Patent ID: 12253649

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

The present invention generally relates to methods and apparatuses for measuring optical turbulence using an unmanned aerial vehicle. In embodiments, the apparatus for measuring optical turbulence using an aerial vehicle may be used in conjunction with a remote control system. In embodiments, the measurements of optical turbulence may be transmitted to optical systems, and used to design, modify, or calibrate the optical systems.

As noted above, current optical turbulence measurement systems using the DTS method to measure optical turbulence at nodal locations without the need for a minimum measurement path, beacon, system path averaging, or additional hardware to set up and align. While these DTS systems allowed for multiple DTS systems to be combined to measure an atmospheric turbulence ‘area’ that is not possible to measure with optical devices, they do not allow for accurate determination of nodal measurement values which are used to measure optical turbulence at different points in time based on various weather measurement factors, including at least temperature and wind speed. The DTS method used in these conventional apparatuses assigns a predetermined spacing value between two temperature measurement sensors in order to calculate a temperature structure coefficient, which would then be used to calculate a refractive-index structure coefficient (as a measurement for optical turbulence). In embodiments of the present invention, a wind speed sensor (e.g., a three-dimensional anemometer) may be used in conjunction with temperature sensors, with each sensor mounted on an unmanned aerial vehicle to more accurately measure optical turbulence over a period of time and through different nodal locations in three-dimensional space while allowing for varying of the spacing value used to calculate the temperature structure coefficient.

In embodiments, the measurement approach used for present disclosure uses an anemometer and differential temperature sensor system with high resolution, low cost, digital temperature sensors used in conjunction with a wind speed measurement sensor (such as a three-dimensional anemometer) to more accurately provide the refractive-index structure coefficient, Cn2, of turbulent air at respective nodes. In one embodiment, a custom integrated set of digital differential temperature sensors, as well as a three-dimensional anemometer may be used for the data collection, and provide very fine temperature and wind speed resolution.

Without meaning to be bound by theory, atmospheric turbulence is commonly driven by temperature changes in the environment with a local background mean pressure and temperature, wind speed, and wind direction. Other experiments have considered the effects of humidity fluctuations and solar loading as additional sources of atmospheric turbulence. These changes generally result 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.

A known parameter for measuring optical turbulence is the refractive-index structure coefficient, Cn2, which is a function of local temperature, local pressure, and a temperature structure coefficient, Ct2, and may be calculated by the equation:

C⁢n2=[79PT2]2×1⁢0-1⁢2⁢Ct2Equation⁢1$
where P is pressure in millibars and T is temperature in degrees Kelvin. In the conventional DTS method, the Ct2value can be measured experimentally using differential temperature sensors and then calculated using the Kolmogorov spectrum of turbulence by:

Ct2=〈ΔT2〉rp2/3Equation⁢2
$
where ΔT is the temperature difference obtained from a pair of temperature sensors separated by a predetermined distance rp. The angle brackets indicate an ensemble average.

Assuming a differential temperature sensor separation where r=1 m, then ΔT2and Cr2are mathematically identical. In previously disclosed atmospheric characterization systems utilizing only two differential temperature sensors to measure the refractive index structure coefficient, it was assumed that rp, in Equation 2, was a predetermined value indicating the spacing between the first differential temperature sensor and the second differential temperature. In embodiments of the present invention, the value r may be estimated by using the wind speed measurements generated by a three-dimensional wind speed sensor (such as an anemometer) to generate an estimated sensor spacing value based on the mean wind speed between two points in time. In embodiments, wind speed measurement information may be measured in meters per second, miles per hour, or feet per second, to name a few. Accordingly, based on varying the two points in time, the value of r may also be varied to simulate different spaces between the differential temperature sensors.

In conventional systems, the sensor separation distance was a fixed, predetermined value based on the separation between two differential temperature sensors. In embodiments of the present invention, varying estimated r values may be calculated by using varying the length of time between a first sampled temperature measurement and a second sampled measurement, as well as the average wind speed between the measurements. This means that in embodiments of the present invention, it is possible to evaluate multiple sensor spacing values with one sensor. In embodiments of the present invention therefore, the use of wind speed allows for more flexibility (by requiring only one sensor), as well as more accuracy (by calculating a variable r value between different measurements). In embodiments, the estimated sensor spacing value, r, may be evaluated by the formula:

r=U¯(t2-t1)Equation⁢3
wherein r is the first estimated sensor spacing value, Ū is a first wind speed value from the first wind speed measurement information, t1corresponds to the first start time associated with the first period of time, and t2corresponds to the first end time associated with the first period of time. The use of the estimated sensor spacing value is discussed further with respect to the anemometer method of calculating a refractive index structure coefficient.

In embodiments of the present invention, the Ct2value can be measured using a differential temperature sensor and/or an anemometer temperature sensor in conjunction with a wind speed sensor (e.g., an anemometer) based on measurements taken by the temperature sensor and the wind speed between two points in time, and may be evaluated by the formula:

Ct2=(T1(t⁢1)-T2(t⁢2))2r2/3Equation⁢4
where Ct2is the temperature structure coefficient, T1(t1) is a first temperature measurement value taken by the temperature sensor at the first start time, T2(t2) is a second temperature measurement value taken by the temperature sensor at the first end time, and r is the estimated sensor spacing value (determined by Equation 3).

In embodiments, the Ct2value can also be measured using the differential temperature sensor and/or the anemometer temperature sensor in conjunction with the wind speed sensor (e.g., an anemometer) based on measurements taken by the temperature sensor and the wind speed between two points in time, as well as a power spectral density temperature profile generated based on the power dissipated by the temperature sensor across a spectral frequency range over a period of time, and may be evaluated by the formula:

Ct2=-83⁢Φ⁡(2⁢πUm)f-2/3Equation⁢5
wherein Ct2is the temperature structure coefficient, Φ0is the temperature power spectrum of the temperature sensor, f is the spectral frequency range information associated with the temperature sensor, and Umis the mean wind speed.

In embodiments, the temperature structure coefficient, Ct2, may then be used to determine the refractive-index structure coefficient indicative of optical turbulence (as indicated by Equation 1).

FIGS.1,1A,1B,1C, and1Dare schematic illustrations of conventional optical turbulence measurement apparatuses (1000as shown inFIG.1;1002as shown inFIG.1A:1004as shown inFIG.1B:1006as shown inFIG.1C; and1008as shown inFIG.1D) mounted on unmanned aerial vehicles. A conventional unmanned aerial vehicle102may include a central body104, at least one motor108, a mounting element122, a plurality of mounting rods106, a plurality of mounting rod interfaces114, a plurality of support rods112, a first differential temperature sensor526, a second differential temperature sensor528, and an anemometer124.

FIG.2is a schematic illustration of a conventional optical turbulence measurement apparatus. A conventional optical turbulence measurement apparatus may include a base120including an enclosure120-1, which may include a navigation system (e.g., GPS), a mast mount208, a plurality of signal conditioners206, a weather board204, and an LCD screen150; a mast122; and a sensor head202which may include a first differential temperature sensor126, a second differential temperature sensor128, a conventional anemometer124, and a pyranometer130;

FIG.3is a schematic illustration of a conventional optical turbulence measurement apparatus. The conventional optical turbulence measurement apparatus may include a sonic anemometer124, a first differential temperature sensor126, a second differential temperature sensor128, a mast122, a base120, and a live display150.

FIG.4is a graphical user interface400depicting atmospheric characterization measurements taken by a conventional optical turbulence measurement apparatus. The graphical user interface400may display temperature measurements generated by a plurality of temperature sensors, wind speed measurements taken by a conventional anemometer124, refractive index structure coefficient measurements over a period of time generated by using the temperature sensors, and power spectral density measurements associated with the anemometer124over a frequency range.

FIG.5is a schematic illustration of an apparatus for measuring optical turbulence in accordance with embodiments of the present invention. In embodiments, the apparatus for measuring optical turbulence may include a base520, a mounting element522, a first differential temperature sensor526, a second differential temperature sensor528, and a three-dimensional anemometer524.

FIG.5Ais a schematic illustration of an apparatus for measuring optical turbulence in conjunction with an unmanned aerial vehicle502in accordance with embodiments of the present invention. In embodiments, the unmanned aerial vehicle502may be a drone. In embodiments, the unmanned aerial vehicle502may include a central body504, at least one motor508, the mounting element522, the first differential temperature sensor526, the second differential temperature sensor528, and the three-dimensional anemometer524.FIG.5Cis a schematic illustration of the central body504of an apparatus for measuring optical turbulence in conjunction with an unmanned aerial vehicle502in accordance with embodiments of the present invention. In embodiments, the unmanned aerial vehicle502may further include a first transceiver610. In embodiments, the unmanned aerial vehicle502may be operated by a remote control618via the first transceiver610. In embodiments, the central body504may include a first enclosure housing a flight controller602, a navigation system604, and a payload mounting interface562. In embodiments, the central body504may be completely enclosed. In embodiments, the central body504may be open on one or more sides. In embodiments, the flight controller602may be configured to direct the movement of the unmanned aerial vehicle502. In embodiments, the unmanned aerial vehicle502may be preprogrammed with memory616operatively connected to the flight controller602. In embodiments, the unmanned aerial vehicle502may be preprogrammed via a wired connection (e.g., data port606). In embodiments, the unmanned aerial vehicle502may be preprogrammed via removeable memory (via e.g., memory card port608). For example, in embodiments, the removeable memory608may be an SD Card, such as a Secure Digital Card, Secure Digital High Capacity Card, a Secure Digital Extended Capacity Card, or a Micro Secure Digital Card to name a few. In embodiments, the unmanned aerial vehicle502may be configured to receive instructions via the first transceiver610. In embodiments, the navigation system604may be configured to generate three-dimensional position information associated with the unmanned aerial vehicle502in three-dimensional space. For example, in embodiments the navigation system604may be a GPS system. In embodiments, the central body504may further include a plurality of mounting rod interfaces514. In embodiments, the central body504may further include a plurality of support rod interfaces. In embodiments, the central body may include a plurality of motor mounting rods506wherein each motor mounting rod of the plurality of motor mounting rods506is operatively connected to the central body504via a respective mounting rod interface of the plurality of mounting rod interfaces514.

In embodiments, the unmanned aerial vehicle502may include at least one motor508operatively connected to the central body504with at least one respective propeller509, wherein each motor508is operatively connected to the flight controller602. In embodiments, each propeller509has two or more blades. In embodiments, the at least one motor508is mounted to a respective motor mounting rod of the plurality of motor mounting rods506. In embodiments, the at least one motor508may be a three-phase motor. In embodiments, the unmanned aerial vehicle502may have any number of motors508and corresponding propellers509. For example, in embodiments, the unmanned arial vehicle502may include 2 motors508, along with2corresponding propellers509. In embodiments, the unmanned arial vehicle502may include 4 motors508, along with4corresponding propellers509. In embodiments, the unmanned arial vehicle502may include 6 motors508, along with6corresponding propellers509. In embodiments, the unmanned arial vehicle502may include 8 motors508, along with8corresponding propellers509.

In embodiments, the unmanned arial vehicle502may include a mounting element522. In embodiments, the mounting element522may be, for example, a rod, shaft, mast, or bracket to name a few. In embodiments the mounting element522may be a support rod. In embodiments, the mounting element522may be mounted to the base520using a masting mount.

In embodiments, the three-dimensional anemometer524may be mounted on the mounting element522and may be configured to generate first wind speed measurement information associated with a first wind speed at the three-dimensional anemometer524. In embodiments, the three-dimensional anemometer524may be further configured to generate first temperature measurement information associated with a first temperature at the three-dimensional anemometer524. In embodiments, the three-dimensional anemometer524may be configured to generate the first wind speed measurement information at a first sampling rate. In embodiments, the three-dimensional anemometer524may be configured to generate the first temperature measurement information at the first sampling rate. In embodiments, the three-dimensional anemometer524may be a sonic anemometer. In embodiments, the three-dimensional anemometer524may be a standing wave anemometer. In embodiments, the three-dimensional anemometer524may be configured to generate first wind direction information associated with a first wind direction at the three-dimensional anemometer524. In embodiments, the three-dimensional anemometer524may be configured to generate first three-dimensional wind speed information associated with a first three-dimensional wind speed at the three-dimensional anemometer524. In embodiments, the three-dimensional anemometer524may be configured to generate wind speed measurements between a range of 0-50 meters per second, with a resolution of at least 0.1 meters per second. In embodiments, the three-dimensional anemometer524may include a magnetometer configured to measure magnetic field. In embodiments, the three-dimensional anemometer524may be configured to generate measurement information between a range sampling rates, up to a maximum of 100 Hz. In embodiments, the three-dimensional anemometer524may include an anemometer temperature sensor524-2. In embodiments, the anemometer temperature sensor524-2may be operable to generate temperature measurement information between a range of temperatures (e.g., 40° C. to 80° C.). In embodiments, the three-dimensional anemometer524may include an accelerometer configured to generate pitch, yaw and roll axis rotation measurement information. In embodiments, the three-dimensional anemometer524may be spherically shaped so as to reduce shadow correction, which is a problem with conventional anemometers. Conventional anemometers may be shadowed by up to 30%, making wind speed measurements unsuitable for generating optical turbulence information accurately. In embodiments, the open spherical design of the three-dimensional anemometer524may increase the accuracy of vertical wind measurements, thereby increasing the accuracy of optical turbulence measurements by the system.

In embodiments, the first differential temperature sensor526may be mounted on the mounting element522and may be configured to generate second temperature measurement information associated with a second temperature at the first differential temperature sensor526. In embodiments, the first differential temperature sensor may be configured to generate the second temperature measurement information at the first sampling rate.

In embodiments, the second differential temperature sensor528may be mounted to the mounting element522and may be configured to generate third temperature measurement information associated with a third temperature at the second differential temperature sensor528. In embodiments, the second differential temperature sensor528may be configured to generate the third temperature measurement information at the first sampling rate. In embodiments, the unmanned aerial vehicle502may further include a pyranometer530mounted to the mounting element522and may be configured to generate solar irradiance measurement information associated with a solar irradiance at the pyranometer530. In embodiments, the pyranometer530may be configured to generate the solar irradiance information at the first sampling rate.

In embodiments, the base520may be mounted to the central body504via the payload mounting interface562.FIG.5Bis a schematic illustration of the base520of an apparatus for measuring optical turbulence in conjunction with an unmanned aerial vehicle502in accordance with embodiments of the present invention. In embodiments, referring toFIG.5B, the base520may include a second enclosure housing a first barometric pressure sensor544, a central processing board540, memory542operatively connected to the central processing board540, and a processor560operatively connected to the memory542. In embodiments, the second enclosure may include one or more openings to allow for external connections. In embodiments, the base520may further include one or more of an accelerometer546, an altimeter548, a hydrometer558, a cooling fan552, a data port554, a removeable memory card port556, and/or a display screen550.

In embodiments, the first barometric pressure sensor544may be configured to generate first barometric pressure measurement information associated with a first barometric pressure at the first barometric pressure sensor544. In embodiments, the first barometric pressure sensor544may be configured to generate the first barometric pressure information at the first sampling rate. In embodiments, the accelerometer546may be configured to generate three-dimensional position measurement information associated with a three-dimensional position at the accelerometer546. In embodiments, the accelerometer546may be configured to generate the three-dimensional position information at the first sampling rate. In embodiments, the altimeter548may be configured to generate altitude measurement information associated with an altitude at the altimeter548. In embodiments, the altimeter548may be configured to generate the altitude information at the first sampling rate. In embodiments, the hydrometer558may be configured to generate humidity measurement information associated with a humidity at the hydrometer558. In embodiments, the hydrometer558may be configured to generate the humidity measurement information at the first sampling rate.

In embodiments, the central processing board540may be configured to obtain during a first period of time: the first temperature measurement information from the three-dimensional anemometer524; the second temperature measurement information from the first differential temperature sensor526; the third temperature measurement information from the second differential temperature sensor528; the first wind speed information from the three-dimensional anemometer524; and the first barometric pressure information from the first barometric pressure sensor544. In embodiments, the central processing board540may be further configured to obtain the first altitude measurement information from the altimeter548. In embodiments, the central processing board may be configured to obtain the first three-dimensional position measurement information from the accelerometer546. In embodiments, the central processing board may be configured to obtain the first humidity measurement information from the hydrometer558.

In embodiments, the memory542operatively connected to the central processing board540may be configured to store the first temperature measurement information, the second temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information with a respective associated time stamp associated with the first period of time.

In embodiments, the processor560operatively connected to the memory542may be configured to generate refractive-index structure coefficient information based at least on the first temperature measurement information, the second temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information obtained during the first period of time. In embodiments, the processor560may be configured to generate the first refractive-index structure coefficient information by a first step of calculating, by the processor560, a first estimated sensor spacing value based at least on the first wind speed measurement information, and a first start time and a first end time associated with the first period of time. In embodiments, the first sensor spacing value may be calculated by the formula:

r=U¯(t2-t1)Equation⁢6
wherein r is the first estimated sensor spacing value, Ū is a first wind speed value from the first wind speed measurement information, t1corresponds to the first start time associated with the first period of time, and t2corresponds to the first end time associated with the first period of time.

In embodiments, the processor560in a second step may determine a first temperature structure coefficient based at least on the first estimated sensor spacing value and at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information generated during the first period of time. In embodiments, the first temperature structure coefficient may be determined by the formula:

Ct2=(Δ⁢T)2r2/3Equation⁢7
wherein Ct2is the first temperature structure coefficient, ΔT is a first temperature differential value based on at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information, and r is the first estimated sensor spacing value. In embodiments, the processer560may be configured to determine a second temperature structure coefficient based at least on the first estimated sensor spacing value and at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information generated during the first period of time. In embodiments, the processer560may be configured to determine a third temperature structure coefficient based at least on the first estimated sensor spacing value and at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information generated during the first period of time.

In embodiments, the processor560in a third step may determine first refractive-index structure coefficient information indicative of optical turbulence during the first period of time based at least on the first temperature structure coefficient, the first barometric pressure measurement information, and at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information. In embodiments, the first refractive-index structure coefficient information may be determined by the formula:

Cn⁢12=[7⁢9⁢PT2]2×1⁢0-1⁢2⁢CT2Equation⁢8
wherein Cn12is the first refractive-index structure coefficient, P is a first barometric pressure value based on the first measurement information, Ct2is the first temperature structure coefficient, and T is a first temperature measurement value based on at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information. In embodiments, the processor560may determine second refractive-index structure coefficient information indicative of optical turbulence during the first period of time based at least on the second temperature structure coefficient, the first barometric pressure measurement information, and at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information. In embodiments, the processor560may determine third refractive-index structure coefficient information indicative of optical turbulence during the first period of time based at least on the third temperature structure coefficient, the first barometric pressure measurement information, and at least one of the first temperature measurement information, the second temperature measurement information, and the third temperature measurement information.

In embodiments, the processor560in a fourth step may transmit the first refractive-index structure coefficient information to an optical system. In embodiments, the processor560may transmit the second refractive-index structure coefficient information to the optical system. In embodiments, the processor560may transmit the third refractive-index structure coefficient information to the optical system.

In embodiments, the first differential temperature sensor526may be operatively connected to the central processing board540via a first communication interface532. In embodiments, the second differential temperature sensor528may be operatively connected to the central processing board540via a second communication interface534. In embodiments, the three-dimensional anemometer524may be operatively connected to the central processing board540via a third communication interface536.

In embodiments, the base520may further include a second transceiver564. In embodiments, the second transceiver564may be operatively connected to the processer540. In embodiments, the second transceiver564may be operatively connected to the memory542. In embodiments, the processor560may be configured to communicate with an optical system. In embodiments, the refractive-index structure coefficient information may be provided to the optical system via the second transceiver. In embodiments, the second transceiver564may be the same as the first transceiver610.

FIG.6is a schematic illustration of the base520of an apparatus for measuring optical turbulence in accordance with embodiments of the present invention. In embodiments, the display screen550may be operatively connected to the processor560. In embodiments, the display screen550may be operatively connected to the memory542. In embodiments, the display screen550may be configured to display in real time at least one or more of: the first temperature measurement information; the second temperature measurement information; the third temperature measurement information; the first wind speed measurement information; the humidity measurement information; the altitude measurement information; the solar irradiance measurement information; and/or turbulence measurement information. In embodiments, the display screen may be an LCD display screen.

FIGS.11A,11B, and11A-1-11A-11are schematic diagrams of process flows for measuring optical turbulence using an unmanned aerial vehicle500in accordance with embodiments of the present invention. In embodiments, the unmanned aerial vehicle500may be configured to move between a plurality of positions in three-dimensional space. For example, in embodiments, the unmanned aerial vehicle may be configured to move between the plurality of positions in three-dimensional space based on instructions provided via a remote control. In embodiments, the unmanned aerial vehicle500may include an accelerometer546configured to generate pitch angle measurement information, roll angle measurement information, and heading angle information associated with a respective position of the unmanned aerial vehicle500. In embodiments, the accelerometer546may be located within the base520of the unmanned aerial vehicle500. In embodiments, the unmanned aerial vehicle500may include an altimeter548configured to generate altitude measurement information associated with a respective position of the unmanned aerial vehicle500. In embodiments, the accelerometer548may be located within the base520of the unmanned aerial vehicle500.

In embodiments, referring toFIG.11A, an exemplary process for measuring optical turbulence using an unmanned aerial vehicle may begin with step S1002. At step S1002, in embodiments, a first temperature sensor operatively connected to a central processing board540, both of which are mounted on the unmanned aerial vehicle500, may generate first temperature measurement information at a first sampling rate (e.g., 50 Hz, 75 Hz, 100 Hz, to name a few), the first temperature measurement information associated with a first temperature at the first temperature sensor during a first period of time defined by a first start time and a first end time. In embodiments, the first temperature sensor may be operatively connected to the central processing board540via a first communication interface532. In embodiments, temperature measurement information may be measure in degrees Celsius, Fahrenheit, or Kelvin, to name a few. In embodiments, referring toFIG.11A-1, the process may continue with step S1002A. However, in embodiments, the process may instead skip step S1002A, and proceed directly to step S1004. At S1002A, in embodiments, a second temperature sensor mounted on the unmanned aerial vehicle500and operatively connected to the central processing board540may generate second temperature measurement information at the first sampling rate, the second temperature information associated with a second temperature at the second temperature sensor during the first period of time. In embodiments, the second temperature sensor may be operatively connected to the central processing board540via a second communication interface534. In embodiments, the second temperature measurement information may be the same as the first temperature measurement information. In embodiments, the second temperature measurement information may be different from the first temperature measurement information. In embodiments, the first temperature sensor may be an anemometer temperature sensor524-2. In embodiments, the second temperature sensor may be a first differential temperature sensor526. In embodiments, the first temperature sensor may be a first differential temperature sensor526. In embodiments, the second temperature sensor may be a second differential temperature sensor528. In embodiments, the second temperature sensor may be anemometer temperature sensor524-2.

In embodiments, referring toFIG.11A-1, the process may continue with step S1002B. However, in embodiments, the process may instead skip step S1002A, and proceed directly to step S1004. At step S1002B, a third temperature sensor mounted on the unmanned aerial vehicle500and operatively connected to the central processing board540may generate third temperature measurement information at the first sampling rate, the third temperature measurement information associated with a third temperature at the third temperature sensor during the first period of time. In embodiments, the third temperature sensor may be operatively connected to the central processing board540via the fourth communication interface538. In embodiments, the first temperature sensor may be an anemometer temperature sensor524-2, the second temperature sensor may be a first differential temperature sensor526, and the third temperature sensor may be a second differential temperature sensor528. In embodiments, the first temperature sensor may be a first differential temperature sensor526, the second temperature sensor may be an anemometer temperature sensor524-2, and the third temperature sensor is a second differential temperature sensor528. In embodiments, the first temperature sensor may be a first differential temperature sensor526, the second temperature sensor may be a second differential temperature sensor528, and the third temperature sensor may be an anemometer temperature sensor524-2.

In embodiments, referring toFIG.11A, the process may continue with step S1004. In embodiments, at step S1004, a first wind speed sensor524-1mounted on the unmanned aerial vehicle500and operatively connected to the central processing board540may generate first wind speed measurement information at the first sampling rate associated with a first wind speed at the first wind speed sensor524-1during the first period of time. In embodiments, the first wind speed sensor524-1may be a three-dimensional anemometer524. In embodiments, the anemometer524may include a wind speed sensor524-1and an anemometer temperature sensor524-2. In embodiments, the first wind speed sensor524-1may be a sonic anemometer. In embodiments, the first wind speed sensor524-1may be a standing wave anemometer.

In embodiments, referring toFIG.11A, the process may continue with step S1006. At step S1006, a first barometric pressure sensor544mounted on the unmanned aerial vehicle500and operatively connected to the central processing board540may generate first wind speed measurement information at the first sampling rate associated with a first wind speed at the first wind speed sensor544during the first period of time. In embodiments, the first barometric pressure sensor544may be located within the base520of the unmanned aerial vehicle500. In embodiments, the first barometric pressure sensor544may be a barometer. In embodiments, steps S1002, S1004, and S1006and their respective sub-steps may be rearranged or omitted.

In embodiments, referring toFIG.11A, the process may continue with step S1008. At step S1008, the first temperature measurement information generated during the first period of time may be transmitted from the first temperature sensor to the central processing board540. In embodiments, referring toFIG.11A-2, the process may continue with step S1008A. However, in embodiments, the process may instead skip step S1008A, and proceed directly to step S1010. At step S1008A, the second temperature measurement information generated during the first period of time may be transmitted from the second temperature sensor to the central processing board540. In embodiments, referring toFIG.11A-2, the process may continue with step S1008B. However, in embodiments, the process may instead skip step S1008B, and proceed directly to step S1010. At step S1008B, the third temperature measurement information generated during the first period of time may be transmitted from the third temperature sensor to the central processing board540.

In embodiments, referring toFIG.11A, the process may continue with step S1010. At step S1010, the first wind speed measurement information may be transmitted from the first wind speed sensor to the central processing board540. In embodiments, the process may continue with step S1012. At step S1012, the first barometric pressure measurement information generated during the first period of time may be transmitted from the first barometric pressure sensor to the central processing board540. In embodiments, barometric pressure measurement information may be measured in bars, millibars, Pascals, or Kilopascals to name a few. In embodiments, steps S1008, S1010, and S1012may be rearranged or omitted.

FIG.12is a table depicting exemplary sensor output information in accordance with embodiments of the present invention. In embodiments, the information depicted in the table ofFIG.12may be similar to the data generated by each sensor in the previous steps of the process.

In embodiments, referring toFIG.11A, the process may continue with step S1014. In embodiments, at step S1014, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be stored in memory542operatively connected to the central processing board540. In embodiments, the memory542may be nonremovable memory. In embodiments, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be stored on the nonremovable memory. In embodiments, the memory542may be a removable memory card. For example, in embodiments, the memory may be an SD card, such as a Secure Digital Card, Secure Digital High Capacity Card, a Secure Digital Extended Capacity Card, or a Micro Secure Digital Card, to name a few. In embodiments, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be stored on the removeable memory card. In embodiments, the removeable memory card may be held in memory card port556of the base520while the unmanned aerial vehicle500is being used, and may be removed for data processing.

In embodiments, referring toFIG.11A-3, the process may continue with step S1014A. However, in embodiments, the process may instead skip step S1014A, and proceed directly to step S1016. In embodiments, at step S1014A, the second temperature measurement information may be stored in the memory542operatively connected to the central processing board540. In embodiments, the second temperature measurement information may be stored on the nonremovable memory. In embodiments, the second temperature measurement information may be stored on the removable memory card. In embodiments, referring toFIG.11A-3, the process may continue with step S1014B. However, in embodiments, the process may instead skip step S1014B, and proceed directly to step S1016. At step S1014B, the third temperature measurement information may be stored in the memory542operatively connected to the central processing board540. In embodiments, the third temperature measurement information may be stored on the nonremovable memory. In embodiments, the third temperature measurement information may be stored on the removeable memory card. In embodiments, steps S1014,1014A, and1014B may be rearranged or omitted.

In embodiments, referring toFIG.11A, the process may continue with step S1016. In embodiments, at step S1016, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be obtained from the memory by a digital software system (e.g., a processor560). In embodiments, the digital software system560may be any data processing system or file. In embodiments, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be transmitted to the digital software system560via a communication system. In embodiments, the digital software system560may be operatively connected to the central processing board540. In embodiments, the digital software system560may be located remotely from the unmanned aerial vehicle540and may be operatively connected to the central processing board540via a wireless connection. In embodiments, the digital software system560may be operatively connected to the central processing board540via a wired connection. For example, the digital software system560may obtain information by wired connection via USB port554. In embodiments, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be obtained wirelessly. In embodiments, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be obtained periodically. In embodiments, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be obtained aperiodically. In embodiments, the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information may be obtained in real time as part of a streaming data stream.

In embodiments, referring to step S11A-4, the process may continue step S1016A. However, in embodiments, the process may instead skip step S1016A, and proceed directly to step S1018A. In embodiments, at step S1016A, the second temperature measurement information may be obtained by the digital software system560from the memory542. In embodiments, the second temperature measurement information may be obtained wirelessly. In embodiments, the second temperature measurement information may be obtained periodically. In embodiments, the second temperature measurement information may be obtained aperiodically. In embodiments, the second temperature measurement information may be obtained in real time as part of a streaming data stream. In embodiments, referring to step S11A-4, the process may continue step S1016B. However, in embodiments, the process may instead skip step S1016B, and proceed directly to step S1018A. In embodiments, at step S1018A, the third temperature measurement information may be obtained by the digital software system560from the memory542. In embodiments, the third temperature measurement information may be obtained wirelessly. In embodiments, the third temperature measurement information may be obtained periodically. In embodiments, the third temperature measurement information may be obtained aperiodically. In embodiments, the third temperature measurement information may be obtained in real time as part of a streaming data stream. In embodiments, steps S1016, S1016A, and S1016B may be rearranged or omitted.

In embodiments, referring toFIG.11B, the process may continue with step S1018A. At step S1018A, the digital software system560may determine first power spectral density information associated with a plurality of frequencies based at least on the first temperature measurement information. In embodiments, the first power spectral density information may include a power spectral density temperature profile over a range of the plurality of frequencies. In embodiments, the first power spectral density information may be determined based on a Fourier transform of the first temperature information during the first period of time. In embodiments, the power spectral density information may be determined by integrating the Fourier transform of the first temperature measurement information across the first period of time to get a power profile over a range of frequencies. In embodiments, the Fourier transform may be a Walsh transform. A Walsh transform is analogous to a Fourier transform, but instead uses rectangular waves, rather than sine and/or cosine waves. Walsh functions form an orthogonal set of functions that be used to represent a discrete function, and thus can be viewed as discrete, digital counterparts of the continuous analog system of trigonometric functions associated with a Fourier transform. In embodiments, power spectral density information determined by a Walsh transform may be generated in MATLAB®. In embodiments, the first power spectral density information determined by the Walsh transform may be determined by taking a “pWalsh( )” function of the first temperature measurement information.FIG.7is a graph depicting the power spectral density temperature profile of a plurality of weather measurement sensors in accordance with embodiments of the present invention. Referring toFIG.7, in embodiments, the power spectral density temperature profile of a first differential temperature sensor, a second differential temperature sensor, and an anemometer temperature sensor are shown. In embodiments, the power spectral density profile may be taken over a range of frequencies, or example from 10−2Hz to 10 Hz.

In embodiments, the process may continue with step S1018B. At step S1018B, the digital software system560may determine second power spectral density information associated with the plurality of frequencies based at least on the first wind speed measurement information. In embodiments, as described above, the second power spectral density information may be determined based on a Fourier transform and/or Walsh transform of the first wind speed measurement information during the first period of time. In embodiments, the second power spectral density information may then be determined by integrating the Fourier and/or Walsh transform function over the first period of time to get the power spectral density temperature profile.

In embodiments, referring toFIG.11A-5, the process may continue with step S1018C. However, in embodiments, the process may instead skip step S1018C, and proceed directly to step S1020. At step S1018C, the digital software system560may determine third power spectral density information associated with the plurality of frequencies based at least on the second temperature measurement information. In embodiments, as described above, the third power spectral density information may be determined based on a Fourier transform and/or Walsh transform of the second temperature measurement information. In embodiments, the third power spectral density information may then be determined by integrating the Fourier and/or Walsh transform function over the first period of time to get the power spectral density temperature profile. In embodiments, referring toFIG.11A-5, the process may continue with step S1018D. However, in embodiments, the process may instead skip step S1018D, and proceed directly to step S1020. At step S1018C, the digital software system560may determine fourth power spectral density information associated with the plurality of frequencies based at least on the third temperature measurement information. In embodiments, the fourth power spectral density information may be determined based on a Fourier and/or Walsh transform of the third temperature measurement information. In embodiments, the fourth power spectral density information may then be determined by integrating the Fourier and/or Walsh transform function over the first period of time to get the power spectral density temperature profile. In embodiments, steps1018A,1018B,1018C, and1018D may be rearranged or omitted.

In embodiments, referring toFIG.11Bthe process may continue with step S1020. At step S1020, the digital software system560may determine a first sensor cutoff frequency associated at least one of the first temperature sensor and the first wind speed sensor. In embodiments, the first sensor cutoff frequency may be based on at least one or more of the first power spectral density information and the second power spectral density information. In embodiments, the first sensor cutoff frequency may be a predetermined frequency. In embodiments, the first sensor frequency may be a predetermined frequency selected from a group of predetermined frequencies. In embodiments, the first sensor cutoff frequency may be a predetermined frequency based at least on the first wind speed measurement information. In embodiments, the first sensor cutoff frequency may be associated with the second temperature sensor. In embodiments, the first sensor cutoff frequency may be based at least on the third power spectral density information. In embodiments, the first sensor cutoff frequency may be associated with the third temperature sensor. In embodiments, the first sensor cutoff frequency may be based at least on the fourth power spectral density information.

In embodiments, the first sensor cutoff frequency may be determined based at least on a linear relationship between the first power spectral density information and the first plurality of frequencies. In embodiments, the first sensor cutoff frequency may be determined based at least on a linear relationship between the second power spectral density information and the first plurality of frequencies. In embodiments, the first sensor cutoff frequency may be determined based at least on a linear relationship between the third power spectral density information and the first plurality of frequencies. In embodiments, the first sensor cutoff frequency may indicate a point on the frequency spectrum frequency where a sensor (e.g., a differential temperature sensor, or a three-dimensional anemometer, to name a few) will no longer be able to discern changes in power dissipation at the sensor. The Kolmogorov −5/3 spectrum is generally observed in turbulent flow, which is characterized by a hierarchy of cascading energy (e.g., power dissipation by a sensor over a spectrum frequency range). In embodiments, based on Kolmogorov's theory of turbulence, the slope of the power spectral density temperature profile over a spectrum frequency range should be approximately −5/3. For example, referring toFIG.7in embodiments, the power spectral density temperature profile of a three-dimensional anemometer over a full spectrum frequency range from 102Hz to 10 Hz has an approximate slope of −5/3. However, in embodiments, the power spectral density temperature profile of a first differential temperature sensor and a second differential temperature sensor does not match the approximate −5/3, indicating that each differential temperature sensor has a cutoff frequency less than 10 Hz. In embodiments, the differential temperature sensor may not be able to discern changes in power dissipation at frequencies above the sensor cutoff frequency. Therefore, in embodiments, the first sampling rate may need to be decreased, so that the approximate slope of the power spectral density temperature profile of the first differential temperature sensor and/or the second differential temperature sensor matches the −5/3 line.

In embodiments, referring toFIG.11B, the process may continue with step S1022. At step S1022, the digital system may decimate the first temperature measurement information, the first wind speed measurement information, and the first barometric pressure measurement information generated at the first sampling rate to a second sampling rate during the first period of time based at least on the first power spectral density information, the second power spectral density information, and the first sensor cutoff frequency. In embodiments, decimating the data may include discarding data points generated by the sensors from the data stream such that the sampling frequency is reduced from the first sampling rate (e.g., 50 Hz, 75 Hz, 100 Hz, to name a few) to the second sampling rate (e.g., 1 Hz, 2 Hz, 5 Hz, to name a few).FIG.8is a graph depicting the power spectral density temperature profile of a plurality of weather measurement sensors in accordance with embodiments of the present invention. In embodiments, referring toFIG.8, decimating the temperature sensor data and/or the wind speed data to the determined first sensor cutoff frequency may correct the power spectral density temperature profile such that slope of each temperature profile matches −5/3. In embodiments, for example, by reducing the sampling rate to 1 Hz by discarding a plurality of data points generated in the above steps at the first sampling rate, the first power spectral density information and the second power spectral density information match the approximate −5/3 slope. In embodiments, this will allow for more accurate data processing. In embodiments, the process for reducing the sampling rate by decimating data may be repeated until the power spectral density temperature profile of each sensor reaches a slope of −5/3.

In embodiments, referring to step11A-6, the process may continue with step S1022A. However, in embodiments, the process may instead skip step S1022A, and proceed directly to step S1024. At step S1022A, the digital software system560may decimate the second temperature measurement information generated at the first sampling rate to the second sampling rate based at least on the third power spectral density information. In embodiments, referring to step11A-6, the process may continue with step S1022B. However, in embodiments, the process may instead skip step S1022B, and proceed directly to step S1024. At step S1022B, the digital software system560may the decimate the third temperature measurement information generated at the first sampling rate to the second sampling rate based at least on the fourth power spectral density information.

FIG.10is a schematic diagram of a process flow for measuring optical turbulence using an unmanned aerial vehicle in accordance with embodiments of the present invention. In embodiments,FIG.10depicts a process flow for the raw data collection described above and the process for decimating data described in step S1022and its sub-steps.

FIG.13is a table depicting exemplary decimated sensor output information in accordance with embodiments of the present invention. In embodiments, for example the first sampling rate may be 100 Hz, and the second sampling rate may be 1 Hz. In embodiments, the tables inFIG.13depict an exemplary data decimation in accordance with embodiments of the present invention.

In embodiments, after steps S1022, S1022A, and/or S1022B, digital software system560may transmit the first temperature measurement information decimated to the second sampling rate during the first period of time, the first wind speed information decimated to the second sampling rate during the first period of time, and the first barometric pressure measurement information decimated to the second sampling rate during the first period of time to a remote control system566, where the decimated data will be used to measure optical turbulence using one of the below methods. In embodiments, the digital software system560may complete the process without transmitting the decimated data to the remote control system566. In embodiments, the data may be transmitted to the remote control system566from the digital software system560before it is decimated from the first sampling rate to the second sampling rate. In embodiments, the second temperature measurement information decimated to the second sampling rate during the first period of time may be transmitted from the digital software system560to the remote control system566. In embodiments, the third temperature measurement information decimated to the second sampling rate during the first period of time may be transmitted from the digital software system560to the remote control system566.

In embodiments, the conventional process for measuring optical turbulence may continue with the conventional DTS method, wherein the refractive-index structure coefficient is determined without using wind speed measurement information. In embodiments, the process for measuring optical turbulence using an unmanned aerial vehicle502may continue with calculating one or more refractive-index structure coefficients using an anemometer method and/or using a power spectrum method. In embodiments, the refractive-index structure coefficients determined by the anemometer method may be based on a combination of measurements taken by the first wind speed sensor, the first temperature sensor, the second temperature sensor and/or the third temperature sensor. In embodiments, the refractive-index structure coefficients determined by the power spectrum method may be based on power spectral density temperature profile information associated with the first temperature sensor, the second temperature sensor and/or the third temperature sensor as well as the wind speed measurement information generated by the first wind speed sensor.

Conventional DTS Method

In embodiments, referring toFIG.11A-7after step S1022, S1022A, or S1022B, the process for measuring optical turbulence using an unmanned aerial vehicle502may skip step1024, and continue with a conventional differential temperature sensor (DTS) method starting at step S1026B. In embodiments, this method may not use wind speed to calculate a refractive-index structure coefficient, and may therefore be less accurate than the anemometer method and power spectrum method presented in accordance with embodiments of the present invention. At step S1026B, the digital software system560may determine a third temperature structure coefficient based at least on the predetermined sensor spacing value, the second temperature measurement information, and the third temperature measurement information. In embodiments, the step may be performed by the remote control system566. In embodiments, the third temperature structure coefficient may be determined by the formula:

Ct⁢32=(Δ⁢T2-Δ⁢T3)2rp2/3Equation⁢9
wherein Ct32is the second temperature structure coefficient, ΔT2is a second temperature differential value based on the second temperature measurement information, ΔT3is a third temperature differential value based on the third temperature measurement information, and rpis the predetermined sensor spacing value. In embodiments, the second temperature differential value may be the difference between a first temperature measurement generated at the start time by a second temperature sensor and a second temperature measurement generated at the end time by the second temperature sensor. In embodiments, the second temperature differential value may be calculated by performing a statistical mean subtraction. In embodiments, the third temperature differential value may be the difference between a first temperature measurement generated at the start time by a third temperature sensor and a second temperature measurement generated at the end time by the third temperature sensor. In embodiments, the third temperature differential value may be calculated by performing a statistical mean subtraction. In embodiments, the predetermined sensor spacing value may be, for example, the distance between two temperatures sensor.

In embodiments, referring toFIG.11A-9, the process may continue from step S1028A-1or step S1028A-2with step S1028B-1. However, in embodiments, the process may continue from step S1028A-1or step S1028A-2, and instead proceed to step S1028B-2. In embodiments, the process may continue from step S1028A-1or step S1028A-2, and instead proceed to step S1028B-3. Additionally, in embodiments, the process may instead skip step S1028B-1and proceed directly to step S1030. In embodiments, the digital software system560may determine a third refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the third temperature structure coefficient, the first temperature measurement information, and the first barometric pressure measurement information. In embodiments, the step may be performed by the remote control system566. In embodiments, the third refractive-index structure coefficient may be determined by the formula:

Cn⁢32=[7⁢9⁢PT12]2×1⁢0-1⁢2⁢CT⁢32Equation⁢10
wherein Cn32is the third refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T1is the first temperature measurement value based on the first temperature measurement information, and Ct32is the third temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-9, the process may skip step S1028B-1, and continue from step S1028A-1or step S1028A-2with step S1028B-2. In embodiments, the process may instead skip step S1028B-2, and proceed directly to step S1030. In embodiments, at step S1028B-2, the digital software system560may determine the third refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the third temperature structure coefficient, the second temperature measurement information, and the first barometric pressure measurement information. In embodiments, the step may be performed by the remote control system566. In embodiments, the third refractive-index structure coefficient may be determined by the formula:

Cn⁢32=[7⁢9⁢PT22]2×1⁢0-1⁢2⁢CT⁢32Equation⁢11
wherein Cn32is the third refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T2is the second temperature measurement value based on the second temperature measurement information, and Ct32is the third temperature structure coefficient. In embodiments, the second temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-9, the process may skip step S1028B-2, and continue from step S1028A-1or step S1028A-2with step S1028B-3. In embodiments, the process may instead skip step S1028B-2, and proceed directly to step S1030. In embodiments, at step S1028B-2, the digital software system560may determine the third refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the third temperature structure coefficient, the third temperature measurement information, and the first barometric pressure measurement information. In embodiments, the step may be performed by the remote control system566. In embodiments, the third refractive-index structure coefficient may be determined by the formula:

Cn⁢32=[7⁢9⁢PT32]2×1⁢0-1⁢2⁢CT⁢32Equation⁢12
wherein Cn32is the third refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T3is the third temperature measurement value based on the third temperature measurement information, and Ct32is the third temperature structure coefficient. In embodiments, the third temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-11, the process may continue with step S1030B. At step S1030B, the digital software system560may transmit the third refractive-index structure coefficient to an optical system (described in greater detail with respect to the anemometer method and the power spectrum method of measuring optical turbulence). In embodiments, the step may be performed by the remote control system566.

Anemometer Method

In embodiments, referring toFIG.11Bafter step S1022, S1022A, or S1022B, the process for measuring optical turbulence using an unmanned aerial vehicle502may continue with the anemometer method starting at step S1024. At step S1024, the digital software system560may calculate a first estimated sensor spacing value based at least on the first wind speed measurement information, and the first start time and the first end time associated with the first period of time. In embodiments, the step may be performed by the remote control system566. In embodiments, the first estimated sensor spacing value may be the value r. It has been previously disclosed (as in the Smolin et al. published patent referenced above) that in methods using only two differential temperature sensors to calculate optical turbulence (e.g., refractive-index structure coefficient), the sensor spacing value, r, was a fixed value based on the distance between the two differential temperature sensors. In embodiments, when using a wind speed sensor (e.g., a three-dimensional anemometer) in conjunction with a temperature sensor to determine optical turbulence, the estimated sensor spacing value r may actually vary based on the average wind speed between two points in time. In embodiments, the first estimated sensor spacing value may be calculated by the formula:

r=U¯(t2-t1)Equation⁢13
wherein r is the first estimated sensor spacing value, Ū is a first wind speed value from the first wind speed measurement information, t1corresponds to the first start time associated with the first period of time, and t2corresponds to the first end time associated with the first period of time. In embodiments, the first time period (t2−t1) may be, for example, 30 seconds, 60 seconds, or 90 seconds, to name a few. In embodiments, the first wind speed value may be an average wind speed of the first wind speed measurement information generated at the first sample rate or the second sample rate (after data decimation). In embodiments, the estimated sensor spacing value may vary between different periods of time where optical turbulence (e.g., refractive-index structure coefficient) is being measured by a sensor due to the changes in wind speed. In embodiments, the first estimated sensor spacing value may be a predetermined sensor spacing value. For example, in embodiments, the predetermined sensor spacing value used in a differential temperature sensor method for calculating refracture index structure coefficient may be the distance between two differential temperature sensors. In embodiments, a plurality of refractive-index coefficients may be determined and transmitted using any combination of a first differential temperature sensor526, a second differential temperature sensor528, a three-dimensional wind speed sensor524-1, and/or an anemometer temperature sensor524-2. In embodiments, calculating a plurality of refractive-index structure coefficients may increase the accuracy of the measurements taken.

In embodiments, referring toFIG.11B, the process may continue with step S1026. At step S1026, in embodiments, the digital software system560may determine a first temperature structure coefficient based at least on the first estimated sensor spacing value and the first temperature measurement information during the first period of time. In embodiments, the step may be performed by the remote control system566. In embodiments, the first temperature structure coefficient may be determined by the formula:

Ct⁢12=(Δ⁢T1)2r2/3Equation⁢14
wherein Ct12is the first temperature structure coefficient, ΔT1is a first temperature differential value based on the first temperature measurement information, and r is the first estimated sensor spacing value. In embodiments, the first temperature differential value may be the difference between a first temperature measurement generated at the start time by a first temperature sensor and a second temperature measurement generated at the end time by the first temperature sensor.

In embodiments, referring toFIG.11A-7, the process may continue with step S1026A. However, in embodiments, the process may instead skip step1026A, and proceed directly to step S1028. In embodiments, at step S1026B, the digital software system560may determine a second temperature structure coefficient based at least on the first estimated sensor spacing value and the second temperature measurement information during the first period of time. In embodiments, this step may be performed by the remote control system566. In embodiments, the second temperature structure coefficient may be determined by the formula:

Ct⁢22=(Δ⁢T2)2r2/3Equation⁢15
wherein Ct22is the second temperature structure coefficient, ΔT2is a second temperature differential value based on the second temperature measurement information, and r is the first estimated sensor spacing value. In embodiments, second differential temperature value may be the difference between a first temperature measurement generated at the start time by a second temperature sensor and a second temperature measurement generated at the end time by the second temperature sensor.

In embodiments, referring toFIG.11A-7, the process may continue with step S1026C. However, in embodiments, the process may instead skip step1026C, and proceed directly to step S1028. At step S1028C, the digital software system560may determine a fourth temperature structure coefficient based at least on the first estimated sensor spacing value and the third temperature measurement information during the first period of time. In embodiments, this step may be performed by the remote control system566. In embodiments, the fourth temperature structure coefficient may be determined by the formula:

Ct⁢42=(Δ⁢T3)2r2/3Equation⁢16
wherein Ct42is the fourth temperature structure coefficient, ΔT3is a third temperature differential value based on the third temperature measurement information, and r is the first estimated sensor spacing value. In embodiments, the third temperature differential value may be the difference between a first temperature measurement generated at the start time by a third temperature sensor and a second temperature measurement generated at the end time by the third temperature sensor. In embodiments, steps S1026, S1026A, S1026B, and S1026C may be rearranged or omitted.

In embodiments, referring toFIG.111B, the process may continue from step S1026with step S1028. At step S1028, the digital software system560may determine a first refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the first temperature structure coefficient, the first temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the first refractive-index structure coefficient may be determined by the formula:

Cn⁢12=[7⁢9⁢PT12]2×1⁢0-1⁢2⁢CT⁢12Equation⁢17
wherein Cn12is the first refractive-index structure coefficient, P is a first barometric pressure value based on the first measurement information, T1is a first temperature measurement value based on the first temperature measurement information, and Ct12is the first temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-8, the process may instead continue from step S1026with step S1028-2and skip step S1028. In embodiments, at step S1028-2, the digital software system560may determine the first refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the first temperature structure coefficient, the second temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the first refractive-index structure coefficient is determined by the formula:

Cn⁢12=[7⁢9⁢PT22]2×1⁢0-1⁢2⁢CT⁢12Equation⁢18
wherein Cn12is the first refractive-index structure coefficient, P is a first barometric pressure value based on the first barometric pressure measurement information, T2is a second temperature measurement value based on the second temperature measurement information, and Ct12is the first temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-8, the process may continue from step S1028or step S1028-2with step S1028A-1. However, in embodiments, the process may continue from step S1028or step S1028-2, and instead proceed to step S1028A-2. Additionally, in embodiments, the process may instead skip step S1028A-1and proceed directly to step S1030. At step S1028A-1, the digital software system560may determine a second refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the second temperature structure coefficient, the second temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the second refractive-index structure coefficient may be determined by the formula:

Cn⁢22=[7⁢9⁢PT22]2×1⁢0-1⁢2⁢CT⁢22Equation⁢19
wherein Cn22is the second refractive-index structure coefficient, P is a first barometric pressure value based on the first barometric pressure measurement information, T2is the second temperature measurement value based on the second temperature measurement information, and Ct22is the second temperature structure coefficient. In embodiments, the second temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-8, the process may skip step S1028A-1, and continue from step S1028or step S1028-2with step S1028A-2. However, in embodiments, the process may instead skip step S1028A-2, and proceed directly to step S1030. In embodiments, at step S1028A-2, the digital software system560may determine the second refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the second temperature structure coefficient, the first temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the second refractive-index structure coefficient may be determined by the formula:

Cn⁢22=[7⁢9⁢PT12]2×1⁢0-1⁢2⁢CT⁢22Equation⁢20
wherein Cn22is the second refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T1is the first temperature measurement value based on the first measurement information, and Cn22is the second temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-10, the process may continue from step S1028B-1, step S1028B-2, or step S1028B-3with step S1028C-1. However, in embodiments, the process may continue from step S1028B-1, step S1028B-2, or step S1028B-3, and instead proceed to step S1028C-2. In embodiments, the process may continue from step S1028B-1, step S1028B-2, or step S1028B-3, and instead proceed to step S1028C-3. Additionally, in embodiments, the process may instead skip step S1028B-1and proceed directly to step S1030. In embodiments, at step S1028C-1, the digital software system560may determine a fourth refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the fourth temperature structure coefficient, the third temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the fourth refractive-index structure coefficient may be determined by the formula:

Cn⁢42=[7⁢9⁢PT32]2×1⁢0-1⁢2⁢CT⁢42Equation⁢21
wherein Cn42is the fourth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T3is the third temperature measurement value based on the third temperature measurement information, and Ct42is the fourth temperature structure coefficient. In embodiments, the third temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-10, the process may skip step S1028C-1, and continue from step S1028B-1, step S1028B-2, or step S1028B-3with step S1028C-2. However, in embodiments, the process may continue from step S1028B-1, step S1028B-2, or step S1028B-3, and instead proceed to step S1028C-3. Additionally, in embodiments, the process may instead skip step S1028C-2and proceed directly to step S1030. In embodiments, at step S1028C-2, the digital software system560may determine the fourth refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the fourth temperature structure coefficient, the first temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the fourth refractive-index structure coefficient is determined by the formula:

Cn⁢42=[7⁢9⁢PT12]2×1⁢0-1⁢2⁢CT⁢42Equation⁢22
wherein Cn42is the fourth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T1is the first temperature measurement value based on the first temperature measurement information, and Ct42is the fourth temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11A-10, the process may skip step S1028C-1and step S1028C-2, and continue from step S1028B-1, step S1028B-2, or step S1028B-3with step S1028C-3. However, in embodiments, the process may instead skip step S1028C-3and proceed directly to step S1030. In embodiments, at step S1028C-3, the digital software system560may determine the fourth refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the fourth temperature structure coefficient, the second temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the fourth refractive-index structure coefficient may be determined by the formula:

Cn⁢42=[7⁢9⁢PT22]2×1⁢0-1⁢2⁢CT⁢42Equation⁢23
wherein Cn42is the fourth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T2is the second temperature measurement value based on the second temperature measurement information, and Cn42is the fourth temperature structure coefficient. In embodiments, the second temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring back toFIG.111B, the process may continue from step S1028or step S1028-2with step S1030. At step1030, in embodiments, the digital software system560may transmit the first refractive-index structure coefficient to an optical system. In embodiments, this step may be performed by the remote control system566. In embodiments, the optical system may use the first refractive-index structure coefficient to modify, calibrate, or correct the optical system. For example, in embodiments, an optical weapon system may use the refractive-index structure coefficient for atmospheric profiling. In embodiments, an optical system may use the refractive-index structure coefficient for urban terrain profiling, such as for determining the optical turbulence around buildings or other structures. In embodiments, an optical system may use the refractive-index structure coefficient monitoring wildfires. That is, in embodiments, the optical system may determine the turbulent profile of the fire to determine and the predict the path of the wildfire.

In embodiments, the process may stop at step S1030. In embodiments, referring toFIG.11A-11, the process may continue with step S1030A. At step S1030A, the digital software system560may transmit the second refractive-index structure coefficient to the optical system. In embodiments, this step may be performed by the remote control system566. In embodiments, the process may stop at step S1030A. In embodiments, referring toFIG.11A-11, the process may continue with step S1030B. At step S1030B, the digital software system560may transmit the third refractive-index structure coefficient to the optical system. In embodiments, the process may stop at step S1030B. In embodiments, this step may be performed by the remote control system566. In embodiments, referring toFIG.11A-11, the process may continue with step S1030C. At step S1030C, the digital software system560may transmit the fourth refractive-index structure coefficient to the optical system. In embodiments, this step may be performed by the remote control system566.

Power Spectrum Method

In embodiments, referring toFIG.11Cafter steps S1022, S1022A, or S1022B, the process may continue with the power spectrum method starting at step S1032. At step S1032, the digital software system560may determine first temperature power spectrum information based at least on the first power spectral density information and the first sensor cutoff frequency. In embodiments, this step may be performed by the remote control system566.FIG.14is a graph depicting an exemplary power spectral density temperature profiles of a plurality of sensors in accordance with embodiments of the present invention. In embodiments, referring toFIG.14, the first temperature power spectrum information may include the y-axis range of the first power spectral density information associated with the first temperature sensor. In embodiments, referring toFIG.11C, the process may continue with step S1034. At step S1034, the digital software system560may determine first spectral frequency range information based at least on the first power spectral density information and the first sensor cutoff frequency. In embodiments, this step may be performed by the remote control system566. In embodiments, referring toFIG.14, the first spectral frequency range information may include the x-axis range of the first power spectral density information associated with the first temperature sensor.

In embodiments, referring toFIG.11C, the process may continue with step S1036. At step1036, the digital software system560may determine a fifth temperature structure coefficient based at least on the first temperature power spectrum, the first spectral frequency range information, and the first wind speed measurement information during the first period of time. In embodiments, this step may be performed by the remote control system566. In embodiments, the fifth temperature structure coefficient may be determined by the formula:

CT⁢52=-83⁢Φ1(2⁢πUm)f1-2/3Equation⁢24
wherein CT52is the fifth temperature structure coefficient, Φ1is the first temperature power spectrum, f1is the first spectral frequency range information, and Umis the first wind speed value from the first wind speed measurement information. In embodiments, the first wind speed value may be an average wind speed of the first wind speed measurement information generated at the first sample rate or the second sample rate (after data decimation) during the first period of time.

In embodiments, referring toFIG.11C, the process may continue with step S1038. In embodiments, the process may instead skip step S1038and continue with step S1038A or step S1038B. At step S1038, the digital software system560may determine a fifth refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the fifth temperature structure coefficient, the first temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, wherein the fifth refractive-index structure coefficient may be determined by the formula:

Cn⁢52=[7⁢9⁢PT12]2×1⁢0-1⁢2⁢CT⁢52Equation⁢25
wherein Cn52is the fifth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T1is the first temperature measurement value based on the first temperature measurement information, and Ct52is the fifth temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11C-1, the process may skip step S1038and continue with step S1038A. At step S1038A, the digital software system560may determine the fifth refractive-index structure coefficient based at least on the fifth temperature structure coefficient, the second temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the fifth refractive-index structure coefficient may be determined by the formula:

Cn⁢52=[7⁢9⁢PT22]2×1⁢0-1⁢2⁢CT⁢52Equation⁢26
wherein Cn52is the fifth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T2is the second temperature measurement value based on the second temperature measurement information, and Ct52is the fifth temperature structure coefficient. In embodiments, the second temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11C-1, the process may instead skip steps S1038and S1038A and continue with step S1038B. At step S1038B, the digital software system560may determine the fifth refractive-index structure coefficient based at least on the fifth temperature structure coefficient, the third temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the wherein the fifth refractive-index structure coefficient may be determined by the formula:

Cn⁢52=[7⁢9⁢PT32]2×1⁢0-1⁢2⁢CT⁢52Equation⁢27
wherein Cn52is the fifth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T3is the third temperature measurement value based on the third temperature measurement information, and Ct52is the fifth temperature structure coefficient. In embodiments, the third temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11C, the process may continue from steps S1038, S1038A, or S1038B with step S1040. At step S1040, the digital software system560may transmit the fifth refractive-index structure coefficient to an optical system. In embodiments, this step may be performed by the remote control system566.

In embodiments, referring toFIG.11D, after step S1020and prior to proceeding to step S1022, the process may instead continue with step S1020A. At step S1020A, in embodiments, the digital software system560may determine a second sensor cutoff frequency associated with at least one of the first temperature sensor and the first wind speed sensor. In embodiments, this step may be performed by the remote control system566. In embodiments, the second sensor cutoff frequency may be based at least on at least one or more of the first power spectral density information and the second power spectral density information. In embodiments, the second sensor cutoff frequency may be determined in the same way as discussed with respect to the first sensor cutoff frequency. In embodiments, after step S1020A and prior to step S1022, the process may continue with step S1020B. At step S1020B, the digital software system560may determine a third sensor cutoff frequency associated with the second temperature sensor. In embodiments, this step may be performed by the remote control system566. In embodiments, the third sensor cutoff frequency may be determined based at least on the second power spectral density information.

In embodiments, referring toFIG.11Eafter steps S1022, S1022A, or S1022B, the process may continue with step S1042. In embodiments, at step S1042, the digital software system560may determine second temperature power spectrum information based at least on the second power spectral density information and the second sensor cutoff frequency. In embodiments, this step may be performed by the remote control system566. In embodiments, referring toFIG.14, the second temperature power spectrum information may include the y-axis range of the second power spectral density information associated with the second temperature sensor. In embodiments, referring toFIG.11E, the process may continue with step S1044. At step S1044, the digital software system560may determine second spectral frequency range information based at least on the second power spectral density information and the second sensor cutoff frequency. In embodiments, this step may be performed by the remote control system566. In embodiments, referring toFIG.14, the second spectral frequency range information may include the x-axis range of the second power spectral density information associated with the second temperature sensor.

In embodiments, referring toFIG.11E, the process may continue with step S1046. At step S1046, the digital software system560may determine a sixth temperature structure coefficient based at least on the second temperature power spectrum, the second spectral frequency range information, and the first wind speed measurement information during the first period of time. In embodiments, this step may be performed by the remote control system566. In embodiments, the sixth temperature structure coefficient is determined by the formula:

CT⁢62=-83⁢Φ2(2⁢πUm)f2-2/3Equation⁢28
wherein CT62is the sixth temperature structure coefficient, Φ2is the second temperature power spectrum, f2is the second spectral frequency range information, and Umis the first wind speed value from the first wind speed measurement information. In embodiments, the first wind speed value may be an average wind speed of the first wind speed measurement information generated at the first sample rate or the second sample rate (after data decimation) during the first period of time.

In embodiments, referring toFIG.11E, the process may continue with step S1048. In embodiments, the process may instead skip step S1048and continue with step S1048A or step S1048B. At step S1048, the digital software system560may determine a sixth refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the sixth temperature structure coefficient, the second temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the sixth refractive-index structure coefficient may be determined by the formula:

Cn⁢62=[7⁢9⁢PT22]2×1⁢0-1⁢2⁢CT⁢62Equation⁢29
wherein Cn62is the sixth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T2is the second temperature measurement value based on the second temperature measurement information, and Ct62is the sixth temperature structure coefficient. In embodiments, the second temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11E-1, the process may instead skip step S1048and continue with step S1048A. In embodiments, at step S1048A, the digital software system560may determine the sixth refractive-index structure coefficient based at least on the sixth temperature structure coefficient, the first temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the sixth refractive-index structure coefficient is determined by the formula:

Cn⁢62=[7⁢9⁢PT12]2×1⁢0-1⁢2⁢CT⁢62Equation⁢30
wherein Cn61is the sixth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T1is the first temperature measurement value based on the first temperature measurement information, and Ct62is the sixth temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11E-1, the process may instead skip steps S1048and S1048A and continue with step S1048B. In embodiments, at step S1048B, the digital software system560may determine the sixth refractive-index structure coefficient based at least on the sixth temperature structure coefficient, the third temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the sixth refractive-index structure coefficient is determined by the formula:

Cn⁢62=[7⁢9⁢PT32]2×1⁢0-1⁢2⁢CT⁢62Equation⁢31
wherein Cn62is the sixth refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T3is the third temperature measurement value based on the third temperature measurement information, and Ct62is the sixth temperature structure coefficient. In embodiments, the third temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11E, the process may continue from steps S1048, S1048A, or S1048B with step S1050. At step S1050, the digital software system560may transmit the sixth refractive-index structure coefficient to an optical system. In embodiments, this step may be performed by the remote control system566.

In embodiments, referring toFIG.11Fafter steps S1022, S1022A, or S1022B, the process may continue with step S1052. In embodiments, at step S1052, the digital software system560may determine third temperature power spectrum information based at least on the second power spectral density information and the third sensor cutoff frequency. In embodiments, this step may be performed by the remote control system566. In embodiments, referring toFIG.14, the third temperature power spectrum information may include the y-axis range of the third power spectral density information associated with the third temperature sensor. In embodiments, referring toFIG.11F, the process may continue with step S1054. At step S1054, the digital software system560may determine third spectral frequency range information based at least on the third power spectral density information and the third sensor cutoff frequency. In embodiments, this step may be performed by the remote control system566. In embodiments, referring toFIG.14, the third spectral frequency range information may include the x-axis range of the third power spectral density information associated with the third temperature sensor.

In embodiments, referring toFIG.11F, the process may continue with step S1056. At step S1056, the digital software system560may determine a seventh temperature structure coefficient based at least on the third temperature power spectrum, the third spectral frequency range information, and the first wind speed measurement information during the first period of time. In embodiments, this step may be performed by the remote control system566. In embodiments, the seventh temperature structure coefficient is determined by the formula:

CT⁢72=-83⁢Φ3(2⁢πUm)f3-2/3Equation⁢32
wherein Ct72is the seventh temperature structure coefficient, Φ3is the third temperature power spectrum, f2is the third spectral frequency range information, and Umis the first wind speed value from the first wind speed measurement information. In embodiments, the first wind speed value may be an average wind speed of the first wind speed measurement information generated at the first sample rate or the second sample rate (after data decimation) during the first period of time.

In embodiments, referring toFIG.11F, the process may continue with step S1058. In embodiments, the process may instead skip step S1058and continue with step S1058A or step S1058B. At step S1058, the digital software system560may determine a seventh refractive-index structure coefficient indicative of optical turbulence during the first period of time based at least on the seventh temperature structure coefficient, the third temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the seventh refractive-index structure coefficient may be determined by the formula:

Cn⁢72=[7⁢9⁢PT32]2×1⁢0-1⁢2⁢CT⁢72Equation⁢33
wherein Cn72is the seventh refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T3is the third temperature measurement value based on the third temperature measurement information, and Ct72is the seventh temperature structure coefficient. In embodiments, the third temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11F-1, the process may instead skip step S1058and continue with step S1058A. In embodiments, at step S1048A, the digital software system560may determine the seventh refractive-index structure coefficient based at least on the seventh temperature structure coefficient, the first temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the seventh refractive-index structure coefficient is determined by the formula:

Cn⁢72=[7⁢9⁢PT12]2×1⁢0-1⁢2⁢CT⁢72Equation⁢34
wherein Cn72is the seventh refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T1is the first temperature measurement value based on the first temperature measurement information, and Ct72is the seventh temperature structure coefficient. In embodiments, the first temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11F-1, the process may instead skip step S1058A and continue with step S1058B. At step1058B, the digital software system560may determine the seventh refractive-index structure coefficient based at least on the seventh temperature structure coefficient, the second temperature measurement information, and the first barometric pressure measurement information. In embodiments, this step may be performed by the remote control system566. In embodiments, the seventh refractive-index structure coefficient may be determined by the formula:

Cn⁢72=[7⁢9⁢PT32]2×1⁢0-1⁢2⁢CT⁢72Equation⁢35
wherein Cn72is the seventh refractive-index structure coefficient, P is the first barometric pressure value based on the first barometric pressure measurement information, T2is the second temperature measurement value based on the second temperature measurement information, and Ct7is the seventh temperature structure coefficient. In embodiments, the second temperature measurement value may be a local temperature measurement value. In embodiments, the first barometric pressure value may be a local pressure measurement value.

In embodiments, referring toFIG.11F, the process may continue with step S1060. At step S1060, the digital software system560may transmit the seventh refractive-index structure coefficient to an optical system. In embodiments, this step may be performed by the remote control system566.

FIG.9is a graph depicting the refractive index structure coefficient measured by an unmanned aerial vehicle502in accordance with embodiments of the present invention. In embodiments, the measured Cn2values may be plotted over time and at specific nodal locations. In embodiments, referring toFIG.9, the Cn2measurements generated by the unmanned aerial vehicle502closely match the expected vertical profile of optical turbulence determined known by a conventional optical turbulence measurement system (BLS900).

FIG.9Ais a graph depicting the refractive index structure coefficient measured by a plurality of unmanned aerial vehicles502in accordance with embodiments of the present invention. In embodiments, referring toFIG.9A, a plurality of unmanned aerial vehicles502may be used to generate Cn2measurements at a plurality of three-dimensional space locations simultaneously. In embodiments, the Cn2measurements may be generated over a period of time and across a vertical profile.

Now that embodiments of the present invention have been shown and described in detail, various modifications and improvements thereon can become readily apparent to those skilled in the art. Accordingly, the exemplary embodiments of the present invention, as set forth above, are intended to be illustrative, not limiting. The spirit and scope of the present invention is to be construed broadly.