CN107368617B - Ground-air detection infrared imaging system action distance calculation method based on Lowtran7 atmospheric software - Google Patents

Ground-air detection infrared imaging system action distance calculation method based on Lowtran7 atmospheric software Download PDF

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CN107368617B
CN107368617B CN201610319373.4A CN201610319373A CN107368617B CN 107368617 B CN107368617 B CN 107368617B CN 201610319373 A CN201610319373 A CN 201610319373A CN 107368617 B CN107368617 B CN 107368617B
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任侃
田杰
陈钱
顾国华
钱惟贤
周骁骏
张海越
汪鹏程
万敏杰
顾煜洁
王伟杰
姚哲毅
呙星
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Nanjing University of Science and Technology
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Abstract

The invention provides a method for calculating the acting distance of an earth-air detection infrared imaging system based on Lowtran7 atmospheric software. Firstly, analyzing ground and air detection targets and background radiation, modeling the acting distance of an infrared system from the angle of contrast, secondly, calling Lowtran7 atmospheric software to generate databases of atmospheric radiance and atmospheric transmittance, wavelength, path distance and observation zenith angle under different atmospheric conditions, integrating discrete data by using a spectrum segmentation method, calculating the acting distance under the corresponding path distance, and calculating the maximum path distance which enables the path distance to be equal to the calculated distance to be used as the final acting distance of the infrared system. The method has the characteristics of high efficiency, strong applicability, high calculation accuracy and the like.

Description

Ground-air detection infrared imaging system action distance calculation method based on Lowtran7 atmospheric software
Technical Field
The invention belongs to the technical field of infrared system modeling simulation, mainly relates to the technical field of target detection acting distance modeling of an infrared system, and particularly relates to a method for calculating the acting distance of an earth-air detection infrared imaging system based on Lowtran7 atmospheric software.
Background
The infrared imaging system has great advantages in the aspects of poor weather or night tracking, guidance and the like, so that the infrared imaging system is more and more widely applied, and the importance of the performance evaluation of the infrared imaging system is more and more prominent. For an infrared imaging system, the working distance is the most important evaluation index, and the working distance refers to the farthest distance for the infrared imaging system to find, distinguish or identify a target under certain atmospheric conditions. The methods for evaluating the action distance mainly include two methods: measurement and modeling. The measuring method is used for measuring the acting distance in an actual external field, the method has the advantages of huge material consumption and high cost, and the whole measuring process is limited or influenced by factors such as the external field environment, the identification time and the like; the model method takes a computer as a tool, predicts the action distance by fully simulating an actual infrared scene, has less consumption and low cost, and is widely applied to the action distance evaluation of an infrared imaging system.
The action distance model method can be started from the aspects of noise equivalent temperature difference, contrast, signal-to-noise ratio and the like. The noise equivalent temperature difference method can be approximated only when the target background temperature difference is not large, and has no universal applicability to the detection scene with large temperature difference. In the process of establishing the model, atmospheric transmission parameters are influenced by factors such as environment and the like to change complicatedly, and the atmospheric transmission parameters are always an insurmountable obstacle in the calculation of the working distance. The atmospheric transmission parameters comprise atmospheric radiance and atmospheric transmittance, and at present, two ways for calculating the atmospheric radiance and the atmospheric transmittance in China generally exist: and carrying out precise calculation by using professional software or carrying out rough calculation by using an empirical formula. Professional atmospheric software is high in calculation accuracy but complex in use, and an empirical formula is usually simple, limited in application range and large in calculation error, and cannot describe the complex atmospheric condition.
Disclosure of Invention
The invention aims to provide a method for calculating the acting distance of an earth-air detection infrared imaging system based on Lowtran7 atmospheric software, which adds the correction to the detection wavelength on the basis of the traditional acting distance model, and obtains a database of atmospheric radiance and transmittance by using Lowtran7 atmospheric software so as to quickly calculate the acting distances of different targets under different detection modes.
In order to solve the technical problem, the invention provides a method for calculating the acting distance of an air-ground detection infrared imaging system based on Lowtran7 atmospheric software, which comprises the following steps:
calling Lowtran7 atmospheric software to generate atmospheric radiance and atmospheric transmittance corresponding to each wave number in a wavelength range; calculating the atmospheric radiance and the atmospheric transmittance between wavelength intervals according to the atmospheric radiance and the atmospheric transmittance corresponding to each wave number to form an atmospheric radiance and atmospheric transmittance database;
step two, calculating the target radiance and the background radiance;
solving the maximum action distance according to an action distance equation;
the equation of the acting distance of the space-based infrared imaging system for detecting the ground target is shown in formula (1)
Figure BDA0000989142350000021
The equation of the acting distance of the ground-based infrared imaging system for detecting the aerial target is shown in formula (2)
Figure BDA0000989142350000022
In the formula (1) and the formula (2), Rk-d C(Rj) Is a path distance RjActing distance, R, of ground target detection by lower space-based infrared imaging systemd-k C(Rj) Is a path distance RjActing distance, A, of lower ground-based infrared imaging system on aerial target detectionTIs the effective radiation area of the target surface, Ad＝d2Is the pixel area of the detector, d is the pixel size, f is the focal length, CthIs detector threshold contrast, LT(Rj) The path received for the detector is at a distance RjFar target radiance, LB(Rj) The path received for the detector is at a distance RjFar background radiance; l isA(Rj) The path received for the detector is at a distance RjThe atmospheric radiance of (a);
assuming that the infrared imaging system range is equally divided into m segments, for each path distance RjCalculating a working distance RK by using a calculation mode of the right side of the equal sign of the formula (1) or the formula (2)jWherein j is 1, 2.. multidot.m; calculating each path distance R from 1 to m in turnjCorresponding range RKj(ii) a At all said range RKjIn the presence of RKj-RjAnd RKj+1-Rj+1Point p, p of opposite sign 1,2, m, the maximum distance of action RKAs shown in the formula (3),
Figure BDA0000989142350000023
further, a target radiance L is calculatedT(Rj) The method comprises the following steps:
firstly, calculating the radiance L of the target by a Planck radiance formula according to the temperature of the target on the ground or in the airT' (λ), the Planck formula is given by equation (4):
Figure BDA0000989142350000031
in the formula (4), c1＝3.742×10-16W·m2Is a first radiation constant, c2＝1.439×10-2m.K is a second radiation constant,0as the emissivity of the target, e is a natural constant, λ is the wavelength, TTIs the target temperature;
then, the target radiance L is calculated according to the formula (5)T(Rj)，
Figure BDA0000989142350000032
In the formula (5), n is the working wavelength range lambdaa～λbEqually divided by the number of intervals of the wave number interval, Δ λiIn order to be a wavelength interval between the first and second wavelength bands,
Figure BDA0000989142350000033
for a wavelength interval of Δ λiAnd a path distance RjCorresponding atmospheric transmission rate.
Further, the background radiance L is calculatedB(Rj) The method comprises the following steps:
for the ground background, in the working wavelength range lambda of the detectora～λbDistance detector R received by inner and empty base detectorsjFar ground background radiance LB(Rj) As shown in equation (6).
Figure BDA0000989142350000034
In formula (6), L'B(lambda) represents the radiance of the floor background itself, which is shown in equation (7),
Figure BDA0000989142350000035
in the formula (7), TBTemperature representative of ground background;
for an airborne background, atmospheric radiance at infinity is taken as background radiance.
Compared with the prior art, the method has the obvious advantages that (1) the method adds the correction based on the detection wavelength, so that the calculation of the target radiance and the background radiance is more in line with the requirement of actual detection, and meanwhile, the efficiency of calculating the integral is improved by using a spectrum segmentation method; (2) the Lowtran7 software is used for obtaining a database of atmospheric radiance and atmospheric transmittance, wavelength, path and observation zenith angle, any detector and target parameters can be calculated, and universal applicability is enhanced; (3) using the method of traversing all paths from 0 to 100km ensures that all solutions can be computed compared to methods using iterative computations.
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FIG. 1 is a schematic flow diagram of the process of the present invention.
FIG. 2 is a detailed flow chart of the method of the present invention.
FIG. 3 is a graphical representation of tropical atmospheric radiance versus wavelength and path distance.
FIG. 4 is a graph of mid-latitude summer atmospheric radiance versus wavelength and path distance.
FIG. 5 is a graph of mid-latitude winter atmospheric radiance versus wavelength and path distance.
FIG. 6 is a graph showing the relationship between the intensity of atmospheric radiation in the summer range of the dipole band and the wavelength and path distance.
FIG. 7 is a graph of sub-band winter atmospheric radiance versus wavelength and path distance.
FIG. 8 is a graphical representation of tropical atmosphere transmission rate versus wavelength and path distance.
FIG. 9 is a graphical illustration of mid-latitude summer atmospheric transmittance versus wavelength and path distance.
Fig. 10 is a graphical representation of mid-latitude winter atmospheric transmittance versus wavelength and path distance.
FIG. 11 is a schematic representation of sub-band summer atmospheric transmittance versus wavelength and path distance.
FIG. 12 is a graphical representation of sub-zone winter atmospheric transmittance versus wavelength and path distance.
Fig. 13 is a schematic view of a two-dimensional planar distribution of range.
Detailed Description
It is easily understood that according to the technical solution of the present invention, without changing the spirit of the present invention, a person skilled in the art can imagine various embodiments of the present invention of the method for calculating the range of the ground-air exploration infrared imaging system based on the Lowtran7 atmospheric software. Therefore, the following detailed description and the accompanying drawings are merely illustrative of the technical aspects of the present invention, and should not be construed as all of the present invention or as limitations or limitations on the technical aspects of the present invention.
With reference to fig. 1 and fig. 2, the method for calculating the range of the ground-air detection infrared imaging system based on Lowtran7 atmospheric software provided by the invention comprises the following steps:
the method comprises the following steps: atmospheric radiance and atmospheric transmittance calculation
1.1 calling Lowtran7 atmospheric software to generate atmospheric radiance and atmospheric transmittance corresponding to each wave number in wavelength range
The Lowtran7 atmosphere software is a low resolution atmosphere model proposed by the united states air force geophysical laboratory, meaning a low resolution atmosphere transmittance calculation program. The data entry file for the Lowtran7 atmospheric software is a text file named tap 5, containing a total of 5 lines of data corresponding to 5 data cards. The first 2 lines of the file are atmospheric mode inputs and the first 2 lines remain unchanged for the set simulation environment. The data in row 3 correspond in turn to the atmospheric path initial altitude, end altitude, initial zenith angle, path length, geocentric angle, earth radius, and program operation mode, and the data in row 4 correspond to the wavelength lower limit, wavelength upper limit, and wavelength interval. In the setting process, the final height, the initial zenith angle and the path length of the third row are sequentially assigned according to the height and the angle interval, Lowtran7 is operated once every time the setting is finished, and the atmospheric radiance and the atmospheric transmittance corresponding to each wave number in the wavelength interval are read in a data output file TAPE 6.
1.2 calculating the atmospheric radiance L between wavelength intervalsA(lambda, R) and atmospheric transmittance taua(λ,R)
In calculating the atmospheric radiance and atmospheric transmittance, the Lowtran7 atmospheric software typically operates over a wavelength range λa～λbThe light is divided into n equal wave number intervals, and the atmospheric radiance and transmittance corresponding to the wave numbers are calculated. The integration of the atmospheric radiance requires converting the wave number into the corresponding wavelength, and then summing the atmospheric radiance of each wavelength interval. Wavelength interval delta lambdai＝λi+1-λiWherein i ═ 1,2,3iRepresenting the wavelength converted from the wavenumber. For wavelength interval Δ λiCorresponding atmospheric band radiance
Figure BDA0000989142350000051
And transmittance in the atmospheric band
Figure BDA0000989142350000052
Can be obtained as formula (1) and formula (2), respectively:
Figure BDA0000989142350000053
Figure BDA0000989142350000054
in the formula (1) and the formula (2)
Figure BDA0000989142350000055
And
Figure BDA0000989142350000056
respectively wavelength lambdaiAnd λi+1Corresponding atmospheric radiance and atmospheric transmittance, the larger the value of n, the longer the wavelength interval Delta lambdaiThe closer the distance is to each other,
Figure BDA0000989142350000057
and
Figure BDA0000989142350000058
the more accurate.
Generally, the acting distance of the infrared imaging system does not exceed a certain maximum value RmFrom 0 to RmIs equally divided into m segments, each segment having a distance interval Δ R, RjJ · Δ R denotes the path distance from 0 to j, j being 1, 2. At a given observation zenith angle, Lowtran7 software is called by a 1.1-step method, and a set of path and wavelength-dependent atmospheric radiance L is obtained by using formula (1) and formula (2)A(lambda, R) and atmospheric transmittance tauaThe database of (λ, R) is shown in equation (3) and equation (4):
Figure BDA0000989142350000059
Figure BDA0000989142350000061
at the same time, in the operating wavelength range lambdaa～λbThe distance of the path received by the detector is RjOf the atmospheric radiance LA(Rj) As shown in the formula (5),
Figure BDA0000989142350000062
step two: calculating target radiance and background radiance
2.1 calculating target radiance received for detection
Radiance L of the target itselfT' (λ) is determined mainly by the target temperature, λ being the wavelength. For a ground target, the difference between the target temperature and the ambient background temperature is not large, and modeling analysis is not performed independently.
For common aerial targets such as airplane missiles and the like, the infrared search system mainly detects the skin on the target surface, and the skin stagnation temperature is the target temperature TTCan be calculated from equation (6).
TT＝TH[1+0.164Ma2](6)
In the formula (6), Ma is the local Mach number of the free flow on the surface of the aerial target, and can be regarded as the flight speed of the aerial target, THWhich may be considered to be the ambient temperature at the altitude of the airborne target. For an air target with a flying height H, the ambient temperature THValues can be simplified according to the rule of formula (7):
Figure BDA0000989142350000063
in the slope observation, the flying height H of the target is Rcos θ, θ is the zenith angle of the slope observation, and R is the path distance.
After the temperature of the ground or air target is obtained, the radiance L of the target is calculated through a Planck radiation formulaT' (λ), the Planck formula is given by equation (8):
Figure BDA0000989142350000064
in the formula (8), c1＝3.742×10-16W·m2Is a first radiation constant, c2＝1.439×10-2m.K is a second radiation constant,0e is a natural constant for the emissivity of the target. Since the atmospheric transmittance obtained by Lowtran7 is a discrete variable, the Planck's formula is integrated by a spectral segmentation method, and λ is within the working wavelength rangea～λbCalculating the distance R received by the detectorjFar target radiance LT(Rj) As shown in formula (9):
Figure BDA0000989142350000071
2.2 calculating the background radiance received by the detector
For terrestrial background, in the operating wavelength range λa～λbOff detector R received by the space-based detectorjFar ground background radiance LB(Rj) As shown in equation (10).
Figure BDA0000989142350000072
In formula (10), L'B(lambda) represents the radiance of the ground background itself, and is also calculated by Planck's formula, if TBIndicating the temperature of the ground background, the radiance L 'of the ground background itself'B(λ) is shown in formula (11).
Figure BDA0000989142350000073
For an airborne background, the airborne background received by a ground-based probe is the atmosphere at infinity. The following conclusions can be drawn due to the call to Lowtran7 software: when the altitude exceeds a certain distance, the atmospheric radiance does not change any more. So that R can be substitutedmRemote atmospheric radiance LA(Rm) Atmospheric radiance L considered to be at infinityA(∞)。
Step three: establishing a working distance calculation model
3.1 parameter input
Before calculating the acting distance of the infrared imaging system, firstly, the parameters of the infrared imaging system are determined, including the pixel area A of the detectordFocal length f, working band lambdaa～λbAnd detector threshold contrast Cth(ii) a Secondly, determining the parameters of the target, for the ground target, mainly the target temperature TTBackground temperature TBAnd the effective radiation area A of the target surfaceTFor aerial targets, mainly the flight height H, the flight speed Ma and the effective radiation area A of the target surfaceT(ii) a Finally, determining atmospheric transmission parameters including atmospheric mode, observation zenith angle, path distance and working wavelength range lambdaa～λb。
3.2 establishing a function distance formula according to the target radiance and background radiance model
The equation of the acting distance of the space-based infrared imaging system for detecting the ground target is shown in formula (12)
Figure BDA0000989142350000081
The equation of the acting distance of the ground-based infrared imaging system for detecting the aerial target is shown in formula (13)
Figure BDA0000989142350000082
In the formula (12) and the formula (13), ATIs the effective radiation area of the target surface, Ad＝d2Is the pixel area of the detector, d is the pixel size, f is the focal length, CthIs the detector threshold contrast.
Step four: solving the formula of action distance
For each path distance RjAn action distance can be calculated by using the equal sign right side of the formula (12) or the formula (13)RKjWherein j is 1, 2.. times.m, and all R are calculated sequentially from 1 to mjCorresponding range structure RKj. At these discrete results RKjIn the presence of RKj-RjAnd RKj+1-Rj+1The point p of opposite sign, p being a certain point from 1 to m, the solution R of the equation of action distance equation (12) and equation (13)KAs shown in equation (14).
Figure BDA0000989142350000083
If there are multiple solutions, the maximum solution is the final range.
In a common iterative calculation method, the Lowtran7 software needs to be called repeatedly when calculating the acting distances of different targets under the same weather condition, so that unnecessary processing time is increased. The method reduces the calling times of Lowtran7 software and improves the calculation efficiency.
According to the invention, the infrared system action distance is modeled based on the contrast of radiance between a target and a background, the influence of wavelength which is not considered originally on radiance calculation is added, a database of atmospheric radiance and atmospheric transmittance, wavelength and path distance is obtained by calling Lowtran7 atmospheric software, any target can be calculated through the database, the atmospheric software is not required to be called circularly for each target, and the action distance calculation efficiency and accuracy are improved.
In the invention, the calculation of the radiation contrast between the target and the background is divided into two types according to the detection mode: one is the detection of an aerial target by the ground, the aerial target can be an aircraft such as an airplane, a missile and the like, the aerial background is the atmosphere above the target, and the contrast between the target and the background can be considered as the ratio of the target radiance plus the atmospheric radiance between the target and a detector to the atmospheric radiance above the target; another is the detection of ground objects in the air, which may be vehicles, people or buildings, the ground background is the ground environment near the object, and the contrast between the object and the background is the ratio of the object radiance plus the atmospheric radiance between the object and the detector to the ground radiance plus the atmospheric radiance between the ground and the detector.
In the present invention, the calculation of the radiation contrast between the target and the background is divided into two types. When a ground aerial target is detected, the calculation of the target radiance is determined by the target temperature according to the Planck's law, the calculation of the aerial target temperature requires to know the height of the target and the flying speed of the target, and the target radiance reaching a detector needs to be multiplied by the atmospheric transmittance between the target and the detector; the atmospheric radiation above the target can be regarded as atmospheric radiation at infinity to a certain extent, and in actual calculation, the atmospheric radiation at infinity can be approximately equal to the atmospheric radiation at 100 km; the atmospheric path radiation between the target and the detector is related to the path distance, and a database of atmospheric path radiation and transmittance and the path distance and wavelength can be obtained by assigning the path distance in Lowtran7 atmospheric software. When the ground target is detected in the air, the radiance of the target only needs to consider the temperature of the target, the ground background radiation also needs to know the temperature of the ground environment, and the atmospheric path radiation between the target and the detector can be calculated through Lowtran7 atmospheric software.
In the invention, a Lowtran7 atmosphere software is used for calling to obtain a database of atmosphere radiance and atmosphere transmittance, wavelength and path distance. When the target and the atmospheric radiance are calculated, the wavelength range is divided by using a spectrum division method, so that the wavelength range is conveniently integrated in a Planck formula, and the calculation efficiency is improved in actual programming calculation.
In the invention, a Lowtran7 atmosphere software is used for calling to obtain a database of atmosphere radiance and atmosphere transmittance, wavelength and path distance. In the process of calling Lowtran7 atmospheric software, firstly, a TAPE5 file is set, and after the Lowtran7.exe file is executed, data of the TAPE6 file, of which the wavelength corresponds to the atmospheric radiance and the atmospheric transmittance, are read. By setting the path distance, the height and the zenith angle in the TAPE5 file, a three-dimensional database of the atmospheric radiance, the transmittance, the wavelength, the path distance and the zenith angle is formed, calling in the calculation of the action distance is facilitated, and the efficiency of calculation of an action distance equation is improved.
The invention considers that the influence of the wavelength on the action distance is not negligible, the action distance is calculated for the path from 0 to 100km in sequence, the solution of the action distance equation is obtained by utilizing the solution formula, if a plurality of solutions exist, the maximum solution is considered as a final result, and the situation that the detector can detect not only a bright target but also a dark target can be proved.
To illustrate the advantage of the present invention in the calculation of the range of the infrared system, the method of the present invention was used to create an atmospheric radiance and transmittance database for 5 typical atmospheric modes, as shown in fig. 3 to 7, where X-axis is the wavelength, Y-axis is the path distance, Z-axis is the atmospheric radiance, as shown in fig. 8 to 12, X-axis is the wavelength, Y-axis is the path distance, and Z-axis is the atmospheric transmittance. And calculating the distribution condition of the acting distance in the whole zenith angle range in the mid-latitude summer. As shown in fig. 13, the abscissa is the horizontal distance, the ordinate is the vertical distance, the dotted line is the detection of the ground target by the air base, and the solid line is the two-dimensional plane distribution diagram of the action distance established by the detection of the ground target by the air base. Through calculation, the horizontal observation action distance calculated in the middle latitude summer atmosphere mode is closer to the real measured value.

Claims (1)

1. A ground-air detection infrared imaging system action distance calculation method based on Lowtran7 atmospheric software is characterized by comprising the following steps:
calling Lowtran7 atmospheric software to generate atmospheric radiance and atmospheric transmittance corresponding to each wave number in a wavelength range; calculating the atmospheric radiance and the atmospheric transmittance between wavelength intervals according to the atmospheric radiance and the atmospheric transmittance corresponding to each wave number to form an atmospheric radiance and atmospheric transmittance database;
step two, calculating the target radiance and the background radiance;
solving the maximum action distance according to an action distance equation;
the equation of the acting distance of the space-based infrared imaging system for detecting the ground target is shown in formula (1)
Figure FDA0002524332980000011
The equation of the acting distance of the ground-based infrared imaging system for detecting the aerial target is shown in formula (2)
Figure FDA0002524332980000012
In the formula (1) and the formula (2), Rk-d C(Rj) Is a path distance RjActing distance, R, of ground target detection by lower space-based infrared imaging systemd-k C(Rj) Is a path distance RjActing distance, A, of lower ground-based infrared imaging system on aerial target detectionTIs the effective radiation area of the target surface, Ad＝d2Is the pixel area of the detector, d is the pixel size, f is the focal length, CthIs detector threshold contrast, LT(Rj) The path received for the detector is at a distance RjFar target radiance, LB(Rj) The path received for the detector is at a distance RjFar background radiance; l isA(Rj) The path received for the detector is at a distance RjOf the atmospheric radiance, LA(Rm) Is RmThe ambient radiance at a distance;
assuming that the infrared imaging system range is equally divided into m segments, for each path distance RjCalculating a working distance RK by using a calculation mode of the right side of the equal sign of the formula (1) or the formula (2)jWherein j is 1, 2.. multidot.m; calculating each path distance R from 1 to m in turnjCorresponding range RKj(ii) a At all said range RKjIn the presence of RKj-RjAnd RKj+1-Rj+1Point p, p of opposite sign 1,2, m, the maximum distance of action RKAs shown in the formula (3),
Figure FDA0002524332980000013
further, calculating the orderAmplitude brightness LT(Rj) The method comprises the following steps:
firstly, calculating the radiance L 'of the target by a Planck radiance formula according to the temperature of the ground or air target'T(λ), the Planck formula is given by formula (4):
Figure FDA0002524332980000021
in the formula (4), c1＝3.742×10-16W·m2Is a first radiation constant, c2＝1.439×10-2m.K is a second radiation constant,0as the emissivity of the target, e is a natural constant, λ is the wavelength, TTIs the target temperature;
then, the target radiance L is calculated according to the formula (5)T(Rj)，
Figure FDA0002524332980000022
In the formula (5), n is the working wavelength range lambdaa～λbEqually divided by the number of intervals of the wave number interval, Δ λiIn order to be a wavelength interval between the first and second wavelength bands,
Figure FDA0002524332980000023
for a wavelength interval of Δ λiAnd a path distance RjA corresponding atmospheric transmittance;
further, the background radiance L is calculatedB(Rj) The method comprises the following steps:
for the ground background, in the working wavelength range lambda of the detectora～λbDistance detector R received by inner and empty base detectorsjFar ground background radiance LB(Rj) As shown in the formula (6),
Figure FDA0002524332980000024
in formula (6), L'B(λ) represents the ground background itselfRadiance, which is shown in equation (7),
Figure FDA0002524332980000025
in the formula (7), TBTemperature representative of ground background;
for an airborne background, atmospheric radiance at infinity is taken as background radiance.
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