalized filter transmission curve and a Rayleigh line shape corresponding to one or more estimated air parameters. Also included within the software product are instructions for determining one or more air parameters by correlating the at least one actual ratio to the at least one reference ratio.

[0010] FIG. 1 shows one Optical Air Data System (“OADS”), according to an embodiment.

[0011] FIG. 2 shows one OADS, according to an embodiment.

[0012] FIG. 3 shows one graph useful in illustrating an exemplary air speed calculation with an OADS, according to an embodiment.

[0013] FIGS. 4-7 show graphs illustrating exemplary calculations for other air parameters with an OADS, according to an embodiment.

[0014] FIG. 8 is a flowchart showing one exemplary method of operation of an OADS, according to an embodiment.

[0015] FIG. 9 is a flowchart showing one exemplary method of operation of an OADS, according to an embodiment.

[0016] FIG. 1 shows one Optical Air Data System (“OADS”) 101 mounted on or within an aircraft 102. In this embodiment, OADS 101 is configured for projecting laser radiation 103 to air 104. Laser radiation 103 impinges on air 104 and aerosol particles 105 (in air 104), causing scattering of laser radiation 103, which is represented in FIG. 1 as a scatter field 106. Distance between aircraft 102 and scatter field 106 is controlled by overlap between laser radiation 103 and the transceiver 110 field of view at a distance from aircraft 102, to provide an optimized intensity for return laser radiation 107 and to eliminate possible measurement error arising from displaced air proximate to aircraft 102. OADS 101 detects backscattered laser radiation 107 that is backscattered from air 104 at laser scatter field 106. Radiation 107 may be in the ultra-violet (UV) spectrum, for example, having a wavelength within a range of 250 nm to 270 nm; however, other ranges may alternatively be used to produce scatter field 106.

[0017] Return laser radiation 107 typically contains molecular scattered (e.g., Rayleigh) components 107A and/or aerosol scattered (e.g., Mie) components 107B. OADS 101 distinguishes the molecular scattered components 107A from the aerosol scattered components 107B and correspondingly determines one or more air parameters based on backscattered laser radiation 107. Examples of such air parameters include air speed, air pressure, air temperature and/or aircraft orientation angles relative to the local wind. OADS 101 may be configured with other aircraft as well, such as unmanned air vehicles (UAVs), helicopters, gliders and space shuttles. Although illustrated within a “nose” 108 of aircraft 102, OADS 101 may be configured in any other part of aircraft 102.

[0018] As shown in FIG. 1, OADS 101 includes a laser 109 configured for generating laser radiation 103. Transceiver 110 is configured for transmitting laser radiation 103, from laser 109 via optical coupling 111, and receiving backscattered laser radiation 107. Optical coupling 111 may exist in the form of a fiber optic connection or free space transmission. Accordingly, transceiver 110 projects the laser radiation as laser radiation 103 to air 104. Air 104 scatters laser radiation 103 at scatter field 106 in a plurality of directions (e.g., illustrated as vectors 112). Scatter field 106 also returns, or backscatters, radiation 107 towards transceiver 110, which subsequently receives the backscattered laser radiation 107. Transceiver 110 converts backscattered laser radiation 107 to processable electronic signals, via computer 113, to determine the air parameters.

[0019] Computer 113 communicatively couples with transceiver 110 and processes signals from transceiver 110 to distinguish a molecular scattered component 107A from an aerosol scattered component 107B. Computer 113 determines the air parameters based on laser radiation 107 backscattered from molecules and/or aerosols in air 104. Accordingly, as described below, computer 113 may employ one or more digital signal processing algorithms to determine such parameters.

[0020] While OADS 101 illustrates one transceiver 110 in an exemplary embodiment, a plurality of transceivers may be used, depending on an application. For example, a helicopter employing OADS 101 may use two transceivers 110 to determine air parameters such as a forward velocity (e.g., air speed) and a horizontal plane, or “yaw”, of the helicopter. An airplane may use three transceivers 110 positioned in a particular manner to determine various aircraft geometries, such as angle of attack and sideslip, in addition to the air parameters of air speed, air pressure and air temperature. In addition, air vehicles (fixed wing and rotary) may employ three or more transceivers and/or lasers to increase Optical Air Data System reliability through a redundant system architecture. Using three OADS transceivers mounted orthogonally to one another may fully resolve a total airspeed vector by providing three independent measurements for the air speed vector (i.e., corresponding to three axes of a Cartesian coordinate system). The transceivers are for example located in uncommon planes and their geometry respective of a known aircraft center-line. Vector algebra may then be used to determine the full airspeed vector, including forward air speed, angle-of-sideslip and angle-of-attack.

[0021] FIG. 2 shows one OADS 140. OADS 140 illustrates another embodiment used for determining air parameters, such as those described in FIG. 1, based upon laser radiation backscattered from both air molecules and aerosols. In this embodiment, OADS 140 includes laser 141 configured for generating laser radiation 142. Laser 141 may be a tunable laser having a tuned center wavelength of about 253.7 nm, although other wavelengths may be used. For example, laser 141 may be a frequency quadrupled, Nd:YAG (i.e., neodymium:yttrium-aluminum-garnet) pumped Ti:Sapphire (titanium-sapphire) laser. Alternatively, frequency-quadrupled Yb-doped (ytterbium-doped) fiber lasers may be used that offer important benefits of smaller size, lighter weight, increased robustness and improved reliability, as compared to Nd:YAG-pumped Ti:Sapphire lasers. Laser 141 may generate laser radiation that is tunable across a frequency range of about 40 GHz; laser 141 may be a continuous wave laser which sweeps in frequency across this range, or it may be a pulsed laser controlled such that each pulse has a frequency distribution centered about a tunable peak frequency. In one embodiment, the peak frequency increments by about 100 MHz from each pulse to the next. Laser 141 may tune ±20 GHz about a center frequency of approximately 1182.5 THz, or c/253.7 nm, where c is the speed of light (approximately 3×10⁸ M/s). In the illustrated embodiment, laser 141 radiates laser radiation 142 to beam splitter 143, which splits the beam into two components, 143A and 143B. Component 143A is directed through air 144; component 143B is directed to beam splitter 145.

[0022] In particular, component 143A of laser radiation 142 directed to air 144 is scattered into scatter field 146. Scattering of component 143A is illustrated by scattering vectors 147 in scatter field 146, whereas return scattering is illustrated by backscattered laser radiation 148. Component 143B of the laser radiation 142 is used as a reference for comparison to backscattered laser radiation 148. Such a comparison is for example useful in determining air parameters such as air speed, since transmitted and received frequencies of the laser radiation may be ascertained for use in a Doppler equation; such a process is explained in greater detail herein below.

[0023] In the illustrated embodiment, backscattered laser radiation 148 is received through optics 149. In one example, optics 149 is a telescope that gathers backscattered laser radiation 148 into a beam 150. Optics 149 also directs beam 150 to beam splitter 151, to split beam 150 into two components 150A/150B. Component 150B of beam 150 passes through vapor filter 152 to detector 153 to produce electronic signal 158 representative of the component 150B impinging detector 153; whereas component 150A is directed by beam splitter 151 to detector 154.

[0024] In one embodiment, detector 154 is a photodetector that receives radiation 150A and converts it into an electronic signal 155. Detector 154 connects to a central computer 156 to process electronic signal 155. Similarly, detector 153 is a photodetector configured for detecting component 150B, which is filtered by vapor filter 152 as filtered component 157. Detector 153 converts component 157 to an electronic signal 158 for processing by central computer 156.

[0025] Accordingly, electronic signal 158 corresponds to backscattered laser radiation 148 as filtered by vapor filter 152; and electronic signal 155 corresponds to unfiltered backscattered laser radiation 150A. Electronic signal 155 is thus used to nullify certain anomalies as computer 156 processes electronic signal 158. For example, when processed with electronic signal 158, signal 155 may be used to remove, from signal 158, certain laser transmission power fluctuations in filtered component 157 caused by atmospheric changes in air 144. Such a process is explained in more detail in connection with FIGS. 4-7.

[0026] Computer 156 includes lookup tables 170 and 172 that may be utilized to determine temperature and/or pressure as discussed below.

[0027] Reference component 143B of the laser radiation 142 is split into two components 159 and 160 by beam splitter 145. Component 160 is directed by beam splitter 145 to vapor filter 152 via mirrored surface 161, to measure filter characteristics, whereas component 159 is directed by beam splitter 145 to detector 162, to generate electronic signal 163. Electronic signal 163 is for example used to normalize power fluctuations in the return of backscattered laser radiation 148 caused by power fluctuations in the generation of laser radiation 142 by laser 141. Such a process is explained in more detail in FIGS. 4-7.

[0028] Vapor filter 152 filters component 160 to produce filtered component 164. Filtered component 164 is directed to detector 165, via mirrored surface 166, and then converted to an electronic signal 167. Central computer 156 processes electronic signal 167 to determine filter characteristics, such as frequencies and suppression features of the band stop region of vapor filter 152. One such process is also explained in more detail in context of FIGS. 4-7.

[0029] It should be noted that while FIG. 2 shows OADS 140 as having free space optical transmission and optical components such as beam splitters 143, 145 and 151 and mirrors 161 and 166, optical fiber may be used for laser 141 transmission along paths 142, 143A, 143B, 159, 160, 164, 150, 150A, 150B and/or 157; in such an embodiment, fiber splitters may be used in place of beam splitters 143, 151 and 145, and mirrors 161 and/or 166 may be eliminated.

[0030] It will also be appreciated that although the embodiment shown in OADS 140 of FIG. 2 employs vapor filter 152, other types of filters may be utilized. For example, notch or band-stop filters such as interference filters, dichroic filters, fiber Bragg grating filters and/or Rugate filters may be utilized. A filter used in place of vapor filter 152 may advantageously have properties such as: (1) high optical absorption within a stop-band region on the order of 40-60 dB or more; (2) a notch filter absorption width between about 5 GHz and 40 GHz, with an absorption width under 10 GHz being preferred; and (3) steep absorption sidewalls, with a 10% -90% absorption transition occurring within about 5 GHz or less. Pass-band filters may also be used, such as when they operate in a reflection mode such that a reflection produces a stop-band filter. Single filters with multiple absorption features may be utilized, or optical or fiber splitters may be used to route optical signals through multiple filters, each filter having a single absorption feature.

[0031] Filters other than atomic vapor filters may provide certain advantages. For example, while the absorption frequencies of atomic vapor filters are reliably tied to properties of an atomic vapor used, their use may constrain an OADS to include a tunable laser having output at such frequencies. However, certain tunable lasers may have improved performance and/or stability at frequencies that do not conveniently match atomic vapor filter absorption frequencies. Certain filters such as interference filters, dichroic filters, fiber Bragg grating filters and/or Rugate filters may be designed to have absorption features tuned to a preferred frequency output range of a tunable laser, rather than tuning the laser to the filter. The use of a tunable laser selected on its merits, and a matching notch filter in an OADS may thus (1) enable use of higher laser output power for improved return signal strength, (2) make the OADS more robust with respect to thermal stability, vibration and shock, (3) eliminate hazardous materials (e.g., mercury) from the OADS, and/or (4) reduce size, weight and/or cost of the OADS.

[0032] FIG. 3 shows one graph 200 useful in illustrating an exemplary air speed calculation with OADS 140. Graph 200 shows two curves, 201 and 202, comparing normalized laser radiation magnitudes as a function of frequency (signal strength, that is, normalized laser radiation magnitude, is plotted with respect to axis 205, and frequency is plotted with respect to axis 204). Curve 202 exemplifies filtered radiated laser radiation such as that of filtered component 164 of FIG. 2. As such, curve 202 shows filter characteristics of vapor filter 152 of FIG. 2 determined by processing of electronic signal 167. Curve 202 shows a peak absorption of filter 152 occurring at a down-translated frequency of 0 GHz. By way of example, the actual peak absorption frequency of filter 152 may be about 1182.5 THz (i.e., having a corresponding wavelength of about 253.7 nm).

[0033] Laser radiation 142 generated by laser 141 passes through filter 152 to provide filtered component 164. Once filtered component 164 is converted to electronic signal 167 by detector 165, computer 156 analyzes and stores features of vapor filter 152 through digital signal processing of signal 167 (e.g., computer 156 stores reference features, obtained under controlled conditions, for use in future calculations). As shown in this example, features of vapor filter 152 have approximately 10% normalized absorption at approximately ±5 GHz (i.e., 0.9 normalized transmission factor at approximately ±5 GHz according to axis 205) about the peak absorption frequency. Other types of suitable filters may include different absorption/transmission features.

[0034] Curve 201 exemplifies filtered backscattered laser radiation such as that of filtered component 157 of FIG. 2. In one embodiment, curve 201 is used to determine air speed by comparison to curve 202. For example, curve 202 illustrates how vapor filter 152 affects laser radiation 142; curve 201 similarly illustrates how vapor filter 152 affects laser radiation 142 as laser radiation 142 is backscattered (e.g., returns as radiation 148) from air 144. Frequency shift 203 represents the change in frequency of peak absorption for vapor filter 152 between transmitted laser radiation 142 and returned laser radiation 148. Computer 156 processes algorithms applying Doppler velocity equation to determine air speed from frequency shift 203.

[0035] To determine air speed in one embodiment, computer 156 determines how far in frequency the peak absorption frequency of filtered component 157 has shifted from the initial laser frequency by comparing curve 202 to curve 201 (e.g., comparing peak absorption frequencies of filtered components 157 and 164). Frequency shift 203 substantially equates to a radial wind velocity through the Doppler velocity equation: $\begin{array}{cc}\Delta v_D=\frac{2V_R}{\lambda },& \left(\mathrm{Eq}.1\right)\end{array}$
where Δv_D represents the Doppler frequency shift, V_R represents velocity component of the vehicle (e.g., aircraft 101 of FIG. 1) along the laser direction of propagation 143A and λ represents the wavelength of laser radiation 142.

[0036] In one embodiment, wind velocity component V_R may be measured by determining the frequency shift from curve 202 of graph 200 as compared to curve 201 of graph 200. This is accomplished by calculating a symmetry point of each curve 201 and 202 and determining a difference in symmetry points between the two curves.

[0037] Vapor filter 152 may have a plurality of absorption features. Consequently, OADS may have a plurality of absorption maxima, such as those illustrated by curves 201 and 202 of FIG. 3, which may be used to provide a more accurate estimate of the vehicle's velocity. The vehicle's velocity, V_R, may be calculated using equation 1 for each absorption feature. An average velocity of the vehicle may then be calculated from each value of V_R.

[0038] FIGS. 4-7 show graphs illustrating exemplary calculations for other air parameters with OADS 140. For example, after determining frequency shift due to air speed as shown in FIG. 3, other air parameters such as air temperature and air pressure may be calculated. In one example, computer 156 initially determines an intensity measurement of the detected backscattered laser radiation (e.g., filtered component 157 detected by detector 153) from electronic signal 158. This experimentally verified intensity measurement of returned laser radiation corresponds to the following equation:
S_S(v)=P_LT_LD_ST_RE_S∫dv_r∫dv_laser[L(v_laser)F(v_r−v)(r R(v_r−(v_laser−Δv_D))+mM(v_r−(v_laser−Δv_D)))]  (Eq. 2)
where S_S(v) is electronic signal 158 from detector 153; P_L is the laser power, T_L is the transmission coefficient through air 144 along laser path 143A, L(v_laser) is the laser line shape inherent to the laser 141 output as a function of laser frequency v_laser, T_R is the transmission coefficient through air 144 along laser path 148, E_S is optical efficiency of the detector channel through detector 153, F(v) is the band stop frequency range of vapor filter 152 centered at a frequency of v, R is Rayleigh scattering as a function of frequency (applicable to the Rayleigh regime) v_r for backscattered laser radiation minus the quantity of laser frequency v_laser minus the Doppler shift Δv_D, r is the Rayleigh scattering magnitude coefficient dependent on air density and the Rayleigh backscattering coefficient, M is Mie scattering as a function of v_r minus the quantity of v_laser minus Δv_D, m is the Mie scattering magnitude coefficient dependent on aerosol concentration and the Mie backscattering coefficient, and D_S is detector 153 efficiency. The Rayleigh backscattering coefficient r and the Mie backscattering coefficient m are constant for a particular atmosphere. These coefficients correspond to the number of scatterers (i.e., molecules for Rayleigh, aerosols for Mie) per unit volume of atmosphere.

[0039] Next, computer 156 may determine other air parameters, utilizing the result obtained for the measured intensity of the returned laser energy. Such a process, for example, may begin by determining characteristics of vapor filter 152 by transmitting of reference laser radiation 160 through vapor filter 152. For example, measuring band stop characteristics of vapor filter 152 with laser 141 (e.g., via component 143B to electronic signal 167) during experimentation yields a convolution of the laser wavelength and the filter according to the following equation:
S_F(v)=P_LE_FD_F∫dv_laser[L(v_laser)F(v_laser−v)], (Eq. 3)
where S_F(v) is signal 167 from detector 165 as a function of frequency v (e.g., as illustrated in curve 221 of FIG. 4); E_F is the optical efficiency of filter 152 collection along paths 160 and 164, and D_F is detector 165 efficiency.

[0040] Note that all optical efficiencies E_F and E_S capture signal losses that are optical in nature. For example, E_F, the optical efficiency for detector 165, includes the optical beam splitting ratios for beam splitters 143 and 145, the optical transmission and coupling across filter 152 and the optical delivery efficiency onto detector 165. E_S, the optical collection efficiency for detector 153, includes the collection efficiency of telescope 149, the optical coupling efficiency into path 150, the beam splitter ratio of beam splitter 151, the transmission efficiency across filter 152 and the delivery efficiency onto detector 153. Detector efficiencies D_F and D_S include the detector conversion efficiencies for detectors 165 and 153, respectively. Thus, D_F is the conversion efficiency whereby detector 165 converts laser radiation along path 164 into an electrical signal 167. Likewise, D_S is the conversion efficiency whereby detector 153 converts laser radiation along path 157 into an electrical signal 158.

[0041] Backscattered laser radiation 148 may include power fluctuations that are caused by laser 141 while generating laser radiation 142. Accordingly, laser radiation detected by detector 162 (e.g., via component 159) may be utilized to normalize power fluctuations attributable to laser 141. In one embodiment, detector 162 converts component 159 into electronic signal 163. In turn, computer 156 processes and normalizes according to the following equation:
S_L(v)=P_LE_LD_L∫dvL(v),   (Eq. 4)
where S_L(P) is the electronic signal 163 from detector 162, E_L is the optical collection efficiency for detector 162, D_L is the conversion efficiency of detector 162 and P_L is the power of laser 141. Note that the optical collection efficiency E_L includes the beam splitting ratios of beam splitters 143 and 145 and the delivery efficiency of laser beam path 159 onto detector 162.

[0042] Curve 221 of graph 220 of FIG. 4 represents the magnitude of laser radiation (component 164) filtered by vapor filter 152 and normalized between 0 and 1. Curve 221 represents the magnitude of the laser radiation as a function of frequency (i.e., laser radiation magnitude plotted with respect to axis 222 and frequency plotted with respect to on axis 223). Curve 221, therefore, illustrates filtered laser radiation via component 160 as determined by computer processing of electronic signal 167, plotted as laser radiation magnitude normalized between 0 and 1, versus frequency.

[0043] In one embodiment, absorption/transmission characteristics of vapor filter 152 are normalized using Eq. 3 and Eq. 4. Eq. 3 yields stop band characteristics of filter 152 and Eq. 4 accounts for power fluctuations in the generation of laser radiation 142. With the power fluctuations of Eq. 4 substantially removed, a “normalization channel” is created, and power fluctuations attributable to atmospheric changes may be accounted for.

[0044] In one embodiment, additional power fluctuations caused by atmospheric changes in air 144 are also removed. For example, laser radiation detected by detector 154 (e.g., via component 150A) assists in removing laser power fluctuations caused by atmospheric changes in air 144. Accordingly, detector 154 converts received laser radiation into electronic signal 155. Computer 156, in turn, processes electronic signal 155 to determine the normalized laser radiation magnitude according to the following equation:
S_N=P_LT_LT_RE_ND_N∫dv∫dv_laser[L(v_laser)(rR(v−(v_laser−Δv_D))+mM(v−(v_laser−Δv_D)))]  (Eq. 5)
where S_N is the signal 155 from detector 154; E_N is optical collection efficiency of the detector 154 and D_N is the conversion efficiency of detector 154.

[0045] In one embodiment, it is advantageous to normalize the various characteristic functions to enable a closed-loop solution to the process of determining temperature and pressure. In one example, therefore, computer 156 calculates the normalized laser line shape according to following equation:
∫L(v_laser)dv_laser=1,   (Eq. 6)
where (as before) v_laser is laser line shape frequency and L denotes the laser line shape as a function of frequency. In another example, computer 156 calculates normalized Rayleigh Function according to the following equation:
∫R(v_r)dv_r=1,   (Eq. 7)
where R denotes the Rayleigh line shape as a function of frequency v_r, applicable to the Rayleigh regime. In another example, computer 156 scales the electronic signal 167 recorded from detector 165 by dividing all recorded values by the maximum value according to the following equation:
MAX(S_F(v))=1,   (Eq. 8)
where MAX denotes an operation that finds a maximum value of a particular function, and S_F denotes electronic signal 167 measured from detector 165, as a function of frequency v (e.g. as illustrated in curve 221 of FIG. 4). In another example, computer 156 normalizes the Mie Function according to the following equation:
M(v)=δ(v),   (Eq. 9)
where δ(v) is the delta function.

[0046] In one embodiment, dividing the signal 167 collected from detector 165 (and represented by Eq. 3, above) by the signal 163 collected from detector 162 (and represented by Eq. 4, above) removes laser 141 power fluctuations, as follows: $\begin{array}{cc}\frac{S_F\left(v\right)}{S_L\left(v\right)}=\frac{P_L{E}_F{D}_F\int d{v}_{\mathrm{laser}}\left[L\left(v_{\mathrm{laser}}\right)F\left(v_{\mathrm{laser}}-v\right)\right]}{P_L{E}_L{D}_L\int dvL\left(v\right)}& \left(\mathrm{Eq}.10\right)\end{array}$

[0047] Equation 10 simplifies to: $\begin{array}{cc}\frac{S_F\left(v\right)}{S_L\left(v\right)}=\frac{E_F{D}_F}{E_L{D}_L}\mathrm{LF}\left(v\right)& \left(\mathrm{Eq}.11\right)\end{array}$

[0048] where LF(p) represents a convolution of functions L and F (that is, a function that represents the effects of functions L and F combined at each frequency v).

[0049] In one embodiment, tuning the laser 141 to a reference frequency v_ref far enough removed from the effects of the vapor filter 152 enables the measurement of the ratio of the optical and detector efficiencies of the signal channels 167 (S_F, represented by Eq. 3 above) and 163 (S_L,, represented by Eq. 4 above). This, in turn, enables the normalization of the signal 167 measurement to one, for simultaneously checking for laser, detector and filter abnormalities on a scan-by-scan basis: $\begin{array}{cc}\frac{S_F\left(v_{\mathrm{ref}}\right)}{S_L\left(v_{\mathrm{ref}}\right)}=\frac{E_F{D}_F}{E_L{D}_L}& \left(\mathrm{Eq}.12\right)\end{array}$

[0050] In one embodiment, LF(v) are determined to generate a look up table of the convolution of theoretical Rayleigh functions (calculated in terms of temperature and pressure) with the measured filter function. Since the measured filter function is already the convolution of the laser and filter spectra, convolving the Rayleigh function with the measured filter signal 167 yields the expected return signal from an atmosphere of pure Rayleigh scatterers.

[0051] In one embodiment, the measured signal 158, which is the backscatter return from the atmosphere 144 that passes through the vapor filter 152 (and is represented by Eq. 2 above), is divided by the signal 155, which is the backscatter return from the atmosphere 144 that does not pass through vapor filter 152 (and is represented by Eq. 5 above). This calculation removes changes in signal transmission that are independent of the factors to be measured: $\begin{array}{cc}\frac{S_S\left(v\right)}{S_N\left(v\right)}=\frac{\begin{array}{c}{P}_L{T}_L{D}_S{T}_R{E}_S\int dv\int d{v}_{\mathrm{laser}}\\ \left[\begin{array}{c}\left(L\left(v_{\mathrm{laser}}\right)F\left(v_r-v\right)\right)(\mathrm{rR}(v_r-(v_{\mathrm{laser}}-\\ \Delta v_D))+\mathrm{mM}\left(v_r-\left(v_{\mathrm{laser}}-\Delta v_D\right)\right))\end{array}\right]\end{array}}{\begin{array}{c}{P}_L{T}_L{T}_R{E}_N{D}_N\int dv\int d{v}_{\mathrm{laser}}\\ \left[\begin{array}{c}L\left(v_{\mathrm{laser}}\right)(\mathrm{rR}\left(v_r-\left(v_{\mathrm{laser}}-\Delta v_D\right)\right)+\\ \mathrm{mM}\left(v_r-\Delta v_D\right)))\end{array}\right]\end{array}}& \left(\mathrm{Eq}13\right)\end{array}$
Since M is a delta function, Equation 13 simplifies to: $\begin{array}{cc}\frac{S_S\left(v\right)}{S_N\left(v\right)}=\left[\frac{E_S{D}_S}{E_N{D}_N}\right]\frac{\mathrm{rLFR}\left(v_{\mathrm{laser}}-\Delta v_D\right)+\mathrm{mLF}\left(v_{\mathrm{laser}}-\Delta v_D\right)}{r+m}& \left(\mathrm{Eq}.14\right)\end{array}$

[0052] where LFR(P) represents a convolution of functions L, F and R in the sense of the convolution LF(v) discussed above.

[0053] In one embodiment, tuning laser 141 to reference frequency v_ref far enough removed from the effects of the vapor filter 152 enables the measurement of the ratio of the optical and detector efficiencies of the signal channels 158 (S_S as represented by Eq. 2 above) and 155 (S_N as represented by Eq. 5 above). This enables a check for abnormalities in the filter on a scan-by-scan basis: $\begin{array}{cc}\frac{S_S\left(v_{\mathrm{ref}}\right)}{S_N\left(v_{\mathrm{ref}}\right)}=\frac{E_S{D}_S}{E_N{D}_N}& \left(\mathrm{Eq}.15\right)\end{array}$

[0054] In one embodiment, a variable K_ref may be defined as: $\begin{array}{cc}{K}_{\mathrm{ref}}=\frac{S_S\left(v_{\mathrm{ref}}\right)}{S_N\left(v_{\mathrm{ref}}\right)}& \left(\mathrm{Eq}.16\right)\end{array}$

[0055] Once both data sets (i.e., S_S and S_N) are symmetric about the same data point, computer 156 calculates temperature and pressure from the return signal. Initially, computer 156 uses theoretical Rayleigh functions that are functions of temperature and pressure in conjunction with the measured filter transmission to generate a lookup table 170 that stores laser, Rayleigh, and filter (LFR(v)) convolutions that are dependent on atmospheric temperature and pressure. Computer 156 may then compare a normalized return signal to a value stored in lookup table 170 to determine atmospheric temperature and pressure. In order to compare the return signal with the lookup table 170, computer 156 accounts for the magnitude of Mie scatterers as well as any changes in air density that may change the magnitude of the Rayleigh signal.

[0056] A vapor filter may be used as a bandstop filter; such filters typically provide frequency stability, optical depth, and optimal filter shape. For the purposes of separating the Rayleigh and Mie scattering, an optical depth of approximately 60 dB provides excellent absorption of Mie scattering within a small frequency variance around v₀ (i.e., where v_f is a normalized frequency of 0 GHz). For example, an atomic vapor filter may provide 60 dB of absorption in a frequency region that is not contaminated by Mie scattering. This region may be used in acquiring initial estimates of pressure and temperature (explained below in FIG. 5). Such absorption is observable in FIG. 5 below as the measured signal S_F which has the magnitude of zero centered about v₀. This data provides information about pure Rayleigh scattering that may be used to calculate the ratio of Mie scattering to Rayleigh scattering, as shown in Eq. 17: $\begin{array}{cc}\frac{S_S\left(v_0\right)}{S_N\left(v_0\right)}=\left[\frac{E_S{D}_S}{E_N{D}_N}\right]\frac{\mathrm{rLFR}\left(v_0\right)+\mathrm{mLF}\left(v_0\right)}{r+m}& \left(\mathrm{Eq}.17\right)\end{array}$
Since the vapor filter fully attenuates the Mie scattering in this region: $\begin{array}{cc}\frac{S_S\left(v_0\right)}{S_N\left(v_0\right)}=\left[\frac{E_S{D}_S}{E_N{D}_N}\right]\frac{\mathrm{rLFR}\left(v_0\right)}{r+m},& \left(\mathrm{Eq}.18\right)\end{array}$
where LFR(v₀) is the value of the theoretical return signal at particular atmospheric temperature and pressure. Accordingly, computer 156 calculates the ratio of Mie scattering by first defining a variable K₀ as follows: $\begin{array}{cc}{K}_0=\frac{S_S\left(v_0\right)}{S_N\left(v_0\right)}& \left(\mathrm{Eq}.19\right)\end{array}$
and then solving for the ratio $\begin{array}{cc}\frac{m}{r}=\frac{K_0}{K_a}\mathrm{LFR}\left(v_0\right)-1& \left(\mathrm{Eq}.20\right)\end{array}$
Using the normalized signal return in the region of interest (i.e., the sloped region between the minimum and maximum of the signal return) and writing the result in terms of the ratio of m over r, yields the following: $\begin{array}{cc}\frac{S_S\left(v\right)}{S_N\left(v\right)}=K_a\frac{\mathrm{LFR}\left(v\right)+\frac{m}{r}\mathrm{LF}\left(v\right)}{1+\frac{m}{r}}& \left(\mathrm{Eq}.21\right)\end{array}$
Substituting the ratio of m and r of Eq. 20 into Eq. 21 yields: $\begin{array}{cc}\frac{S_S\left(v\right)}{S_N\left(v\right)}=K_a\frac{\mathrm{LFR}\left(v\right)}{\mathrm{LFR}\left(v_0\right)}+\mathrm{LF}\left(v\right)\left[1-\frac{K_0}{K_a\mathrm{LFR}\left(v_0\right)}\right]& \left(\mathrm{Eq}.22\right)\end{array}$
Solving for LFR(v) yields: $\begin{array}{cc}\mathrm{LFR}\left(v\right)=\frac{S_S\left(v\right)}{S_N\left(v\right)}\frac{\mathrm{LFR}\left(v_0\right)}{K_a}+\mathrm{LF}\left(v\right)\left[\frac{1}{K_a}-\frac{\mathrm{LFR}\left(v_0\right)}{K_0}\right],& \left(\mathrm{Eq}.23\right)\end{array}$
where the measured signal return LFR(v) is written in terms of measured quantities and the theoretical values of LFR(v₀). Computer 156 then calculates LFR(v) and compares it to the lookup table 170 to determine atmospheric temperature and pressure, described in greater detail in FIG. 5.

[0057] Accounting for power fluctuations, optical efficiencies and detector efficiencies as described herein allows for an independent check on vapor filter 152 while OADS 140 operates. With variable characteristics of detector channels and power fluctuations accounted for, computer 156 may determine, for example, the substantially constant characteristics of vapor filter 152, such that more accurate measurements of received backscattered laser radiation (e.g., laser radiation 148) are obtained.

[0058] In one embodiment, the normalization channel depicted in FIG. 4 is used to remove atmospheric power fluctuations of laser radiation 148. In doing so, computer 156 measures Rayleigh and Mie components of laser radiation 147 in terms of optical efficiencies and detector efficiencies. Such efficiencies are typically measured on a shot-by-shot basis during the analysis process. In an exemplary embodiment of operation, laser 141 generates and transmits laser radiation 142 as a series of pulses at a particular pulse repetition frequency (“PRF”), while in other embodiments laser 141 is a continuous wave laser (as discussed in connection with FIG. 2). Computer 156 then measures the Rayleigh and Mie components in terms of optical efficiencies and detector efficiencies on a pulse-by-pulse basis.

[0059] To measure Rayleigh components and Mie components, in one embodiment, OADS 140 tunes the frequency of the laser radiation 142 transmitted by laser 141. For example, laser 141 transmits the laser radiation 142 at distal frequencies from the peak absorption frequency of filter 152 (illustrated by v_f in FIG. 4) to provide a frequency-independent measurement. Computer 156 then determines the line shape of laser radiation 142 through filter 152.

[0060] In one embodiment, measured intensity of the detected backscattered laser radiation (e.g., as determined by electronic signal 158) is functionally compared to normalized atmospheric factors. The measured intensity often depends upon Mie scatterers (e.g., aerosols) and air density changes due to altitude changes and temperature changes. The air density changes and the temperature changes are not, however, removed through the normalization processes described herein. For computer 156 to accurately determine air parameters such as temperature and pressure of air 144, air density changes are removed from the detected backscattered laser radiation so that computer 156 may accurately determine the air parameters.

[0061] FIG. 5 shows graph 240 with curves 241 (detected backscattered laser radiation at a higher air density causing both Rayleigh and Mie scattering), 242 (detected backscattered laser radiation at an air density causing Rayleigh scattering) and 243 (normalized Rayleigh scattering). Curves 241, 242 and 243 illustrate laser radiation magnitudes (plotted with respect to axis 250) as a function of frequency (plotted with respect to axis 251). In one embodiment, computer 156 processes data from curves 241, 242 and 243 to determine other air parameters. For example, Mie scattering effects are substantially isolated and removed from calculations to determine air temperature and air pressure, since these Mie scattering effects produce inaccurate measurements due to inconsistent aerosol concentrations.

[0062] In one embodiment, to determine the air temperature and air pressure, computer 156 processes the data from curves 241, 242 and 243 to substantially isolate and remove the Mie scattering effects, such as those found in curve 241. In processing the data from curves 241, 242 and 243, computer 156 calculates lookup table 170 in substantially real time using a measured laser/filter profile (i.e., as measured at detector 165 of FIG. 2) convolved with theoretical Rayleigh functions for a particular temperature and pressure (e.g., illustrated by curves 242 and 243). Computer 156 then scales the measured return signal LFR(v) (i.e., illustrated by curve 241 in this example) with the ratio of m to r determined by Eq. 20. Computer 156 then analyzes data near the deepest portion of the filter attenuation (i.e., approximately ±0.5 GHz from v_f) to estimate pressure and/or temperature. This portion corresponds to a 60 dB region of absorption that is not contaminated by Mie scattering. Use of this region is a preferred aspect of the calculation technique that provides temperature and pressure accuracy by providing a reliable temperature base from which to increment temperature and/or pressure estimates.

[0063] Computer 156 calculates theoretical Rayleigh return assuming an initial temperature estimate and performs a Least Square Error (LSE) calculation to determine the accuracy of the temperature with respect to the theoretical Rayleigh function. Computer 156 repeats the process with incremental changes to temperature and/or pressure until an optimal fit (i.e., an LSE calculation that corresponds to design specifications) is achieved. Although discussed in detail with respect to LSE, other approximation methods, such as Newton-Raphson and Monte Carlo, may be used in alternative embodiments. Accordingly this disclosure teaches by way of example and not by limitation.

[0064] Temperature affects air density in a manner that is reciprocal to pressure; increasing pressure increases density, while increasing temperature decreases density. Additionally, increasing temperature increases the Rayleigh lineshape width while increasing pressure increases the Rayleigh lineshape height. Accordingly, for each incremental value of temperature and/or pressure, the Rayleigh lineshape is unique. Such scattering theory is discussed in “On The Kinetic Model Description Of Rayleigh-Brillouin Scattering From Molecular Gases”, G. C. Tenti, D. Boley and R. C. Desai, Canadian Journal of Physics, vol. 52, pg. 285-290 (1974).

[0065] In one example, computer 156 determines air density changes by aligning peak absorption frequencies of curves 241, 242 and 243, illustrated at frequency v_f. Since curve 243 represents detected backscattered laser radiation containing substantially no Mie scattering, curve 243 may be used as a reference where Mie scattering has been eliminated. In one example, computer 156, therefore, uses curve 243 to remove the effects of Mie scattering by aligning curves 241, 242 and 243 and by calculating a ratio of the detected backscattered laser radiation to theoretically pure Rayleigh scattering (the ratio of curves 241 and 242) which may be utilized to determine air density. Mie scattering effects are then removed by subtracting curve 243 from the calculated ratio of curves 241 and 242. With Mie scattering essentially removed from the measurement, computer 156 more accurately determines air temperatures and air pressures.

[0066] FIGS. 6 and 7 show other exemplary graphs that may be used in determining air pressure and air temperature. FIG. 6 illustrates a graph 260 of electronic signals 163 and 167 of FIG. 2 respectively generated by detectors 162 and 165 of FIG. 2. Graph 260 shows electronic signals 163 and 167, that represent light intensity as a function of normalized signal strength (axis 261), versus frequency (axis 262). FIG. 7 illustrates a graph 280 of electronic signals 158 and 155 (see FIG. 2) generated by detectors 153 and 154 respectively, representing light intensity as a function of normalized signal strength (axis 281), versus frequency (axis 282). These four light intensities (represented by electronic signals 163, 167, 158 and 155) may be measured, over time, through transmission and collection of light corresponding to laser pulses, or they may be measured through transmission and collection of light corresponding to a continuous wave laser whose frequency varies continuously. In one example, a transmission frequency of laser radiation 142 of FIG. 2 generated by laser 141 at a certain PRF may sweep such that each laser pulse is emitted at a different frequency. Electronic signals 163 and 167 therefore illustrate how laser radiation 142 of laser 141 may sweep in frequency across an absorption band 263 of the vapor filter 152. Illustratively, FIG. 6 shows one complete frequency sweep of laser radiation 142 generated by laser 141 and detected by detectors 162 and 165. Similarly, electronic signals 155 and 158 of FIG. 7 show detected signals of detectors 153 and 154 as laser radiation 142 of laser 141 performs a complete sweep in frequency across absorption band 283 of vapor filter 152.

[0067] From signals 163 and 167, computer 156 may for example determine a normalized filter transmission, by dividing discrete points of electronic signal 167 by corresponding discrete points of signal 163. Similarly, computer 156 may determine a normalized atmospheric return though vapor filter 152 by dividing discrete points of signal 158 by corresponding discrete points of signal 155. These discrete points, described herein, correspond to individual pulses of laser radiation 142.

[0068] Using normalized calculations of filter transmission (e.g., from graph 260) and the normalized calculations of atmospheric return (e.g., from graph 280), computer 156 determines relative optical efficiencies in the vapor filter 152.

[0069] In one embodiment, computer 156 determines optical transmission for vapor filter 152 using the frequency independent components of data from graph 260, FIG. 6 (there is substantially no change in amplitude for signals 163 and 167 at frequencies greater in magnitude than ±18 GHz from 0 GHz illustrated at points 264, 265, 266 and 267). Computer 156 therefore determines a ratio of optical transmission for vapor filter 152 by calculating a ratio of signal 167 to signal 163, via frequency corresponding points of the signals, for points representing frequencies greater in magnitude than ±18 GHz from 0 GHz.

[0070] Similarly, computer 156 determines a magnitude of intensity of atmospheric-returned laser radiation received through vapor filter 152 using the frequency independent parts of the data from graph 280, FIG. 7 (there is substantially no change in amplitude for signals 155 and 158 at frequencies greater in magnitude than ±18 GHz from 0 GHz illustrated at points 284, 285, 286 and 287). Computer 156 thereby determines a ratio of atmospheric return with the laser power measurement by calculating a ratio of signal 158 to signal 155 via frequency corresponding points of the signals for points representing the frequencies greater in magnitude than ±18 GHz from 0 GHz.

[0071] In one embodiment, computer 156 calculates a ratio of signal 158 to signal 155 for frequencies between ±0.5 GHz (illustrated at points 288 and 289). Such a frequency range includes substantially no Mie scattering of laser radiation 142 for air 144; it thus corresponds to substantially pure Rayleigh scattering. Computer 156 thus compares a Rayleigh to Mie scattering strength based upon the ratio of signal 158 to signal 155. Computer 156 determines Rayleigh to Mie scattering strength by comparing a ratio of signal 158 to signal 155 at frequencies between ±0.5 GHz to the ratio of signal 158 to signal 155 at frequencies greater than ±18 GHz from 0 GHz. In one embodiment, computer 156 performs similar calculations for “non-scattered” laser radiation 142 (e.g., component 143B of FIG. 2) based on data illustrated in FIG. 6 using points 268 and 269. Such a process is further described in FIG. 8.

[0072] Ratios determined for the non-scattered laser radiation 142 and for the scattered laser radiation 142 may be used in tandem to numerically calculate Laser-Rayleigh-Filter convolution (e.g., LRF(v)) from data. The Laser-Rayleigh-Filter convolution is in turn compared to a look up table of theoretical Laser-Rayleigh-Filter convolution values to determine temperature and pressure.

[0073] FIG. 8 shows a flowchart of one exemplary methodical operation 400 of an OADS. Method 400 may be partially or fully performed by computer 156 of OADS 140; computer 156 may receive operating instructions from software and/or firmware. A laser (e.g., laser 141 of FIG. 2) sweeps laser radiation across a predetermined frequency spectrum, in step 401. The laser may sweep the laser radiation across a frequency range of about ±20 GHz by transmitting laser radiation at a certain PRF (or it may sweep frequency continuously, as discussed in connection with FIG. 2 above). In one embodiment, the PRF is about 1 kHz, with a pulse width between about 50 ns and 100 ns, and a swept frequency range is centered about a frequency corresponding to a peak absorption frequency (e.g., 260 nm) of a filter (e.g., vapor filter 152, FIG. 2).

[0074] Laser radiation is typically split into four distinct paths such that the laser radiation may be detected as four different inputs, in step 402. These four paths of laser radiation correspond to: 1) laser radiation transmitted by the laser (e.g., component 159 of FIG. 2); 2) laser radiation transmitted by the laser through the filter (e.g., component 164 of FIG. 2); 3) laser radiation transmitted by the laser into the air and backscattered (e.g., component 150A of FIG. 2); and 4) laser radiation transmitted by the laser into the air and backscattered through the filter (e.g., component 157 of FIG. 2). For simplicity, these components are hereinafter referred to as: 1) unfiltered laser radiation; 2) filtered laser radiation; 3) unfiltered backscattered laser radiation or unfiltered scattered laser radiation; and 4) filtered backscattered laser radiation or filtered scattered laser radiation.

[0075] After detecting the four components of laser radiation, a computer (e.g., computer 156, FIG. 2), determines normalized filter transmission of the vapor filter, in step 403. For example, the computer, in one embodiment, processes the unfiltered laser radiation and filtered laser radiation by dividing the magnitude of the filtered laser radiation by the magnitude of the unfiltered laser radiation. In one embodiment, the division is performed on a pulse by pulse basis, where divided magnitudes of the pulses have corresponding frequencies.

[0076] The computer also determines, in one embodiment, a normalized atmospheric return of the laser radiation, in step 404. For example, the computer may process the filtered backscattered laser radiation and unfiltered backscattered laser radiation by dividing the magnitude of the filtered backscattered laser radiation by the magnitude of the unfiltered backscattered laser radiation. Again, in one embodiment, division is performed on a pulse by pulse basis, where divided magnitudes of the pulses have corresponding frequencies.

[0077] Once normalized filter transmission and normalized atmospheric return of the laser radiation are determined, the computer determines signal strengths for each of the filter transmission and the atmospheric return. For example, the computer determines the optical transmission through the filter by calculating a ratio of the filtered laser radiation to the unfiltered laser radiation at particular frequency ranges, in steps 405 and 407. The computer similarly determines the atmospheric return (scattering) signal strength through the filter by calculating a ratio of the filtered backscattered laser radiation to the unfiltered laser radiation at particular frequency ranges, in steps 406 and 408.

[0078] The computer also determines a signal strength ratio for the normalized filter transmission by dividing filtered laser radiation by unfiltered laser radiation, again on a pulse by pulse basis, at frequencies greater in magnitude than about ±18 GHz about the peak absorption frequency, in step 407. The computer further determines a signal strength ratio for the normalized filter transmission by dividing filtered laser radiation by unfiltered laser radiation on a pulse by pulse basis at frequencies between about ±0.5 GHz, in step 405. These signal strength determinations correspond to frequency ranges where Mie scattering (e.g., ±18 GHz) and Rayleigh scattering (e.g., ±0.5 GHz) are most prevalent, and are thus useful when combined with similar signal strength determinations for the normalized atmospheric return. The computer determines a Mie scattering signal strength ratio for the normalized atmospheric return of the laser radiation by dividing filtered backscattered laser radiation by unfiltered backscattered laser radiation, again on a pulse by pulse basis, at frequencies greater in magnitude than about ±18 GHz about the peak absorption frequency, in step 408. The computer also determines a Rayleigh scattering signal strength ratio for the normalized atmospheric return of the laser radiation by dividing filtered scattered laser radiation by unfiltered backscattered laser radiation on a pulse by pulse basis at frequencies between about ±0.5 GHz in step 406.

[0079] With signal optical transmission for the filter and signal strengths for both Rayleigh scattering and Mie scattering determined, the computer determines a Rayleigh laser filter convolution in step 409. For example, the computer, in one embodiment, performs a convolution of the optical transmission with the Rayleigh and Mie scattering signal strengths corresponding to the frequency ranges for Rayleigh and Mie scattering of ±0.5 GHz and ±18 GHz, respectively. The computer then accesses a lookup table, such as lookup table 170 of FIG. 2, that has theoretical Rayleigh laser filter convolution values to determine temperature and pressure of the air, in step 410.

[0080] It is also possible to calculate a convolution of a measured filter function with a theoretical Rayleigh-Brillouin return (Rayleigh line shape), and directly compare the convolution with filtered scattered laser radiation. This allows calculation of atmospheric parameters without calculating a deconvolution of the Rayleigh-Brillouin signal, reducing the complexity of real-time calculations required to determine the atmospheric parameters. In particular, ratios of measured signals may be compared directly to theoretical ratios of a Rayleigh line shape convolved with measured filter functions to allow self calibrating measurements. For example, signal strength variations across data gathering channels and power of scattered laser radiation may be inherently normalized when such ratios are used. Certain ratios of measured data at laser frequencies that lie within filtered bands of band-stop filters (e.g., absorption features of an atomic vapor cell, or equivalent features of other filters, as discussed above) may be useful for determining temperature and pressure, since Mie scattering is eliminated from the measured data. Calculation of convolutions may represent a lower computational burden on a computer (e.g., computer 156 of OADS 140) as compared to calculating deconvolutions of measured data into and out of a Rayleigh-Brillouin representation.

[0081] For example, filtered scattered laser radiation data in a signal channel may characterized by the equation:
S_S(v)=P_LT_LT_RE_SD_S∫∫dv₁dv_rL(v_laser)F(v₁−v)(rR(v−(v_r−Δv_D))+mM(v−(v_r−Δv_D)))   (Eq. 24)
where parameters are as previously defined, and a subscript 1 indicates a measurement frequency 1. Eq. 24 may be simplified by using the notation LFR(v) for the convolution of laser, filter function and Rayleigh return, as defined above, and a similar notation LFM(v) for a convolution of laser, filter function, and Mie scattering return:
S_S(v₁)=P_L1T_L1T_R1E_S1D_S1[rLFR(v₁+mLFM(v₁)]  (Eq. 25)

[0082] If frequency I is located in a filter absorption band, the Mie scattering term is effectively eliminated, yielding:
S_S(v₁)=P_L1T_L1T_R1E_S1D_S1rLFR(v₁)  (Eq. 26)

[0083] Forming a ratio of a signal obtained at frequency 1 with a signal obtained at another frequency 2 in another filter absorption band yields: $\begin{array}{cc}\frac{S_S\left(v_1\right)}{S_N\left(v_2\right)}=\left[\frac{P_{\mathrm{La}}{L}_{\mathrm{La}}{T}_{\mathrm{Ra}}{E}_{\mathrm{Sa}}{D}_{\mathrm{Sa}}}{P_{\mathrm{Lb}}{L}_{\mathrm{Lb}}{T}_{\mathrm{Rb}}{E}_{\mathrm{Sb}}{D}_{\mathrm{Sb}}}\right]\left[\frac{r_a\left(r_b+m_b\right)}{r_b\left(r_a+m_a\right)}\right]\left[\frac{\mathrm{LFR}\left(v_1\right)}{\mathrm{LFR}\left(v_2\right)}\right]& \left(\mathrm{Eq}.27\right)\end{array}$

[0084] where frequency 1 is measured at time a and frequency 2 is measured at time b. If times a and b are close enough to each other that no atmospheric changes occur between time a and time b (or if measurements are interspersed in such a way that average values of parameters such as P, L, T, E, D and r are identical over a time span of the measurements) then the ratio of Eq. 27 simplifies further to: $\begin{array}{cc}\frac{S_S\left(v_1\right)}{S_N\left(v_2\right)}=\frac{\mathrm{LFR}\left(v_1\right)}{\mathrm{LFR}\left(v_2\right)}& \left(\mathrm{Eq}.28\right)\end{array}$

[0085] In one embodiment, a lookup table stores temperature and pressure pairs that correspond with two of the measurement ratios defined in Eq. 28. The two ratios essentially define two equations with two unknowns (i.e., a single such ratio may not determine both pressure and temperature). Data may also be taken in more than three filtered bands, yielding more than two of the Eq. 28 ratios; when more than two such ratios are available, multiple values of temperature and pressure may be determined that may be averaged or used in “best fit” methods to improve temperature and pressure determination in a noisy measurement environment.

[0086] In an embodiment, theoretical Rayleigh line shapes corresponding to temperature and pressure combinations are stored in a lookup table. A reference curve is calculated by obtaining a Rayleigh line shape corresponding to an estimated temperature and pressure from the lookup table and convolving the Rayleigh line shape with a normalized atmospheric return curve. Values of LFR(v) at absorption feature maxima may then be determined from the reference curve and used to determine one or more air parameters (e.g. temperature and/or pressure) using Eq. 28.

[0087] Calculating convolution of the measured filter function with the theoretical Rayleigh line shape also enables utilization of curve fitting routines to map the convolved curves to true temperature and pressure conditions, such that the deconvolution calculations suggested by the Tenti, Boley and Desai paper above are not required. An OADS may store a pre-compiled table of stored curve shapes that are generated by modeling large databases of known temperature and pressure values (e.g., the table may be stored in computer 156 of OADS 140). As measurements are taken, data curves may be generated from measured data, and curve-fitting routines may be used to compare the data curves to the stored curve shapes to derive true temperature and pressure. The utilization of curve-fitting routines may also have less sensitivity to noisy data, as compared to deconvolution calculations, making the determination of true temperature and pressure more robust.

[0088] FIG. 9 is a flowchart showing one exemplary method of operation 450 of an OADS, which may be used to calculate one or more air parameters. Method 450 may be partially or fully performed by computer 156 of OADS 140; computer 156 may receive operating instructions from software and/or firmware.

[0089] In an embodiment of step 460, a laser (e.g., laser 141 of FIG. 2) sweeps laser radiation across a predetermined frequency range (swept frequency range) that is centered about a deep absorption line of a filter. The laser may sweep the laser radiation across a swept frequency range of about ±20 GHz by transmitting the laser radiation at a certain PRF, or by sweeping the frequency of a continuous wave laser. In one embodiment, a PRF is about 1 kHz, with a pulse width between about 50 ns and 100 ns, and the swept frequency range is centered about a frequency corresponding to a peak absorption frequency (e.g., 260 nm) of a filter (e.g., vapor filter 152, FIG. 2, or an interference filter, a fiber Bragg grating filter, a dichroic filter or a Rugate filter). In an embodiment, the swept frequency range includes frequencies corresponding to at least two absorption features of at least one band stop filter. In another embodiment, the swept frequency range includes frequencies corresponding to at least three absorption features of at least one band stop filter.

[0090] Step 462 detects laser radiation corresponding to filtered scattered laser radiation (e.g. component 157 of FIG. 2), filtered laser radiation (e.g. component 164 of FIG. 2), and unfiltered laser radiation (e.g. component 159 of FIG. 2) at each frequency; each step 460 and 462 is for example performed for each laser pulse in the swept frequency range.

[0091] Step 464 determines a normalized filter transmission curve by dividing a magnitude of filtered laser radiation by a magnitude of unfiltered laser radiation for each pulse in the swept frequency range; step 466 determines a normalized atmospheric return curve by dividing a magnitude of filtered scattered laser radiation by a magnitude of unfiltered laser radiation for each pulse in the swept frequency range. It will be appreciated that since the data required for the calculations in steps 464 and 466 are collected by the operation of steps 460 and 462, steps 464 and 466 may be done in any order or in parallel.

[0092] Step 468 calculates a Doppler shift Δv_D that is a frequency shift between the normalized filter transmission curve (calculated in step 464) and the normalized atmospheric return curve (calculated in step 466), then calculates a local radial wind velocity v_R using Eq. 1 above. As was stated above, a band stop filter may have a plurality of absorption features; consequently, a plurality of Doppler shift Δv_D and radial wind velocity v_R calculations may be calculated in step 468.

[0093] Step 470 utilizes only normalized atmospheric return curve magnitude values (calculated in step 466) within three or more specific filter absorption bands to form two or more normalized atmospheric return ratios (actual ratios). For example, if atmospheric return data is derived for frequencies 1, 2, and 3 (at times that are close enough together, as discussed with reference to Eq. 28 above), then two ratios may be formed using one of the frequencies as a baseline (denominator), such as $\frac{S_S\left(v_1\right)}{S_S\left(v_2\right)}\mathrm{and}\frac{S_S\left(v_3\right)}{S_S\left(v_2\right)}.$
Atmospheric return curve magnitude values corresponding to absorption feature maxima of one or more band stop filters may be used. One atmospheric return ratio (actual ratio) may be determined if for example only one air parameter (e.g. pressure or temperature) is to be calculated.

[0094] Step 472 obtains theoretical temperature and pressure data from a lookup table of normalized filter transmission convolved with theoretically derived Rayleigh line shapes, at the frequencies utilized in step 470. One or more air parameters (e.g. temperature and/or pressure) are then estimated. A Rayleigh line shape corresponding to the estimated one or more air parameters is for example obtained from a lookup table. A reference curve is then calculated by convolving the Rayleigh line shape with the normalized filter transmission curve from step 464.

[0095] In step 474, ratios corresponding to the ratios formed in step 470 are formed from magnitude values of the reference curve calculated in step 472. The ratios formed in step 474 may be referred to as reference ratios.

[0096] In step 476, one or more air parameters (e.g. temperature and pressure) are determined. An error corresponding to the differences between the one or more actual ratios and the corresponding one or more reference ratios may be calculated: if the error is within an acceptable range, the estimated one or more air parameters (corresponding to the Rayleigh line shape) are published as the actual one or more air parameters; but if the error is not within an acceptable range, steps 472, 474, and 476 are repeated with one or more different estimated air parameters until the error is within an acceptable range.

[0097] The error of step 476 may be calculated using a least mean square error algorithm. Steps 470, 474, and 476 may be optional; the normalized atmospheric return curve calculated in step 466 is for example correlated to the reference curve calculated in step 472 using curve fitting routines.

[0098] Certain advantages of embodiments described above may include:

[0099] (1) Obtaining accurate computations of various air parameters, such as air speed, air temperature and air pressure, substantially regardless of altitude and/or Mie scattering;

[0100] (2) Obtaining a system that accurately performs in a variety of vibrational environments;

[0101] (3) Obtaining an ability to determine temperature and pressure within a particular region of atmosphere without a prior knowledge of the atmosphere;

[0102] (4) Reducing need for on-aircraft system calibrations and system health checks, as compared to existing systems;

[0103] (5) Providing robustness with respect to high vibration environments;

[0104] (6) Obtaining faster calculations and/or reduced computational requirements placed on aircraft computers, as compared to existing systems;

[0105] (7) Ability to accurately calculate velocity in environments with changing temperature and/or pressure; and/or

[0106] (8) Ability to accurately calculate one or more air parameters (e.g. velocity, temperature, and/or pressure) without precise control of laser frequency.

[0107] Since certain changes may be made in the above methods and systems without departing from the scope of the disclosure herein, it is intended that all matter contained in the above description or shown in the accompanying drawings be interpreted as illustrative and not in a limiting sense. By way of example, those skilled in the art should appreciate that the OADS and the OADS transceivers, as described herein, may be constructed, connected, arranged, and/or combined in ways that are equivalent to what is shown.