Atmospheric characterization systems and methods

[0001] This application claims priority to U.S. Provisional Patent Application Ser. No. 62/515,299 entitled Atmospheric Characterization Systems and Methods and filed on Jun. 5, 2017, which is incorporated herein by reference.

[0002] As engineers and scientists work to refine free-space optical systems that operate over long terrestrial ranges, it is helpful to better understand, characterize, and quantify the atmospheric properties of the environment. One such atmospheric property of interest is the refractive-index structure coefficient, or Cn², which describes small changes in the base atmospheric refractive index. Over very short distances, small index of refraction changes usually cause negligible problems to all but the most demanding optical systems, such as interferometric systems, but can have a large effect on Optical Path Length (OPL) as short as 1 km.

[0003] At the lowest level of understanding, index of refraction fluctuations in the atmosphere originate with turbulent air motion. The source of atmospheric turbulence originates from temperature gradients on the surface of the earth as solar radiation and daily weather patterns cause a heating and cooling cycle. The large-scale temperature gradient from the surface of the earth to upper atmosphere that is both easily measured and causes atmospheric turbulence also applies to very small temperature gradients that are not separated by such vast distances. These small temperature gradients are considered randomly distributed throughout a larger temperature gradient. The index of refraction of air is sensitive to fluctuations in temperature yielding a randomly distributed index of refraction for air through a slant or horizontal path of small temperature gradients, setting the groundwork for understanding the differential temperature impact on the refractive-index structure coefficient.

[0004] Systems like large terrestrial telescopes, free-space laser communication systems and High Energy Laser (HEL) free space systems require a stable index of refraction for optimum operation. It is understood that Cn² is the most disruptive close to ground level so large telescope construction projects take the ground level atmospheric properties into consideration and are consequently built in locations with higher altitude or, at a minimum, on the highest floor of university buildings away from ground atmospheric turbulence. Mobile HEL systems rarely have the luxury of selecting an ideal operating environment and therefore must either be designed to operate with poor optical atmospheric properties or the environmental impact on performance must be understood and estimable.

[0005] The measurement of the refractive-index structure coefficient, Cn², has been used for several specific purposes related to HEL testing. Recent test events have utilized Cn² measurement at various locations for comparison to historic models such as the Hufnagel-Valley 5/7 model, to help understand performance of HEL in relation to atmospheric turbulence, and to offer comparison of equipment used to collect Cn². While not specifically related to HEL testing, designers investigating adaptive optics systems that are being developed for imaging in high turbulence also understand the atmospheric turbulence parameters they are operating in.

[0006] Collection of measured Cn² data compared to historic models such as Hufnagel-Valley 5/7 model, High Energy Laser End-to-End Operational Simulation (HELEEOS), and the Tunic Model is of interest to understand which models closely predict Cn² per environment and altitude. As more precise models are developed and compared to existing models, the quantifying for accuracy will continue to measure Cn² at a test site.

[0007] HEL field tests are heavily instrumented with a vast array of high speed cameras, beam monitoring and evaluation systems, meteorological data collection systems, and atmospheric scintillation measurement devices. One such atmospheric propagation effects on a HEL system include transmission losses, turbulence, and thermal blooming. The measurements from all these devices are critical to understanding the performance of the HEL under test, with a focus on the measurement of Cn².

[0008] Standalone adaptive optics systems suffer from similar environmental performance factors as HEL systems except for thermal blooming. Adaptive optics systems under test will have a similar set of instrumentation as HEL tests to include devices that measure atmospheric turbulence. The amount of atmospheric turbulence that is induced by environments is also of interest during the adaptive optics design process. With the goal of the adaptive optics system to correct the outgoing wavefront and compensate for atmosphere induced optical aberrations, the amount of atmospheric turbulence will drive the depth of control required for the adaptive optics system. When using a deformable mirror to correct the wavefront, the amount of peak to valley travel available limits the amount of turbulence that can be corrected. Measurements of the refractive-index structure coefficient, Cn², in real environments can help engineers estimate maximum wavefront error and select adaptive optics with sufficient range of motion to control the turbulence.

[0009] Known measurement methods of atmospheric turbulence data includes

[0010] Scintillation Detection and Ranging (SCIDAR)—imaging the shadow patterns in the scintillation of starlight.

[0011] Low Layer Scidar (LOLAS)—small aperture version of SCIDAR designed for low altitude profiling

[0012] Slope Detection and Ranging (SLODAR)—operated by detecting the backscatter from atmospheric conditions.

[0013] Multi-Aperture Scintillation Sensor (MASS)—optical sensor that creates two images of a single target on a focal plane array to estimate atmospheric scintillation.

[0014] Moon Scintillometer (MooSci)—uses multiple photoelectric diodes at various distances to monitor minor changes in light reflected from the Moon.

[0015] Radio Detection and Ranging (RADAR)—RAdio Detection and Ranging mapping of atmospheric turbulence.

[0016] Differential Image Motion Monitor (DIMM)—optical sensor that creates two images of a single target on a focal plane array and uses statistical area of interest tracking to estimate atmospheric scintillation.

[0017] Atmospheric Characterization System (ACS—Shack-Hartmann Wavefront Sensor)—optical system that measures changes in wavefront from a source beacon.

[0018] Scintillometer (Popular name brands are Scintec and Kipp & Zonen)—commercially available scintillation measurement device.

[0019] Balloon-Borne Thermometers—temperature sensing devices that estimate atmospheric characteristics.

[0020] Many atmospheric turbulence profiling systems sampled are optical systems that image a beacon or target from known distance and then compute an estimate of atmospheric turbulence based on the sensor data. All the listed atmospheric turbulence profiling systems, except the Balloon-Borne Thermometers, measure an integrated path of turbulence and not turbulence at a nodal location. Additionally, several of the atmospheric profiling systems are path weighted and require further analysis.

[0021] Advantages of optical atmospheric profilers for measuring Cn² when testing with HEL or adaptive optics systems are that the systems are accepted by the test community as the metric of turbulence measurements. Atmospheric characterization systems measuring the same optical path as a HEL device under test essentially use the same mechanism as an imaging sensor for an adaptive optics system but without any correction for atmospheric effects. Many optical profilers have graduated from university use and become commercial products, which implies data integrity, system stability, and system reliability. These systems can also profile vast horizontal and vertical distances without the need for using multiple characterization devices.

[0022] Disadvantages to measuring Cn² with an optical system share some of their strengths. The downside to measuring an integrated optical turbulence path is that the path is averaged and weighted. Turbulence induced by micro-meteorology over various terrain is essentially path averaged and the instruments do not have the ability to specifically determine the turbulence-generating at any a single point along the optical path. Optical atmospheric turbulence characterization devices are also designed for a minimum and maximum path which they can measure, 250 m-6000 m. (BLS900, 2017). Many optical atmospheric turbulence characterization devices also require a beacon, or light source, to image down range. The addition of a down range component implies two devices, two power sources, and some amount of alignment and setup prior to taking a Cn² measurement. Finally, the majority of Cn² measurement devices are expensive initial investments, and in some cases, cost prohibitive to own and operate.

[0023] The present disclosure is of an atmospheric characterization system that has a central processing board that has a first and a second communication interface. Further, the atmospheric characterization system further has a first precision temperature sensor that is communicatively coupled to the central processing board via the first communication interface and positioned a distance from a first side of the processing board, wherein the precision temperature measures a first temperature and transfers data indicative of the first temperature to the central processing board. In addition, the atmospheric characterization system has a second precision temperature sensor that is communicatively coupled to the central processing board via the second communication interface and positioned the distance from a second opposing side of the processing board such that the first precision temperature sensor and the second precision temperature sensor are equidistance from the processing board and a distance between the first precision sensor and the second precision sensor is a predetermined distance, r, and the second precision temperature sensor measures a second temperature and transfers data indicative of the second temperature to the central processing board simultaneously with the transferring of the first temperature. Additionally, the atmospheric characterization system has a processor that receives the first temperature and the second temperature and calculates a value indicative of atmospheric turbulence based upon the first temperature and the second temperature, wherein the value indicative of the atmospheric turbulence is used for designing, modifying, calibrating, or correcting an optical system.

[0024] Further, the present disclosure describes an atmospheric characterization method that comprises the steps of: (1) measuring a first temperature via a precision temperature sensor communicatively coupled to a central processing board and positioned a distance from a first side of the processing board; (2) measuring a second temperature via a second precision temperature sensor communicatively coupled to the central processing board and positioned the distance from a second opposing side of the processing board such that the first precision temperature sensor and the second precision temperature sensor are equidistance from the central processing board, and the distance between the first precision sensor and the second precision temperature sensor is a predetermined distance, r; (3) transferring data indicative of the first temperature and the second temperature sensor to the central processing board simultaneously; (4) receiving, by a processor, the first temperature and the second temperature; (5) calculating a value indicative of atmospheric turbulence based upon the first temperature, the second temperature, and the distance, r, and (6) designing, modifying, calibrating, or correcting an optical system based upon the value indicative of the atmospheric turbulence.

[0041] The present disclosure is an atmospheric characterization system that measures atmospheric turbulence over a period of time, which can them be used to design, modify, or calibrate optical systems to result in more accuracy of the optical system. The atmospheric characterization system comprises a central processing board. Additionally, the atmospheric characterization system comprises a first temperature sensor communicatively coupled to one side of the processing board a distance d₁ from the processing board. Further, the atmospheric characterization system comprises a second temperature sensor communicatively coupled to an opposing side of the processing board the same distance d₁ from the processing board. In operation, the differential temperature of the first and second sensor is used to calculate atmospheric turbulence at a particular time and location. This data may then be used to design, modify, or calibrate an optical system so that the optical system is more accurate.

[0042] Thus, the measurement approach used for present disclosure is a differential temperature sensor (DTS) system with high resolution, low cost, digital temperature sensors that can measure the refractive-index structure coefficient, Cn², of turbulent air. In one embodiment, a custom integrated set of digital temperature sensors are used for the data collection with a key aspect of sensor selection that there must be a very small temperature resolution.

[0043] The technological improvement of using the constructed DTS system are that the sensors measure a ‘nodal’ location and not the typical integrated path of an optical atmospheric characterization device. The atmospheric turbulence is only measured where the sensor is located. The ‘nodal’ nature of the DTS sensors implies that there is not a minimum measurement path, system path averaging, or additional hardware to set up and align. Multiple DTS systems can be combined to measure an atmospheric turbulence ‘area’ that is not possible to measure with optical devices. The concept of the final DTS system is a low cost, low power consumption, extremely portable and accurate device.

[0044] To better understand the present disclosure, this disclosure begins with a description of the Refractive-Index Structure Coefficient, Cn2, and presents how it is employed to describe the turbulence in the atmosphere. This includes its dependence on, most importantly, local and small temperature gradients. This is followed by the system level definition of the component requirements for the atmospheric characterization system of the present disclosure.

[0045] For the purposes of the present disclosure, it is assumed that most of atmospheric turbulence is driven by temperature changes in the environment with a local background mean pressure and temperature. Other experiments have considered the effects of humidity fluctuations, wind speed, wind direction, and solar loading as additional sources of atmospheric turbulence. The source of these changes comes from the intensity of the vertical convection transfer of heat, moisture, and momentum during the day that is determined from the surface heat flux and thermal structure of the entire mixed turbulent layer.

[0046] The exchange of heat flux which leads to turbulence can be seen in FIG. 1, which shows how heat flux transitions through the lower atmosphere. On the left (a) of FIG. 1 is a vertical profile of the mean potential temperature within and above a forest canopy during the daylight hours. There is a stable layer within the forest canopy that extends to an unstable layer and then transitions to a near-neutral layer. Air above the near-neutral layer becomes stable and has minimal turbulence. The vertical dashed lines show the deep movement of air parcels within the boundary layer.

[0047] The right side (b) of FIG. 1 describes the heat flux that is observed under conditions of panel (a). Heavy vertical arrows indicate the directions and magnitude of vertical fluxes of heat. From FIG. 1 panel (b) larger magnitudes of heat flux correlate to turbulent and unstable air. Assuming a local-closure approximation for the vertical heat flux a direction and magnitude of the flux is defined by the vertical gradient of the potential temperature. This can be described mathematically where θ is potential temperature, w is the vertical component of wind, K_H is the thermal diffusivity of a substrate, and z is the vertical space coordinate (altitude), which is described in the following equation:

[0048] $\begin{array}{cc}\stackrel{\_}{\stackrel{.}{\theta }\stackrel{.}{w}}=-K_H\frac{\partial }{\partial z}\stackrel{\_}{\theta }& \mathrm{Equation}1\end{array}$

[0049] Because the physical source of the index of refraction variations is derived from the temperature gradient in turbulent air motion, the index of refraction can be modeled as the sum of the mean index of refraction, n₀, and the randomly fluctuating term, n₁({right arrow over (r)},t):
n({right arrow over (r)},t)=n₀+n₁({right arrow over (r)},t)  Equation 2

[0050] where {right arrow over (r)} is a three-dimensional position vector, and t is time. These small fluctuating index of refraction terms are inconsequential for short distances but can alter a beam wavefront, Optical Path Length (OPD), or position at longer distances.

[0051] To understand the impact of n₁({right arrow over (r)},t) on an optical system, a simple geometrical optics model is used that utilize Snell's Law,
n₁ sin(θ₁)=n₂ sin(θ₂)  Equation 3

[0052] where n₁ is the first material index of refraction, θ₁ is the angle the ray strikes the interface of the two materials, n₂ is the second material index of refraction, and θ₂ is the angle the ray leaves the interface of the second material. This is illustrated in FIG. 2.

[0053] Expanding Snell's Law from two materials to 5-10 over distances of 100 meters starts to create notable differences in ray height from where the ray would land without a change in index of refraction. FIG. 3 illustrates the basic concept of how a ray will bend as it transitions from material to material over a distance. FIG. 3 depicts ray tracing through isotropic volumes of different refractive index compared to homogeneous volumes of similar refractive index.

[0054] Note that calculations to understand the real impact changes in index of refraction cause over a 100-meter path at various angles using rearranged terms in Snell's law and basic geometry may be performed. If the change of index of refraction were constant, then the traced rays would still arrive at their target. If the change of index of refraction is varying in time, then the arrival angle and arrival height changes from moment to moment. This causes blur and distortion of the image or beam shape.

[0055] For analysis a modified Snell's Law, Equation 4 calculates the angle when moving from one volume index of refraction to the next. The thickness of the refractive index volumes was then used to calculate the height of where the ray would strike the next volume of refractive index. Equation 5, which is derived from finding the height of a right-angle triangle, is used to solve the height value.

[0056] $\begin{array}{cc}{\sin }^{-1}\left(\frac{n_1\sin \left({\theta }_1\right)}{n_2}\right)={\theta }_2& \mathrm{Equation}4\\ b\left(\tan {\theta }_2\right)=a& \mathrm{Equation}5\end{array}$

[0057] Basic calculations are shown in Tables 1A and 1B and then illustrated in FIG. 5. The tables were calculated by following a ray that is starting at distance 0 and then evaluated every 5 meters, b, up to 100 meters. The starting incident angle, θ₁, was set to 60 degrees. The change in height, a, per 5 meters, b, was calculated by using Equation 4 to yield θ₂ and then by using the right-hand triangle relationship from Equation 5. A standard index of refraction was assumed, 1.00029, and a refractive index structure coefficient term, Cn², was added for each 5-meter-thick volume of atmosphere.

[0058] To calculate the change in height caused by flowing through many volumes of atmosphere with different indexes of refraction a homogeneous volume of atmosphere was also calculated, the Control Height. The Control Height assumes that there is no change in index of refraction across the 100-meter path and uses the same starting angle of 60 degrees. The difference between the homogeneous volume of atmosphere and the volumes of air with varying indexes of refraction (IoR) was then calculated as the Height Delta.

[0059] Tables 1A and 1B outline these calculations for the 60-degree propagation case. The difference in height over 100 meters was calculated at 0.001525 meters or 0.1525 cm.

[0060]

TABLE 1A
Height Delta from IoR Change
Distance	Incident Angle	Incident Angle		Air
(m)	(Degrees)	(Radians)	Height	(IoR)
0	60	1.047197551	0	1.00029
5	59.99996158	1.047196881	8.660241	1.00029
10	59.99995773	1.047196814	17.32048	1.00029
15	59.99991931	1.047196143	25.98071	1.00029
20	59.99991547	1.047196076	34.64093	1.00029
25	59.99987704	1.047195405	43.30114	1.00029
30	59.9998732	1.047195338	51.96135	1.00029
35	59.99986936	1.047195271	60.62156	1.00029
40	59.99983093	1.0471946	69.28175	1.00029
45	59.99982709	1.047194533	77.94195	1.00029
50	59.99978867	1.047193863	86.60213	1.00029
55	59.99978483	1.047193796	95.26231	1.00029
60	59.9997464	1.047193125	103.9225	1.00029
65	59.99974256	1.047193058	112.5826	1.00029
70	59.99970414	1.047192387	121.2428	1.00029
75	59.99970029	1.04719232	129.9029	1.00029
80	59.99966187	1.04719165	138.5631	1.00029
85	59.99965803	1.047191583	147.2232	1.00029
90	59.99961961	1.047190912	155.8833	1.00029
95	59.99961576	1.047190845	164.5434	1.00029
100	59.99957734	1.047190174	173.2036	1.00029

[0061]

TABLE 1B
Height Delta from IoR Change
Distance (m)	Cn2	IoR Change	Resulting IoR	Control Height	Height Delta
0	1.50E−13	3.87298E−07	1.000290387	0	0
5	1.50E−15	3.87298E−08	1.000290039	8.660254038	1.34E−05
10	1.50E−13	3.87298E−07	1.000290387	17.32050808	2.82E−05
15	1.50E−15	3.87298E−08	1.000290039	25.98076211	5.63E−05
20	1.50E−13	3.87298E−07	1.000290387	34.64101615	8.58E−05
25	1.50E−15	3.87298E−08	1.000290039	43.30127019	0.000129
30	1.50E−15	3.87298E−08	1.000290039	51.96152423	0.000173
35	1.50E−13	3.87298E−07	1.000290387	60.62177826	0.000219
40	1.50E−15	3.87298E−08	1.000290039	69.2820323	0.000273
45	1.50E−13	3.87298E−07	1.000290387	77.94228634	0.000338
50	1.50E−15	3.87298E−08	1.000290039	86.60254038	0.000412
55	1.50E−13	3.87298E−07	1.000290387	95.26279442	0.000487
60	1.50E−15	3.87298E−08	1.000290039	103.9230485	0.000575
65	1.50E−13	3.87298E−07	1.000290387	112.5833025	0.000665
70	1.50E−15	3.87298E−08	1.000290039	121.2435565	0.000769
75	1.50E−13	3.87298E−07	1.000290387	129.9038106	0.000873
80	1.50E−15	3.87298E−08	1.000290039	138.5640646	0.000991
85	1.50E−13	3.87298E−07	1.000290387	147.2243186	0.001111
90	1.50E−15	3.87298E−08	1.000290039	155.8845727	0.001243
95	1.50E−13	3.87298E−07	1.000290387	164.5448267	0.001377
100	1.50E−15	3.87298E−08	1.000290039	173.2050808	0.001525

[0062] Another way to visualize the effect of Cn² on an optical system is to calculate the Optical Path Difference (OPD) for a base refractive index compared to the base refractive index impacted by Cn². OPD is calculated from knowing a base Optical Path Length (OPL=n₁l) and then a modified OPL that uses different refractive indices. OPD is shown in Equation 6.
OPD=|n₁l−n₂l|  Equation 6

[0063] A modified OPD equation can be generated by replacing n₂ in Equation 6 with a base index of refraction combined with the square root of the refractive index structure coefficient, Cn².
OPD=|n₁l−(n₁+√{square root over (Cn²)})l|  Equation 7
where n₁ is the base refractive index, l is the propagation path length, and Cn² is the refractive index structure coefficient. Units of OPD will be in the same units used for the base length under evaluation.

[0064] The implication with an OPD calculation is not that the light will bend but that the wavefront will become distorted and aberrated as it propagates through turbulent air. The resulting wavefront will create an image that is blurred. The effect of OPD on the phase of the light can be calculated by dividing the OPD by a desired wavelength as seen in Equation 8.
Phase Shift=OPD/λ  Equation 8

[0065] Equation 8 may be used to make calculations for a wavelength of interest, 1064 nm, at various distances and Cn² values. FIG. 6 illustrates the maximum phase shift per distance when compared to a base index of refraction (1.00029) and an index of refraction value that as the maximum Cn² disturbance within it (1.00029+√{square root over (Cn²)}). It is noted that for calculations in FIG. 6 and Table 2 a constant Cn² was used for the calculations.

[0066] Table 2 shows the calculations displayed in FIG. 6 resulting from an index of refraction change because of distance. In the worst case of atmospheric turbulence that was used for analysis, 1.5 e⁻¹³ m^−2/3, at the farthest point, 10,000 m, it is possible to see a phase shift of over 3,500 waves.

[0067]

TABLE 2
OPD/λ Calculations for Cn2 E−13
OPD/λ Calculations for Cn2 E−13
Distance (m)	Air (IoR)	Cn2 E−13	IoR Change	Resulting IoR	OPL	OPL Cn2	OPD	OPD/λ
0	1.00029	1.50E−13	3.87298E−07	1.000290387	0	0	0	0
500	1.00029	1.50E−13	3.87298E−07	1.000290387	500.145	500.1452	0.000194	182.0011
1000	1.00029	1.50E−13	3.87298E−07	1.000290387	1000.29	1000.29	0.000387	364.0022
1500	1.00029	1.50E−13	3.87298E−07	1.000290387	1500.435	1500.436	0.000581	546.0033
2000	1.00029	1.50E−13	3.87298E−07	1.000290387	2000.58	2000.581	0.000775	728.0044
2500	1.00029	1.50E−13	3.87298E−07	1.000290387	2500.725	2500.726	0.000968	910.0055
3000	1.00029	1.50E−13	3.87298E−07	1.000290387	3000.87	3000.871	0.001162	1092.007
3500	1.00029	1.50E−13	3.87298E−07	1.000290387	3501.015	3501.016	0.001356	1274.008
4000	1.00029	1.50E−13	3.87298E−07	1.000290387	4001.16	4001.162	0.001549	1456.009
4500	1.00029	1.50E−13	3.87298E−07	1.000290387	4501.305	4501.307	0.001743	1638.01
5000	1.00029	1.50E−13	3.87298E−07	1.000290387	5001.45	5001.452	0.001936	1820.011
5500	1.00029	1.50E−13	3.87298E−07	1.000290387	5501.595	5501.597	0.00213	2002.012
6000	1.00029	1.50E−13	3.87298E−07	1.000290387	6001.74	6001.742	0.002324	2184.013
6500	1.00029	1.50E−13	3.87298E−07	1.000290387	6501.885	6501.888	0.002517	2366.014
7000	1.00029	1.50E−13	3.87298E−07	1.000290387	7002.03	7002.033	0.002711	2548.015
7500	1.00029	1.50E−13	3.87298E−07	1.000290387	7502.175	7502.178	0.002905	2730.016
8000	1.00029	1.50E−13	3.87298E−07	1.000290387	8002.32	8002.323	0.003098	2912.018
8500	1.00029	1.50E−13	3.87298E−07	1.000290387	8502.465	8502.468	0.003292	3094.019
9000	1.00029	1.50E−13	3.87298E−07	1.000290387	9002.61	9002.613	0.003486	3276.02
9500	1.00029	1.50E−13	3.87298E−07	1.000290387	9502.755	9502.759	0.003679	3458.021
10000	1.00029	1.50E−13	3.87298E−07	1.000290387	10002.9	10002.9	0.003873	3640.022

[0068] At optical wavelengths, the refractive index of air has a dependence on temperature and pressure of the environment given by

[0069] $\begin{array}{cc}{n}_1=n-1=\frac{77.6P}{T}\times {10}^{-6}& \mathrm{Equation}9\end{array}$

[0070] where T is the temperature of the air in degrees Kelvin and P is the pressure of the air in millibars. Temperature will be the dominating factor for calculating the index of refraction for air and can be seen when taking the derivative of n₁.

[0071] $\begin{array}{cc}\frac{{\mathrm{dn}}_1}{\mathrm{dT}}=\frac{-77.6P}{T^2}\times {10}^{-6}& \mathrm{Equation}10\end{array}$

[0072] By multiplying both sides of the equation by dT and then changing dT to ΔT and dn₁ to Δn₁ the equation changes to:

[0073] $\begin{array}{cc}\Delta n_1=\frac{-77.6P}{T^2}\times {10}^{-6}\Delta T& \mathrm{Equation}11\end{array}$

[0074] Recall that the original n₁({right arrow over (r)},t) is considered a randomly fluctuating term like a signal fluctuating above and below zero. By squaring n₁({right arrow over (r)},t), and therefore Δn₁, the signal can be made to a power and evaluated as:

[0075] $\begin{array}{cc}\Delta n_1^2={\left[\frac{-77.6P}{T^2}\times {10}^{-6}\right]}^2\Delta T^2& \mathrm{Equation}12\end{array}$

[0076] Which is very similar to published equations that describe Cn² in terms of a temperature structure coefficient Ct²,
C_n²=[79^P/T2]²×10⁻¹²C_T²  Equation 13

[0077] where P is pressure in millibars and T is temperature in degrees Kelvin. The C_T² value can be measured experimentally using differential temperature sensors and then calculated using the Kolmogorov spectrum of turbulence by

[0078] $\begin{array}{cc}{C}_T^2=\frac{\langle \Delta T^2\rangle }{r^{2/3}},& \mathrm{Equation}14\end{array}$

[0079] where ΔT is the temperature difference obtained from a pair of temperature sensors separated by distance r. The angle brackets indicate an ensemble average.

[0080] Assuming a differential temperature sensor separation where r=1 m, then ΔT² and C_T² are mathematically identical.

[0081] In one embodiment, the desire may be to select instrumentation that is both low cost, high resolution, and easy to implement. High accuracy temperature sensors, such as thermocouples and anemometers, that have been used in previous experiments require high end data collection equipment that is not low cost or size. Lower cost Resistive Temperature Detectors (RTD) and thermistors typically do not have the accuracy or resolution required for differential temperature measurements. To better understand requirements for a differential temperature sensor, a set of commercial off the shelf (COTS) sensors were evaluated. Minimum resolution from selected sensors were inserted as ΔT into Equation 13 and Equation 14 to generate minimum measurable Cn².

[0082] Table 3 displays the minimum measurable Cn² variations, based upon the resolution of the COTS temperature sensors. As seen in the table, the minimum resolvable Cn² is a function of minimum sensor resolution.

[0083]

TABLE 3
COTS Temperature Sensor Trade Study
	COTS Sensors
	TSci 506F (10 bit)	TSci 506F (12 bit) 1083	TMP102 SEN-11931	MPL3115A2 SEN-11084	HRES
dT	0.068359375	0.017089844	0.0625	0.029296875	0.00390625
Ct	0.013663947	0.000853997	0.011421944	0.002509705	4.4617E−05
Cn	5.91005E−15	3.69378E−16	4.94032E−15	1.08552E−15	1.92981E−17

[0084] To illustrate how critical sensor selection is, in one embodiment, two sensors were evaluated against Cn² data collected on a typical day. The goal of the evaluation was to deconstruct a Cn² signal into ΔT increments and then reconstruct the Cn² data using COTS Sensor resolution. FIG. 8 illustrates Cn² data collected using an Atmospheric Characterization System (ACS), or wavefront sensor, on May 5, 2015. The data from FIG. 8 was converted into C_T² using Equation 15 with values of pressure and temperature from Table 4. Data for Table 4 was extracted from the daily weather provided by the Weather Underground (Weather Underground, 2016) website and is shown in FIG. 7.

[0085] $\begin{array}{cc}\frac{C_n^2}{{\left[\frac{{79}^P}{T^2}\right]}^2\times {10}^{-12}}=C_T^2& \mathrm{Equation}15\end{array}$

[0086]

TABLE 4
Values Used for dT Calculations
	Instrument	Measurement	Units
	Temperature	295.37	Kelvin
	Pressure	1023.7	Milibar
	Sensor Spacing	0.2	Meter

[0087] Equation 16 was then used to calculate ΔT of the original Cn² signal.
C_T²(r^2/3)=ΔT²  Equation 16

[0088] Once ΔT increments are populated in Table 3, it is easy to make a sensor selection based upon the minimum Cn² resolution. For comparison, COTS Sensors TMP102 SEN-11931 and HRES were selected for reconstruction of the original Cn² signal. The signal was reconstructed by taking the calculated ΔT from Equation 16 and reducing each ΔT at every time increment into COTS Sensors resolution steps based upon the sensor minimum resolution using Equation 17.

[0089] $\begin{array}{cc}\frac{\Delta T}{\mathrm{SensorResolution}}=\mathrm{ResolutionSteps}& \mathrm{Equation}17\end{array}$

[0090] The resulting Resolution Steps were rounded to the nearest integer number and are shown in FIG. 9. Without further analysis it is easy to see that a higher resolution temperature sensor has many more resolution steps to more closely approximate the original Cn² signal.

[0091] Rounded temperature sensor Resolution Steps are then multiplied by their associated lowest sensor resolution to fully reconstruct the ‘digital’ Cn² plot using Equation 18.
ResolutionSteps*SensorResolution=Cn²  Equation 18

[0092] FIG. 10 shows the impact sensor resolution has in correctly approximating Cn². The low-resolution sensor TMP102 SEN-11931 follows the general Cn² trend but the resolution steps are clearly seen when compared with the original May 5 data. The higher resolution HRES sensor does a better job of following original May 5 Cn² data with differences apparent only upon close inspection of FIG. 10 and the enlarged FIG. 11.

[0093] FIG. 12 depicts a block diagram of an atmospheric characterization system 1200 in accordance with an embodiment of the present disclosure. The atmospheric characterization system 1200 comprises a central processing board 1203. Further, positioned on opposing sides of the processing board 1203 are precision temperature sensors 1201 and 1202. The precision sensors 1201 and 1202 are positioned equidistance from the processing board 1203, such that d₁ is equal to d₂. Further, the distance between the precision temperature sensor 1201 and precision temperature sensor 1202 is a predetermined value r.

[0094] The precision temperature sensors 1201 and 1202 are shown positioned perpendicularly with respect to the processing board 1203. However, the precision temperature sensors 1201 and 1202 may be positioned at an angle relative to the processing board 1203, as is shown in FIG. 12. In this regard, the precision temperature sensors 1201 and 1202 may be positioned, for example, at a forty-five-degree angle relative to the processing board 1203. Note, however, that the precision temperature sensors 1201 and 1202 are still positioned an equidistance from the processing board 1203, and the precision temperature sensors are positioned a predetermined distance r one from the other.

[0095] Further note that the positioning of the precision temperature sensors 1201 and 1202 at a forty-five-degree angle is merely exemplary. The precision temperature sensors 1201 and 1202 may be positioned at other angles relative to the processing board 1203 in other embodiments.

[0096] In one embodiment and in accordance with the temperature sensor study described hereinabove, the precision temperature sensors 1201 and 1202 may be high resolution HRES I2C digital temperature sensors with a minimum resolution of 0.00390625 degrees Celsius. However, other sensors having other resolutions may be used in other embodiments.

[0097] A differential temperature is the measurement of a temperature difference between precision temperature sensor 1201 and precision temperature sensor 1202 that are positioned a distance r one from the other. To allow for sensor spacing, the atmospheric characterization system 1200 incorporates the center processing board 1203 with the separate precision temperature sensors 1201 and 1202 that are communicatively coupled to a data bus on the processing board 1203, which is described further with reference to FIG. 13.

[0098] In this regard, the precision temperature sensors 1201 and 1202 are communicatively coupled to the processing board via connections 1220 and 1221, respectively. In one embodiment, the connections 1220 and 1221 may be cables for transferring data indicative of measured temperatures to the processing board 1203 upon demand or periodically.

[0099] In another embodiment, the connections 1220 and 1221 may represent wireless connections. In such an embodiment, the precision temperature sensors 1201 and 1202 may each comprise a wireless transceiver. Further, the processing board may comprise a wireless transceiver. Thus, data indicative of temperature values may be transmitted periodically or upon demand to the processing board 1203 via the wireless connections 1220 and 1221.

[0100] During operation, each precision temperature sensor 1201 and 1202 measures a respective temperature simultaneously. Thereafter, the precision temperature sensors 1201 and 1202 transmit data indicative of the temperatures measured to the processing board 1203 either periodically or upon demand. As will be described further with reference to FIG. 13, the processing board calculates a value indicative of atmospheric turbulence, which is described further herein.

[0101] The data indicative of atmospheric turbulence may be used to build an atmospheric weather model used to predict, given a certain time of day and ground temperature, a model for what the atmosphere looks like in elevation versus temperature over time. Notably, the atmospheric turbulence data may be used to correct for temperature changes that bend a beam of light in an optical system. As an example, the atmospheric characterization system 1200 and a laser system may be co-mounted on a ground vehicle. The atmospheric turbulence data received from the atmospheric system 1200 may be used to correct a mirror that deforms the laser beam so that the laser points straight at a target. In this regard, the atmospheric turbulence data collected by the atmospheric characterization system 1200 may be used to calibrate the laser system to the surrounding atmospheric conditions.

[0102] FIG. 13 depicts an exemplary embodiment of the atmospheric characterization system 1200. As shown by FIG. 13, the atmospheric characterization system 1200 comprises the precision temperature sensors 1201 and 1202 and the processing board 1203.

[0103] The processing board 1203 comprises a processor 1204, a temperature sensor 1206, a pressure sensor 1207, a global positioning system (GPS) 1205, and a storage device 1210. Further, the processing board 1203 comprises memory 1208 for storing control logic 1209, measured data 1215, and calculated data 1216. Note that the measured data 1215 and the calculated data 1216 may also be stored on an onboard storage device 1210, such as a storage device (SD) card.

[0104] In one embodiment, the processing board 1203 may comprise a data link 1211. In this regard, measured data 1215 and/or calculated data 1216 may be transferred from the processing board 1203 to another computing device (not shown) to use in designing, modifying, or calibrating an optical system. Additionally, the calculated data 1215 may be used to correct an existing onboard optical system.

[0105] The control logic 1209 generally controls the functionality of the processing board 1203, as will be described in more detail hereafter. It should be noted that the control logic 1209 can be implemented in software, hardware, firmware or any combination thereof. In an exemplary embodiment illustrated in FIG. 13, the control logic 1209 is implemented in software and stored in memory 1208.

[0106] Note that the control logic 1209, when implemented in software, can be stored and transported on any computer-readable medium for use by or in connection with an instruction execution apparatus that can fetch and execute instructions. In the context of this document, a “computer-readable medium” can be any means that can contain or store a computer program for use by or in connection with an instruction execution apparatus.

[0107] The processor 1204, such as a digital signal processor (DSP) or a central processing unit (CPU), communicates with and drives the other elements within the processing board 1203 via at least one bus 1214. Further, the processor 1204 is configured to execute instructions of software, such as the control logic 1209.

[0108] The temperature sensor 1206 is configured to measure an ambient temperature of the environment in which the atmospheric characterization system is operating. In this regard, the temperature sensor 1206 measures the surrounding temperature periodically, and the measured temperature is used in generating calculated data 1216, which is described further herein.

[0109] The pressure sensor 1207 is configured to measure an ambient pressure of the environment in which the atmospheric characterization system is operating. In this regard, the pressure sensor 1207 measures the surrounding pressure periodically, and the measured pressure is used in generating calculated data 1216, which is described further herein.

[0110] To account for accurate time stamps on data collected during operation of the atmospheric characterization system 1200, the GPS 1205 is used to accurately record location and time. The GPS 1205 allows for many differential temperature nodes at separate spatial locations to be used during one test with high confidence that recorded time is correct.

[0111] The processing board 1203 further comprises precision temperature sensor interfaces 1212 and 1213. The temperature sensor interfaces 1212 and 1214 communicatively couple the processing board 1203 with the precision temperature sensors 1201 and 1202, respectively, over connections 1220 and 1221, respectively. The precision temperature sensor interfaces 1212 and 1213 may be a port for receiving a cable the couples the precision temperature sensors 1201 and 1202 to the processing board 1203.

[0112] In another embodiment, the connections 1220 and 1221 may be wireless connections that communicatively couple the precision temperature sensors 1201 and 1202 to the precision temperature sensor interfaces 1212 and 1214. In such an embodiment, the precision temperature sensors 1201 and 1202 comprise a wireless transceiver for sending data indicative of measured temperature to the processing board 1203. Further, the precision temperature sensor interfaces 1212 and 1213 comprise a wireless transceiver for receiving data indicative of temperature from the precision temperature sensors 1201 and 1202.

[0113] In operation, the precision temperature sensors 1201 and 1202 periodically measure the atmospheric temperature. Upon request or automatically, the precision temperature sensors 1201 and 1202 transmit data indicative of the temperatures measured to the processing board 1203.

[0114] Upon receipt of the data indicative of the temperatures measured, the control logic 1209 stores the data indicative of the temperatures measured in measured data 1215 correlated with a location and time stamp requested from the GPS 1205.

[0115] Upon receipt of the measured data 1215 or periodically, the control logic calculates a value indicative of atmospheric turbulence at the noted location and time. In this regard, the control logic 1209 calculates a temperature structure coefficient using the following equation 14 described hereinabove, which is repeated here for clarity:

[0116] $\begin{array}{cc}{C}_T^2=\frac{\langle \Delta T^2\rangle }{r^{2/3}},& \mathrm{Equation}14\end{array}$
wherein the ΔT is the difference between the measured temperature from precision temperature sensor 1201 and the measured temperature from precision temperature sensor 1202. In this regard, the control logic 1209 subtracts the measured temperature from precision temperature sensor 1201 from the measured temperature from precision temperature sensor 1202. Further, the r in the dividend is the distance between precision temperature sensor 1201 and precision temperature sensor 1202. The result is the temperature structure coefficient C_T².

[0117] The control logic then uses the temperature structure coefficient C_T² to obtain a value indicative of the atmospheric turbulence C_n² using equation 13 repeated here for clarity:
C_n²=[79^P/T2]²×10⁻¹²C_T²,  Equation 13
wherein the P value is the ambient pressure obtained from the pressure sensor 1207, and the T value is ambient temperature obtained from the temperature sensor 1206.

[0118] Once the atmospheric turbulence is calculated, data indicative of the atmospheric turbulence may be stored as calculated data 1216. In the alternative or in addition, the data indicative of the atmospheric turbulence may be stored on the storage device 1210. In one embodiment, the data indicative of the atmospheric turbulence may be transmitted from the processing board 1203 to a computing device (not shown) over the data link 1211.

[0119] As described hereinabove, the data indicative of the atmospheric turbulence may then be used to generate an atmospheric weather model used to predict what the atmosphere looks like in elevation versus temperature over time, which can be used in design of an optics system to correct for atmospheric effects. Additionally, the data indicative of atmospheric turbulence may be used to correct an optical system so that a laser of the system points in a straight line to its intended target. Further, the data indicative of atmospheric turbulence may be used to calibrate an optical system so that the laser accurately points to its intended target.

[0120] Note that during operation, performance of each of the precision temperature sensors 1201 and 1202 may be affected by solar radiation when exposed to direct sunlight. FIG. 14 depicts an embodiment of the precision temperature sensors 1201 and 1202 of the atmospheric characterization system 1200, wherein each of the precision temperature sensors 1201 and 1202 are coupled to and protected against direct sunlight by respective solar radiation shields 1400 and 1401. The solar radiation shields 1400 and 1401 are configured to allow airflow through the sensor housing but not allow any light above the horizon to reach the precision temperature sensors 1201 and 1202

[0121] In this regard, each solar radiation shield 1400 and 1401 comprises three conical-shaped layers 1402-1404 and 1405-1407, respectively. The conical-shaped layers 1402-1404 and 1405-1407 are coupled together; however, a cylindrical opening under each layer allows air to flow through the solar radiation shields 1400 and 1401 as indicated by reference arrows 1408a-1408f and 1409a-1409f. Because the air flow flows through the solar radiation shields 1400 and 1401, the operation of the precision temperature sensors 1201 and 1202 are un affected by the respective radiation shields 1400 and 1401.

[0122] FIG. 15 depicts a cross-sectional view of the solar radiation shield 1400. Note that the solar radiation shields 1400 and 1401 are identical. Thus, the description of the solar radiation shield 1400 equally applies to the solar radiation shield 1401. For simplicity, only one, solar radiation shield 1400, is discussed herein.

[0123] The solar radiation shield 1400 comprises the three conical-shaped layers 1402-1404. The top layer 1402 is coupled to the middle layer 1403 via connectors 1500 and 1501. Further, the middle layer 1403 is coupled to the bottom layer via connector 1502. Additionally, the bottom layer 1403 is coupled to a bracket 1505.

[0124] The precision temperature sensor 1201 comprises a temperature sensor 1507 and a printed circuit board 1506 to which the sensor 1507 is electrically coupled. The printed circuit board 1506 is coupled to the bracket 1505.

[0125] Each conical-shaped layer 1402-1404 has a radial opening 1508-1510, respectively. These radial openings 1508-1510 allow air to flow freely through the solar radiation shield 1400. Because the air may flow freely through the solar radiation shield 1400, operation of the precision temperature sensor 1201 is unaffected by direct sunlight and the precision temperature sensor 1201 is able to still accurately measure surrounding temperature.

[0126] FIG. 16 is a flowchart of the architecture and functionality of the atmospheric characterization system 1200 (FIG. 13).

[0127] The processor board 1203 (FIG. 13) periodically or upon demand receives data indicative of temperature measurements made by precision temperature sensor 1201 and precision temperature sensor 1202 in step 1600. The precision temperature sensors 1201 and 1202 are spaced apart a distance r, which is predefined during manufacturing of the atmospheric characterization system 1200.

[0128] Upon receipt of the data indicative of the temperature measurements, the control logic 1209 obtains a reading from the global positioning system (GPS) 1205. In step 1601, the control logic 1209 associates the temperature data with a location and time stamp obtained from the GPS 1205.

[0129] In step 1602, the control logic 1209 calculates a temperature structure coefficient by using equation 14 described hereinabove. In calculating the temperature structure coefficient, the control logic 1209 uses the difference in temperature between precision temperature sensors 1201 and 1202 and the distance r between the precision temperature sensors 1201 and 1202.

[0130] In step 1603, the control logic 1209 calculates a value indicative of atmospheric turbulence based upon the temperature structure coefficient, the ambient temperature obtained from temperature sensor 1206 (FIG. 13) and the ambient pressure obtained from pressure sensor 1207 (FIG. 13).

[0131] Once the atmospheric turbulence is calculated in step 1603, in step 1604, the atmospheric turbulence values over time may be used to modify an optical system based upon the atmospheric turbulence value.