Patent Publication Number: US-11050954-B1

Title: Passive clear air turbulence detection system and method

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 13/901,253, filed May 23, 2013, the entire disclosure of which is incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     Clear air turbulence (CAT) is the turbulent movement of air masses in the absence of any visual cues such as clouds, and is caused when bodies of air moving at widely different speeds meet. The atmospheric region most susceptible to CAT is the high troposphere at altitudes of around 7,000-12,000 meters (23,000-39,000 ft) as it meets the tropopause. Here CAT is most frequently encountered in the regions of jet streams. At lower altitudes it may also occur near mountain ranges. Thin cirrus clouds can also indicate a high probability of CAT. 
     CAT can be hazardous to the comfort, and even safety, of air travel. The thermal characteristics of CAT are known. Studies show that gust velocity changes in CAT of at least 20 ft sec −1  are associated with temperature changes of 3° C. or higher; very few being less than 1° C. Such studies show that CAT horizontal temperature gradients with a minimum temperature change of 2° C., and at a rate which equaled or exceeded 0.5° C. per minute. Moderately choppy CAT was observed at a 5° C. temperature change. 
     Conventionally, CAT has been measured using active electro-optical heterodyne laser velocimeter systems at ranges exceeding 10 km. Such active systems typically use 10 micron wavelength LWIR (long wavelength infrared) CO 2  lasers, larger germanium optics and heterodyning optics. Fast, complex signal and data processing renders systems constructed along these lines are expensive, power-hungry, heavy, and physically large. Further such active systems require much maintenance on a use-by-use basis in alignment, cleaning etc. 
     SUMMARY OF THE INVENTION 
     One implementation of the present disclosure is a passive thermal imaging system, according to some embodiments. In some embodiments, the passive thermal imaging system includes multiple detector arrays, imaging optics, and processing electronics. Each of the multiple detector arrays are configured to detect thermal electromagnetic radiation (EMR) within a same band around a desired EMR wavelength. In some embodiments, each of the detector arrays include multiple pixels. In some embodiments, the imaging optics are configured to receive thermal EMR within the band from an object, and to image the received thermal EMR from a same region of the object onto pixels of each of the multiple detector arrays. In some embodiments, the processing electronics are configured to receive a detected signal from each of the pixels of the multiple detector arrays. In some embodiments, the processing electronics are further configured to calculate a correlation value based on a multi-correlation of the received detected signals of corresponding pixels of different detector arrays of the multiple detector arrays, the detected signals based on the thermal EMR from the object. In some embodiments, the processing electronics are configured to compare the correlation value with a threshold correlation value to determine that a detection event has occurred in response to the correlation value exceeding the threshold correlation value, the threshold correlation value being equal to or between 0.8 and 0.85. 
     In some embodiments, the processing electronics are configured to calculate the correlation value based on a covariance of the received detected signals of the corresponding pixels of the different detector arrays, the detection event corresponding to a size of a temperature fluctuation of the object. 
     In some embodiments, the imaging optics are configured to receive thermal EMR from a region of the atmosphere as the object, and where the detection event is clear air turbulence exhibiting thermal fluctuations of air at a distance from the system ≥10 kilometers. 
     In some embodiments, the multiple detector arrays include two detector arrays, and the processing electronics is configured to calculate a correlation value based on cross-correlation of corresponding pixels of the multiple detector arrays. 
     In some embodiments, the multiple detector arrays include three detector arrays, and the processing electronics is configured to calculate a correlation value based on triple-correlation of corresponding pixels of the multiple detector arrays. 
     In some embodiments, the multiple detector arrays include at least one of a nanoparticle plasmonic detector array, a mercury cadmium telluride detection array, or a bolometer detector array. 
     In some embodiments, the multiple detector arrays include a nanoparticle plasmonic detector array. 
     In some embodiments, the processing electronics is configured to time integrate or spatially integrate the detected signals at a rate of 1 to 10 times per second. 
     In some embodiments, the imaging optics include an imaging lens. 
     In some embodiments, the passive thermal imaging system further includes a bandpass filter which filters the received thermal EMR from the object within a EMR wavelength range. 
     In some embodiments, the bandpass filter filters the received thermal EMR from the object within a EMR wavelength range of 10 microns±2 microns. 
     Another implementation of the present disclosure is a system for detecting clear air turbulence, according to some embodiments. In some embodiments, the system includes a structure having a passive thermal imaging system mounted to the structure. In some embodiments, the passive thermal imaging system includes multiple detector arrays, imaging optics, and processing electronics. In some embodiments, each of the detector arrays are configured to detect thermal electromagnetic radiation (EMR) within a same band around a desired EMR wavelength, each of the detector arrays including multiple pixels. In some embodiments, the imaging optics are configured to receive thermal EMR within the band from an object, and to image the received thermal EMR from a same region of the object onto pixels of each of the multiple detector arrays. In some embodiments, the processing electronics are configured to receive a detected signal from each of the pixels of the multiple detector arrays. In some embodiments, the processing electronics are configured to calculate a correlation value based on a multi-correlation of the received detected signals of corresponding pixels of different detector arrays of the multiple detector arrays, the detected signals based on the thermal EMR from the object. In some embodiments, the processing electronics is configured to compare the correlation value with a threshold correlation value to determine that a detection event has occurred in response to the correlation value exceeding the threshold correlation value, the threshold correlation value being equal to or between 0.8 and 0.85. 
     In some embodiments, the structure is one of a vehicle or a ground-based platform. 
     In some embodiments, the structure is a vehicle, which is one of an aircraft, a spacecraft, or an unmanned aerial vehicle. 
     In some embodiments, the processing electronics are configured to calculate the correlation value based on a covariance of the received detected signals of the corresponding pixels of the different detector arrays, the detection event corresponding to a size of a temperature fluctuation of the object. 
     In some embodiments, the imaging optics are configured to receive thermal EMR from a region of the atmosphere as the object, and where the detection event is clear air turbulence exhibiting thermal fluctuations of air at a distance from the system ≥10 kilometers. 
     In some embodiments, the multiple detector arrays include two detector arrays, and the processing electronics is configured to calculate a correlation value based on cross-correlation of corresponding pixels of the plurality of detector arrays. 
     Another implementation of the present disclosure is a method for passively imaging thermal electromagnetic radiation (EMR), according to some embodiments. In some embodiments, the method incudes receiving a detected signal from each of multiple pixels of multiple detector arrays. In some embodiments, the method includes calculating a correlation value based on a multi-correlation of the received detected signals of corresponding pixels of different detector arrays of the multiple detector arrays, the detected signals based on a thermal EMR from an object. In some embodiments, the method includes comparing the correlation value with a threshold correlation value to determine that a detection event has occurred in response to the correlation value exceeding the threshold correlation value, the threshold correlation value being equal to or between 0.8 and 0.85. 
     In some embodiments, calculating the correlation value includes calculating the correlation value based on a covariance of the received detected signals of the corresponding pixels of the different detector arrays, the detection event corresponding to a size of a temperature fluctuation of the object. 
     In some embodiments, the method includes receiving thermal EMR from the object at imaging optics and imaging the received thermal EMR from a same region of the object onto pixels of each of the multiple detector arrays. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic illustrating a passive thermal imaging system according to an embodiment. 
         FIG. 2  is a schematic illustrating a view of a detector array including an array of pixels according to an embodiment. 
         FIGS. 3A and 3B  illustrate the effect of turbulence on EMR radiation received from a region of interest and impinging on a receiver plane. 
         FIG. 4  is graph illustrating standard deviation in arrival angle due to reasonable atmospheric turbulence level as a function of beam diameter d B  for different sizes of index of refraction fluctuation due to turbulence. 
         FIG. 5  illustrates a randomly populated signal matrix. 
         FIG. 6  illustrates a noise matrix. 
         FIG. 7  illustrates a signal plus noise matrix. 
         FIG. 8  is a schematic illustrating a system for detecting air turbulence including a passive thermal imaging system according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     According to certain embodiments, a passive optical system which may discriminate a minimum change of 2° C. from an imaged region and its background, and thus is appropriate for detecting CAT is described. The passive system uses correlation techniques to reduce the effects of thermal background noise to allow for detection of CAT at a distance from the system of ≥10 km. Such a detection distance of CAT provides a warning time of about 30 seconds for an optical system on an aircraft traveling at about 600 miles/hr. Such a small temperature change may be determined in the presence of certain natural background radiation from the day time and night time sky, although not necessarily in the presence of all strengths of natural background radiation. 
       FIG. 1  illustrates a passive thermal imaging system  100  according to an embodiment of the invention. The system  100  includes at least one detector array  110 , ( 110   a  and  110   b  in  FIG. 1 ), imaging optics  120  (imaging optics components  120   a  and  120   b  in  FIG. 1 ), and processing electronics  130 . The imaging optics  120  images an object of interest  150  onto the at least one detector array  110 . While  FIG. 1  illustrates the at least detector array  110  to be two detector arrays  110   a  and  110   b , the at least one detector array  110  may be a single detector array, or more than two detector arrays, such as three detector arrays. Likewise, while  FIG. 1  illustrates the imaging optics to be two imaging optics components  120   a  and  120   b , the imaging optics  120  may be a single imaging optics component, or more than two imaging optics components, such as three imaging optics components. In general, the imaging optics components  120   a  and  120   b  image thermal electromagnetic radiation (EMR) from an object  150  of interest onto detector arrays  110   a  and  110   b , respectively. 
       FIG. 2  illustrates a view of a detector array  110  including an array of pixels  112 . While  FIG. 2  illustrates a 3×3 array of pixels for ease of illustration, in general, the size of the array of pixels will be much larger than 3×3. The detector material for the pixels  112  may be any material appropriate for detecting thermal EMR at an appropriate wavelength. In this regard, the detector array  110  may comprise at least one of a nanoparticle plasmonic detector array, a mercury cadmium telluride detection array, or a bolometer detector array. Nanoparticle plasmonic detector arrays are described in, for example, U.S. patent application Ser. No. 13/243,342 entitled NANO-STRUCTURE ARRAYS FOR EMR IMAGING, filed Sep. 23, 2011, which is incorporated by reference in its entirely herein. 
     Referring back to  FIG. 1 , the system  100  may include at least one bandpass filter  140  (filters  140   a  and  140   b  in  FIG. 1 ) which filters the received thermal EMR from the object  150  within a EMR wavelength range of interest. For example, for a EMR wavelength of interest of 10 microns, the bandpass filter  140  may pass EMR in a wavelength range of 10 microns±2 microns. 
     The imaging optics  120  images the EMR from the object at a desired wavelength of interest. For example, for a EMR wavelength of interest of 10 microns, the imaging optics may comprise a lens, or lenses, made of germanium to image the thermal EMR from the object  150 . 
     The imaging system  100  may be of appropriate dimensions for imaging thermal EMR from an object at an appropriate distance. For example, if the system  100  is intended to image thermal EMR from an object at a distance of about 10 km from the system  100 , the system may be an f/5 system, for example, where the imaging optics  120  has a focal length of about 0.5 meters, for example, and a lens diameter of about 10 cm, for example. 
     The processing electronics  130  receives a detected signal from each of the pixels  112  of the at least one detector array  110 . The processing electronics  130  further calculates a correlation value based on a correlation between the received detected signals from the pixels  112 , and compares the correlation value with a threshold correlation value to determine whether a detection event has occurred. 
     Below is provided a background discussion for determining the signal to noise and event detection capability of the system  100 , where the event is detection of CAT. 
     Basic Optical Principles for System and Signal Strength 
     For an extended source that fills the field of view of a detector, the detector irradiance H is related to the source radiance, N, by the following radiometric equation, where trans is the transmission of the atmosphere and system optics, m is the system magnification, v/u, and FN 0  is the f/# of the system: 
     
       
         
           
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     For a 273° K object temperature, the spectral radiance of the extended body, where emissivity is assumed to be equal to unity, is ˜8 Watts per square meter, steradian, micron. For the above 0.5 m, f/5 lens, operated with an 8-12 micron bandpass filter, and with 50% atmospheric and optical transmission efficiency overall, the detector irradiance H is calculated to be ˜0.5 Watts per square meter. 
     For a 10 micron square nanoparticle plasmonic detector array operated in the LWIR region of 8-12 microns, where such a nanoparticle plasmonic detector array is described in, for example, U.S. patent application Ser. No. 13/243,342 entitled NANO-STRUCTURE ARRAYS FOR EMR IMAGING, filed Sep. 23, 2011, which is incorporated by referenced in its entirely herein, the maximum Responsivity may be estimated to be about 5000 Amps/Watt, with a RMS Noise performance at 2 pico-Amps. Presuming a Responsivity in practice to be about 500 Amps/Watt, the signal to noise ratio in such a nanoparticle plasmonic pixel would be ˜1.4×10 4 , and at least 1,000 even if the detector noise was 10× greater. Alternatively, a typical MCT detector of a 15 micron pixel side cooled to 77° K would yield a signal to noise ratio of ˜40, and an un-cooled typical microbolometer of a 17 micron pixel side would yield a signal to noise ratio of ˜9.5. 
     From a system performance point of view, of concern is the measurement of the difference in temperature of the target object from its adjacent background, which should be about 2° C. for CAT detection. In measuring such a 2° C. temperature difference, the Minimum Resolvable Temperature Difference (MRTD) and Minimum Detectable Temperature Difference (MDTD) are the parameters of importance as is known in thermal imaging. To determine the MRTD, NDTD, as well as Noise Equivalent Temperature Difference (NETD), standard equations may be used as in known [Lloyd, J. M., 1975; ‘Thermal Imaging Systems’, Plenum Press]. 
     In calculating the MRTD and MDTD, a dwell time of 0.2 seconds is presumed. The NETD for the three detectors under consideration noted above is determined to be ˜11 milliKelvin for a nanoparticle plasmonic detector, ˜96 milliKelvin for a typical MCT detector, and ˜980 milliKelvin for a typical microbolometer detector. 
     The MDTD may be calculated for a 1 kHz bandwidth system, which provides for the three detectors under consideration noted above as follows: ˜4.6 milliKelvin for a nanoparticle plasmonic detector, ˜24 milliKelvin for a typical MCT detector, and ˜300 milliKelvin for a typical microbolometer detector. 
     Thus, without accounting for natural background radiation, all three LWIR detectors noted can measure the necessary temperature difference required for CAT detection. 
     Background Radiation, Atmospheric Transmission, Turbulence Effects 
     In practice, however, the natural background radiation, atmospheric transmission and turbulence effects must be taken into account in determining whether or not CAT may be detected. The ability to discriminate against background noise contributions and fluctuations is of critical importance to effective realization in practice of the concept of passive CAT discrimination and reliable measurement. 
     Background noise can enter an optical system for detection of CAT from a wide range of circumstances, such as looking at the sun, the moon as the background, looking at clouds, or the day or night sky, or even at the Earth itself. For the purposes of performance calculations, the magnitude of the different background noise contributions that might be encountered by a CAT system in practice must be considered, where such contributions may come from the, sun, the daytime sky, the full moon, the earth, or the brightest stars. 
     Further, atmospheric transmission must be taken into account in determining whether or not CAT may be detected. The transmittance of the atmosphere at an EMR wavelength of 10 microns is of concern for the system described above. The overall transmissivity of the atmosphere, per km, is about 80% per km for a wavelength region of ˜10 microns. 
     The turbulence of interest is associated with small thermal fluctuations, which along a 10 km path length, may have an appreciable effect on the integrity of the image. In order to estimate the effect of turbulence on the image, information on the thermal fluctuations likely at 10 micron EMR wavelength is needed. The effect of turbulence can be explained with respect to  FIGS. 3A, 3B and 4 . 
       FIGS. 3A and 3B  illustrate the effect of turbulence on EMR radiation received from a region of interest located at the point “Transmitter” and impinging on a receiver plane. The turbulence will cause fluctuation in the index of refraction of the air, thus affecting the imaging onto the image plane. The effect of atmospheric turbulence depends on the relative sizes of the beam diameter, d B , and the size of the fluctuation, 1.  FIG. 3A  illustrates the case where the size of the fluctuation  1  is much less than the beam diameter d B  of the radiation from the point “Transmitter,” while  FIG. 3B  illustrates the case where the size of the fluctuation  1  is much greater than the beam diameter d B  of the radiation from the point “Transmitter.” As seen in  FIGS. 3A and 3B , if d B /1&lt;&lt;1, the major effect of turbulence is to deflect the imaging-beam as a whole. If d B /1&lt;&lt;1, small portions of the beam are diffracted and the imaging beam can become badly distorted. 
       FIG. 4  illustrates standard deviation in arrival angle due to reasonable atmospheric turbulence level as a function of beam diameter d B  for different sizes of index of refraction fluctuation due to turbulence [see W. K. Pratt, (1969), Laser Communications Systems, Wiley]. 
     Basic Performance Estimates 
     Expressions for the background radiation power at the detector are derived from the standard radiometry equation found in many optics textbooks [see Pratt, W. K., Laser Communication Systems, Wiley (1969)]. These expressions are summarized in the table below. 
                                     Source        Background        Relationship    Expression    Radiation Quantity                  Any source             P   B     =           πτ   a     ⁢     τ   r     ⁢     λ   i     ⁢     d   R   2       4     ⁢   ⁢     (   λ   )               Spectal irradiance                Spherical source of  diameter, d s , not filling receiver field of view             P   B     =           πτ   a     ⁢     τ   r     ⁢     λ   i     ⁢     d   S   2     ⁢     d   R   2         16   ⁢     R   2         ⁢   ⁢     (   λ   )               Spectral radiant emittance                     P   B     =           π   2     ⁢     τ   a     ⁢     τ   r     ⁢     λ   i     ⁢     d   S   2     ⁢     d   R   2         16   ⁢     R   2         ⁢   ⁢     (   λ   )               Spectral  radiance                     P   B     =           π   2     ⁢     τ   a     ⁢     τ   r     ⁢     λ   i     ⁢     d   S   2     ⁢     d   R   2     ⁢     hf   c         16   ⁢     R   2         ⁢   ⁢     (   λ   )               Photon spectral  radiance               Extended source filling receiver field of view, θ R               P   B     =           πτ   a     ⁢     τ   r     ⁢     λ   i     ⁢     θ   R   2     ⁢     d   R   2       4     ⁢   ⁢     (   λ   )               Spectral radiant  emittance                     P   B     =           π   2     ⁢     τ   a     ⁢     τ   r     ⁢     λ   i     ⁢     θ   R   2     ⁢     d   R   2       4     ⁢   ⁢     (   λ   )               Spectral radiance                     P   B     =           π   2     ⁢     τ   a     ⁢     τ   r     ⁢     λ   i     ⁢     θ   R   2     ⁢     d   R   2     ⁢     hf   c       4     ⁢   ⁢     (   λ   )               Photon spectral  radiance,                    
where the parameters shown in the table are as follows:
         τ a  atmospheric transmissivity   τ r  receiver transmissivity   λ i  input filter bandwidth in wavelength units (λ is wavelength)   θ R  receiver field-of-view angle   d s  diameter of the background radiation source   d r  diameter of the receiver   H spectral irradiance   N spectral radiance   W spectral radiant emittance in wavelength units   P B  background radiation average power at the detector surface   R Range       

     At 10 microns wavelength, the values of background due to sun, daytime sky, night-time sky, full moon, earth and brightest stars are as follows: 
     Sun: H(λ)˜10 −5  Watts per cm 2 . 
     Daytime Sky: N(λ)˜5×10 −4  Watts per cm 2 , micron, steradian. 
     Night-time Sky: N(λ)˜0.1×10 −10  Watts per cm 2 , micron, steradian. 
     Full Moon: H(λ)˜10 −10  Watts per cm 2 , micron. 
     Earth: W(λ)˜3×10 −3  Watts per cm 2 , micron. 
     Brightest Stars: H(λ)˜10 −14  Watts per cm 2 , micron. 
     Based on these values, the background power at a pixel in our optical system may be calculated. For a pixel side being 10 microns, and the focal-length of the lens being set, as above, at 0.5 meters, the following background power levels at the detector pixel, under the background conditions may be calculated to be: 
     Sun: ˜1.3×10 −3  Watts. 
     Daytime Sky: ˜8×10 −11  Watts. 
     Night-time Sky: ˜1.6×10 −12  Watts. 
     Full Moon: ˜1.3×10 −8  Watts. 
     Earth: ˜4.7×10 −10  Watts. 
     Brightest Stars: negligible. 
     By applying the Responsivity (Amps/Watt) to this natural background noise power, the induced natural background noise current may be calculated and the signal to noise ratio may be estimated (neglecting atmospheric transmission for a worst case calculation). The signal to noise with no natural background noise, and for natural background noise due to daytime sky are estimated as shown in the table below for a nanoparticle plasmonic detector, a typical MCT detector, and a typical microbolometer detector, for responsivity (Resp) values as shown.
         SNR: No background SNR: Daytime Sky Background
 
nanoparticle plasmonic (Resp=500)  ˜10 4  0.63
 
MCT (Resp=120)  ˜40 0.57
 
Microbolometer (Resp=500)  ˜95 0.15
       

     As can be seen, even though the nanoparticle plasmonic detector has extremely low noise compared to both the MCT and microbolometer detectors, the magnitude of the natural background daylight sky noise dominates the detector noise itself. 
     Detector Array Correlation Signal Processing for Passive CAT 
     As noted above, the passive system uses correlation techniques to reduce the effects of thermal background noise to allow for detection of CAT at a distance from the system of ≥10 km. The type of correlation techniques may depend on the number of detector arrays employed in the passive system. Returning to  FIG. 1 , if the detector array  110  comprises a single detector array, the processing electronics  130  may calculate a correlation value based on auto-correlation of the pixels of the single detector array. If the detector array  110  comprises a plurality of detector arrays, the processing electronics  130  may calculate a correlation value based on multi-correlation of corresponding pixels of the plurality of detector arrays. For example, if the detector array  110  comprises two detector arrays, such as the detector arrays  110   a  and  110   b  shown in  FIG. 1 , the processing electronics  130  may calculate a correlation value based on a cross-correlation of corresponding pixels of the two detector arrays. 
     An example of a correlation technique for the detector array  110  comprising two detector arrays is now described. Each of the detector arrays  110   a  and  110   b  are arranged to image an overlapping, though not identical region in space. 
     The correlation coefficient ρ X,Y  between two random variables X and Y having standard deviations σ X  and σ Y  is defined as: 
               p     X   ,   Y       =       corr   ⁡     (     X   ,   Y     )       =       cov   ⁡     (     X   ,   Y     )           σ   X     ⁢     σ   Y                 
where corr(X,Y) is the correlation function, nd cov(X,Y) is the covariance function.
 
     For two detector matrix arrays A and B, the covariance of the elements in the m by n arrays A and B is defined as: 
               cvar   ⁡     (     A   ,   B     )       =       1   mn     ⁢       ∑     i   =   0       m   -   1       ⁢           ⁢       ∑     j   =   0       n   -   1       ⁢           ⁢       [       A     i   ,   j       -     mean   ⁡     (   A   )         ]     ⁢       [       B     i   ,   j       -     mean   ⁡     (   B   )         ]     _                   
where A i,j  and B i,j  are the i, jth elements of the arrays A and B, respectively, and the bar indicates complex conjugation, and
 
     
       
         
           
             
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     The correlation function of the two detector arrays can be calculated by the processing electronics  130  based on the above equation for the covariance of the elements. 
     For small array sizes, perhaps 100 2  elements, the correlation value, Corr (A, B), rapidly computes a scalar between 0 (0%) and 1 (100%) as the correlation value; i.e., Pearson&#39;s r coefficient. 
     The processing electronics may then compare the value of the correlation value with a threshold value, which may be between 0.8 and 0.85 for example, and if the correlation value is above the threshold value, the processing electronics indicates that an event has occurred, where the event may be the existence of CAT. 
     The processing electronics may calculate the correlation coefficient many times per second with dedicated fast logic (&gt;5 times per second dwell/integration time), to provide a continuous stream of correlation values that could be compared to a threshold level, above which a high probability of CAT signals is expected to have been the cause. For example, the processing electronics may calculate the correlation coefficient 1 to 10 times per second. 
     While a cross-correlation coefficient is calculated for two detector arrays, alternatively the auto-correlation coefficient may be calculated for a single detector array, or a triple-correlation coefficient may be calculated for a three detector array arrangement. 
     Correlation Performance Estimates for a Two Detector Array Passive CAT Scheme 
     Below is described a simulation for estimating the correlation performance for a two detector array arrangement. From the calculation above regarding signal to noise ratios in the presence of daytime sky, the RMS noise level is taken to be about 0.5. In this simulation there are two sets of 10×10 matrix elements, corresponding to a 10×10 arrangement of pixels in two detector arrays, with numbers for the noise value taken from a random distribution of range 0 to 1. 
     In this simulation, the peak signal levels, representing CAT fluctuations of around 2° C. will take values from 0.5 (same as the rms noise) to 2, and will only populate 20% of the sensor array elements, to which the noise will also be added. 
     As a simulation, for the 20% of elements, the randomly populated signal matrix is taken as is shown in  FIG. 5 , where L is the signal level for each pixel having the signal level L, while the remaining 80% of the elements have a 0 signal. This simulation corresponds to the situation where a “turbulent cluster” is mostly imaged in the top left hand corner of the signal matrix. The signal matrix for the second detector array has similar but not the same spatial characteristics as that for the first detector array. 
     For the noise backgrounds, two matrices, one for each of the signal matrices, are constructed with random numbers as described, where one of the noise matrices, the one of the first detector array, is shown in  FIG. 6 . 
     Setting the signal level L at 1.0, the signal plus noise matrix has the typical form as shown in  FIG. 7 . The correlation value, Corr (A, B), may be determined based on the signal plus noise matrices of the two detector arrays according to the above equations. 
     The table below illustrates what happens to the correlation coefficient as the value of the signal level L of the 20% filled signal pixels is raised from an RMS noise value of 0.5 up to 2.0. 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 L 
                 Correlation value 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 0.5 
                 0.36 
               
               
                   
                 1.0 
                 0.7 
               
               
                   
                 1.5 
                 0.84 
               
               
                   
                 2.0 
                 0.9 
               
               
                   
                 2.5 
                 0.94 
               
               
                   
                 3.0 
                 0.96 
               
               
                   
                 4.0 
                 0.97 
               
               
                   
                   
               
            
           
         
       
     
     A correlation threshold value in the region of 0.8 to 0.85 allows for the beginning of detection of a fairly low and sparsely populated detector element against a similar level of RMS noise background. 
     Higher correlation values would be expected to be achieved for larger sizes, such as for 100×100 or 1000×1000, presuming the correlation values can be correlated in real time. 
     Mounted Optical System 
     As illustrated in  FIG. 8 , the above described thermal imaging system may be mounted in practice on an appropriate platform.  FIG. 8  illustrates a system  800  for detecting air turbulence. The system  800  comprises a structure  810 , and a passive thermal imaging system  100 , such as that described with respect to  FIG. 1 , mounted on the structure  800 . As can be seen in  FIG. 8 , the detector arrays  110   a  and  110   b  may be arranged in separated regions of the structure  810 , and to image the same object  150 . 
     The structure  800  may be a vehicle or a ground based platform. The vehicle may be an aircraft, a spacecraft, or an unmanned aerial vehicle (UAV), for example. 
     The embodiments of the invention has been described in detail with particular reference to preferred embodiments thereof, but it will be understood by those skilled in the art that variations and modifications can be effected within the spirit and scope of the invention.