CC BY
16
Visnyk N'l'UU KP1 Seriia Radiolekhnika tiadioaparatobuduummia, "2017, Iss. 69, pp. 30—34
УДК 681.78
Calculation Model for Optoelectronic Remote Sensing System's Radiometric Resolution at Arbitrary Viewing Angles
Kolobrodov, V. H.1, Lykholit, M. I.2, Mykytenko, V. I.\ Tiagur, V. M?, Dobrovolska, К. V?
1 National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2Arsenal Special Device Production State Enterprise
E-mail: v. niikil.cnko&nU-pef .kpi.ua
Introduction. One of the urgent, problems, which are facing developers of satellite optoelectronic remote sensing systems (ORSS), is to improve the images quality. Image quality is determined, above all, by its radiometric resolution, which means minimum difference between brightness or reflectivity of object and background, which can be detected by ORSS with a given probability. Modern ORSS make possible viewing angle deviation, which causes significant image distortions.
Formulation of the problem. The purpose of the paper is to develop physical and mathematical radiometric resolution model of satellite remote sensing optoelectronic systems at arbitrary sight angles. Video signal formation model and radiometric resolution study. Solar radiation that is reflected from the Earth's surface on which the object of observation is placed, passes through atmosphere and enters into transmitting camera lens. The lens forms image of the object and the background radiation in the detector plane. Detector converts illuminance distribution to electric signal, which forms video signal after scanning. The object of observation has uniform spectral reflectance over its size and its angular size is much bigger than ORSS instantaneous field of view. The object is situated on Earth's surface with uniform spectral reflection coefficient.. Both object, and background reflect, light, on Lambert's law. An example of ORSS radiometric resolution calculation model was considered.
Conclusions. On the basis of proposed optoelectronic remote sensing system model there was developed method of determination its radiometric resolution at. arbitrary angles of sight.. Study of the model showed that., increasing of viewing angle significantly deteriorates optoelectronic system spatial resolution while the radiometric resolution is unchanged.
Key words: remote sensing: radiometric resolution: spaceborne optoelectronic imager
Intoduction
Optoelectronic remote sensing systems (ORSS) are widely used in various fields of human activity [1]. One of the urgent problems, which are facing developers of snch systems, is to improve the quality of satellite images. Image quality is determined, above all. by-its energy (radiometric) resolution. Energy resolution means minimum difference between brightness or reflectivity of object and background of large size, which can be detected by ORSS with a given probability. Modern ORSS allow yon to change the viewing angle, which is determined by angle between optical axis of sensor and Nadir. However, there are significant image distortions which are cansed by deviation of the optical axis. Considerable amount of researching works [2 5] were devoted to ORSS image quality. At the same time there are not enough studies of satellite ORSS radiometric resolution at arbitrary angles of sight in the scientific literature.
1 Formulation of the problem
The purpose of this paper is to develop physical and mathematical radiometric resolution model of satellite remote sensing optoelectronic systems at arbitrary-sight angles.
2 Video signal formation model
Process of video signal formation in ORSS is as follows. Solar radiation that is reflected from the Earth's surface on which the object of observation is placed, passes through atmosphere and enters into transmitting camera lens. The lens forms image of the object and the background radiation in the detector plane. Detector converts illuminance distribution to electric signal, which forms video signal after scanning. Let's consider elements of the model in detail. The object of observation is placed on a uniform background of Earth's surface, which is characteri-
zed by its albedo pb ■ The object has a reflection coefficient pt, that is greater than the albedo by Ap. Sometimes is Ap determined as follows:
Pt - Pb Pb '
(1)
If the object and background reflect solar radiation according to Lambert's law and Sun creates on the Earth surface spectral illumination E0X then brightness of the object and the background in the working spectral range Ai.. .X2 will be [ ]
Lt = IJ Pt (A) Eox (A) dX;
Ai
A2
Lb = ^ J Pt (A) Eox (A) dX
o linear X x y in the object space (on the Earth's surface):
o linear X' x Y' in the images space (in detector plane):
- spectral range A1 ...X2, taking into account respective spectral channel:
- spectral transmission coefficient t0 (A) and integral transmission coefficient t0 for corresponding spectral channel.
The lens forms an image of object and background in detector plane with illumination contrast
(2)
2
ae'=î (!) / -(A) "(A) ■
That is useful signal is generated duo to object and background reflectance difference according to absolute brightness contrast
ALe = 1 f [Pt (A) - Pb (A)] Eox (A) dX. (3)
The atmosphere transforms the radiation, which propagates from the object and background to the sensor, duo to absorption and scattering. The atmosphere is characterized by the spectral transmi-ttance ta (A) and integral transmittance ta'-
ta = E0/E5,
where E5 is integrated illumination, which is created by the Sun on top of atmosphere in the working spectral range and E0 is integrated illumination of the Earth's surface. In certain cases E5 =4,8 • 10-2 W/cm2 and E0 = 2,4 • 10-2 W/cm2 so for further calculations we assume ta = 0,5. Analysis of the atmosphere influence on the ORSS operation considering spectral range, celestial latitude, the Sun height, time of day and year, cloud cover and atmospheric conditions requires additional research. The optical system consists usually of three principal elements: the main lens, spectral beam splitter and flat mirror, which changes pointing direction (in some cases there is no mirror or beam splitter). The most important element of ORSS the lens will be modeled using these parameters [6]:
- focal length f;
- relative aperture Dp /f0 or effective f-number keff = f /Dp, where DP is diameter of entrance pupil;
field of view: o angular 2wq ;
• E0x (A) [Pt (A) - Pb (A)] dX. (4)
CCD array detectors are commonly used in ORSS. Their features are:
- scanning frequency fd;
- noise equivalent exposure Hn;
- pixel size V^ x Wd',
- distance between pixels centers Al^;
- number of pixels N^;
- sensitivity Rd-
3 Radiometric resolution
To determine the ORSS radiometric resolution let's
1
The Cartesian coordinate system is located on the Earth's surface so that y axis coincides with satellite motion direction and x axis forms angle of 90° — 0VX with the optical axis. Satellite flight altitude is hf.
Let the object of observation has uniform spectral reflectance pt (A) over its size and its angular size is much bigger than ORSS instantaneous field of view. The object is situated on Earth's surface with uniform spectral reflection coefficient pb (A). Both object and background reflect light on Lambert's law.
Then the spectral brightness of object and background surfaces is defined as [2]
Lt (A) = Pt (A) ^(A) = Pb (A) , (5)
where Eq (A) is spectral illumination of the Earth's surface.
2
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Kolobrodov V. H., Lvkholit M. 1., Mvkytonko V. 1., Tiagur V. M., Dobrovolska K. V.
A2
Et = (A) to (A) dX-
AtQ. cos 6V An
At
hf VD WD hf /0 cos2 evx fo cos eVi
( i y
At
cos3 Qv
Ap _ nDl cos2 e„x where Dp is entrance pupil diameter of the lens.
Substitution (5). (8) and (9) into (7) gives
hA2 AD
Et = j ta (A) Lt (A) to (A) dX = (^
■kD^ cos2 0VX cos 6UX
' 4h2 Ad
f0 ) cos3 ev
I rA (A) to (A) Pt (A) ^^dX
Fig. 1. Layout for ORSS spatial resolution determination
If the ORSS optical axis is inclined to object's surface normal at angle 9VX , then spectral radiant flux which enters the lens is
$t (A) = ta (A) Lt (A) AtQo cos d„x, (6)
where ta (A) is atmosphere spectral transmission coefficient and At is object size, which is within ORSS instantaneous field of view, and = Ap/R2 is solid angle within which light enters the entrance pupil of the lens.
Integral illumination of detector by the object of observation is
rA (A) Lt (A) to (A) dX, (7)
= l( if) J TA W to w Eo WPt W dX- (10)
Detector integral illumination, which generates by-Earth's surface, is determined by same equation
Eb j ra (A) to (A) Eo (A) Pb (A) dX. (11)
Detector detects object and Earth's surface illuminance difference
-=« - *=4( D~fr)*
A2
X y TA (A) to (A) Eo (A) [Pt (A) - pb (A)] dX. (12)
ORSS radiometric resolution is determined by minimum difference AEn, which in turn depends on detector exposure threshold Hn
where A^ = V^ Wd is detector pixel area.
For large object its area At that forms the radiation flux on detector pixel is determined by projection of this pixel on the Earth's surface. In fC] it was found that this area is equal to
AEn = ^,
(13)
where ti is detector integration time.
For integrated parameters which are dependent on the wavelength A , equation ( ) turns into
AEn = Kit) tatoEoApn: (14)
(8)
where /0 is lens focal length.
From (8) it is clear that with increasing of viewing angle 9VX the area At increases as well. It causes deterioration of ORSS spatial resolution. At the same time, this should lead to radiometric resolution reduction. To analyze this claim, let's consider Fig. 1, from which the solid angle Q0 can be found
where Apn — pt — pb is reflectance contrast threshold i.e. radiometric resolution.
From the system of equations (13) and (14) radiometric resolution is
Apn
4Hn
( f )' •
(15)
(9)
TAToEoti \ Dp
Analysis of formula (15) shows that ORSS radiometric resolution can be reduced by:
- decreasing of f-number F — f0/Dp or relative aperture Dp/f0 growth. This is most efficient way, since the reduction of F twice leads to improved radiometric resolution in four times:
x
2
2
4
using of low noise detector, which is equivalent to exposure threshold Hn reduction;
increasing integration time ti, which is limited by detector array readout period;
increasing lens transmittance to, which is always less than unity.
Example of ORSS radiometric resolution calculations
Ap„
4 ■ 2 ■ 10-6 ■ 4, 252 0, 5-0, 8 • 295, 3 • 10-3
1, 2-10
-3
As an example of proposed radiometric (energy) resolution calculation model application let's consider ORSS with following parameters:
- lens: focal length is f = 850 mm, entrance pupil diameter is Dp = 200 mm, lens transmittance is to =0,8 in spectral range (Ai — A2) = (0, 5 — 0, 76) pm;
detector silicon CCD array (CCD 151): number of pixels are Nd = 5000, pixel size is V^ x Wd = 7 x 7^m2; scanning frequency is fd = 5 MHz, noise equivalent exposure is Hn = 2 • 10-10 J/m-2.
ORSS radiometric resolution Apn = pt — pb is defined by formula (15) where Hn = 2-10-6 J/m-2 is noise equivalent exposure, ti = Nd/fd = 10-3 s is detector integration time and t0 = 0,8 is average transmittance of the lens.
From Table. 3.10, which is given in monograph [2], with method of numerical integration we find the average illumination, which is created by the Sun at sea level for the solar zenith angle 60o in spectral range (A1 — A2) = (0, 5 — 0, 76). It is E0 = 295, 3 W/m2.
For a vertical path average atmospheric transmission coefficient in cloudless weather is approximately 0.5 in the spectral range (A1 — A2) = (0, 5 — 0,76) [ ]. After substituting all the initial parameters in the formula (15) we obtain ORSS radiometric resolution:
Lens focal length is chosen on condition to ensure ORSS spatial resolution [5]. Therefore, specified radiometric resolution can be achieved by matching the lens entrance pupil diameter Dp. Fig. shows dependence of the ORSS radiometric resolution Apn on the diameter of entrance pupil Dp.
Fig. 2. Dependence of ORSS radiometric resolution on the lens entrance pupil diameter
Conclusions
1. Modern optoelectronic remote sensing systems allow you to change the viewing angle of the Earth's surface. However, there appear significant image distortions which are caused by deviations of viewing axis from nadir. In the scientific literature there are no enough studies of satellite remote sensing optoelectronic systems radiometric resolution at arbitrary angles of sight.
2. On the basis of proposed optoelectronic remote sensing system physico-mathematical model there was developed method of determination its radiometric resolution at arbitrary angles of sight. Study of the model showed that:
(a) Increasing of viewing angle significantly deteriorates optoelectronic system spatial resolution while the radiometric resolution is unchanged;
(6) Radiometric resolution Apn can be reduced by reducing the lens f-number F = /0 /Dp. This is the most effective way, since Apn ~ F2.
(b) Radiometric resolution Apn is also reduced if the system uses a lens with high transmittance and low noise detector.
3. It is advisable to direct further studies on determination how lens aberrations effect on optoelectronic remote sensing system radiometric resolution at arbitrary angles of sight.
References
[1] Jensen .1. R. ("2000) Remote Sensing of the Environment: An Earth Resource Perspective, Prentice-Hall, 592 p.
[2] Kolobrodov V.H. and Lykholit M.l. (2007) Proektuvannia teploviziinykh i televizimykh system sposterezhennia [Design of Thermal Imaging and Television Observation Systems], Kviv, NTUU KP1, 364 p.
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Kolobrodov V. H., Lvkholit M. 1., Mvkytonko V. 1., Tiagur V. M., Dobrovolska К. V.
[3] Gerald C. Holst. ("2008) Electro-Optical Imaging System Performance, Fifth Edition, .ICD Publishing. 538 p.
[4] Vollmerhausen R. H.. Reago D. and Driggers R. G. (2010) Analysis and evaluation of sampled imaging systems, SPIE Press. 304 p. DOl: 10.1117/3.853462
[5] Kolobrodov V.G. (2000) Vplyv aberatsiy ob:yektyva na prostorove rozdilennya kosmichnoho skanera [EIToct of lens aberrations at spaceborne scanner spatial resolution]. Naukovi visit NTUU "КРГ', Vol. 19. No 5. pp. 110 112.
[6] Schuster N. and Kolobrodov V. G. (2004) Infrarotthermographie (Zweite, uberarbeitete und erweiterte Ausgabe), .lohn Wiley & Sons. 354 p.
Ф 1зико-математична модель для ви-значення радюметричного роздшення косм!чних оптико-електронних систем дистанцшного зондування Земл! при довшьних кутах в!зування
Колобродив В. Г., Лихолип М. /., Микитенко В. /., Тягур В. М., Добровольська К. В.
У статт досл!джуеться радюметрнчпе (епергетичпе) роздшеппя косм1чпо1 оптико-електрошю! зображуючо! системи видимого д!апазопу спектра. Епергетпчпе роз-дглеппя представлено як пороговпй контраст коефщь епта в!дбнття земно! поверхш при задапш величин! порогово! експозицп. Розгляпуто змшу епергетичного
роздшеппя при пахпл! в1зирио1 ос! в!д надира. Показано. що з! збглынеппям кута в1зуваппя епергетичпе роздшеппя залишаеться позмшшш.
Клюновг слова: дистапцшпе зопдуваппя: радюметрн-чпе роздглеппя: косм1чпий оптико-електрошшй сканер
Физико-математическая модель для определения радиометрического разрешения космических оптико-электронных систем дистанционного зондирования Земли при произвольных углах визирования
Колобродов В.Г., Лихолит Н.И., Микитенко В.И., Тягур В.Н., Добровольская Е.В.
В статье исследуется радиометрическое (энергетическое) разрешение космической оптико-электрошюй изображающей системы видимого диапазона спектра. Разрешение представлено как пороговый контраст коэффициента отражения земной поверхности при заданной величине пороговой экспозиции. Рассмотрено изменение разрешения при наклоне визирной оси от надира. Показано, что с увеличением угла визирования энергетическое разрешение остается неизменным.
Ключевые слова: дистанционное зондирование: радиометрическое разрешение: космический оптико-электронный сканер
