Correction of Atmospheric Refraction Geolocation Error for High Resolution Optical Satellite Pushbroom Images

Ming Yan, Chengyi Wang, Jianglin Ma, Zhiyong Wang, and Bingyang Yu

Abstract When an optical remote sensing satellite is imaging the Earth by the relative velocity of the satellite platform and target to in-orbit, the propagation direction of the Line of Sight (LOS) correct light aberration. The atmospheric refraction is rarely will be changed because of atmospheric refraction. This will considered and corrected because they are specific to each result in a geolocation deviation on the collinear rigorous acquisition location and information about the atmosphere. geometric model for direct georeferencing, pushbroom images. In this paper, we focus on atmospheric refraction and analyze To estimate and correct the atmospheric refraction geolocation how it can be better processed to reduce the geolocation error. error, the LOS vector tracking algorithm is introduced and a The atmospheric refraction changes the LOS propagation di- weighted mean algorithm is used to simplify the ISO standard rection of satellite imaging in-orbit, which results in the points atmospheric model into a troposphere and stratosphere, i.e., of detector, projection center of imaging payload, and imaged two layers spherical atmosphere. The simulation result shows object no longer following the rigorous collinear model. Several the atmospheric refraction will introduce about 2 m and 7.5 pioneering researches have confirmed the effect of atmospheric m geometric displacement when the spacecraft is off-pointed refraction on rigorous geometric model estimation. For exam- view at 30 and 45 degree angle, respectively. For a state-of-the- ple, Gyer (1996), Wang (2007), and Wei (2006) have found the art high resolution satellite, the atmospheric refraction dis- atmospheric refraction will have an impact on aerial photo- placement shall be corrected. The method has been practiced grammetry. While the aerial refraction correction formulas are in the DMC3/TripleSat Constellation to remove the atmospher- valid up to the normal aircraft flying height, they are delivering ic refraction geolocation error without ground control points. the wrong results for a spaceborne image (Jacobsen, 2004). For atmosphere refraction effects on a space image, Jacobsen (2004) Delivered by andIngenta Dowman (2012) gave the refraction correction formula Introduction IP: 192.168.39.211 On: Fri, for24 theSep nadir 2021 space 20:01:12 image based on the 1959 ARDC standard Satellite remote sensing imageCopyright: geolocation American is about Society determin for Photogrammetry- atmospheric. andNoerdlinger Remote (1999) Sensing targeted on MODIS satellite ing the correspondence between the pixel’s Cartesian coordi- data and researched the atmospheric refraction by developing nate and geodetic coordinate. The geometric transformation an analytical method to calculate the angle of the refraction between these two systems can be expressed by a rigorous assuming a single layer of spherically symmetrical atmosphere. geometric model, which is established based on a collinear Saastamoinen (1972) expressed a simple atmospheric refraction equation with interior orientation parameters from the imag- angle calculation formula for radio ranging of low Earth orbit ing payload and exterior orientation parameters of the satel- satellites. Oh and Lee (2011) simply extended the Saastamoinen lite platform (Crespi et al., 2007; Fan et al., 2011; Habib et al., model to express the constant related to the object’s terrain and 2007; Jeong and Bethel, 2010 and 2014; Jiang et al., 2013 and satellite altitude. However, it rarely has the documentation to 2014; Leprince et al., 2007; Lussy and Greslou, 2012; Mahapa- study the procedure and method regarding the atmospheric tra et al., 2004; Müller et al., 2012; Pan et al., 2013; Poli and refraction correction for a high resolution optical satellite. Toutin, 2012; Radhadevi et al., 2011; Tang et al., 2012; Toutin, This study, based on a ray tracking physical model, rigor- 2004). The accuracy of a rigorous geometric model depends ously describes the LOS propagation direction of the satellite on the interior and exterior orientation parameters, such as imaging sensor to the Earth surface object through the atmo- the focal length, detector size, lens, detector line distortion of sphere. Meanwhile, the International Organization for Stan- the imaging payload, and the ephemeris and attitude system- dardization (ISO) (1975) atmospheric model and the Owens atic error of satellite platform. Also, the atmospheric refrac- (1967) optical refraction index calculation algorithm are used tion and light aberration will have an impact on the rigorous to calculate the atmospheric refraction index at any position. geometric model estimation (Lussy et al., 2012; Oh and Lee, In the following sections, first we will describe the LOS ray 2011). The distortions of the interior and exterior orientation tracking geometric algorithm, and then analyze the geoloca- parameters are generally corrected during satellite in-orbit tion deviation introduced by atmospheric refraction. After geometric calibration and validation operation (Gruen and that, we will reveal how we can use the deviation to cor- Kocaman, 2008; Leprince et al., 2008; Wang et al., 2014; Yas- rect the atmospheric refraction geolocation error in the ECEF tikli and Jacobsen, 2005). Greslou et al. (2008) have analyzed coordinate system. Compared to previous research, more the Line of Sight (LOS) in the Earth Centered Earth Fixed reasonable atmospheric refraction displacement estimation (ECEF) coordinate system for the apparent deflection caused can be achieved. Because we not only take the latitude and Ming Yan, Chengyi Wang, and Jianglin Ma are with altitude into account when calculating atmospheric refraction the Institute of Remote Sensing and Digital Earth, Photogrammetric Engineering & Remote Sensing Chinese Academy of Sciences, 20 Datun Road, Chaoyang Vol. 82, No. 6, June 2016, pp. 427–435. District, Beijing, 100101, P. R. China ([email protected]). 0099-1112/16/427–435 Zhiyong Wang and Bingyang Yu are with the Twenty First © 2016 American Society for Photogrammetry Century Aerospace Technology Co., Ltd., 26 Jiancaicheng East and Remote Sensing Road, Haidian District, Beijing, 100096, P. R. China. doi: 10.14358/PERS.82.6.427

Photogrammetric Engineering & Remote Sensing June 2016 427

05-16 June Peer Reviewed.indd 427 5/16/2016 10:28:43 AM index, we also track the LOS refracted direction in different atmospheric layers. Therefore, the proposed method is more conformal to the LOS propagation characteristics in the stratified atmosphere. By compensating the atmospheric refraction error in the rigorous collinear geometric model, the geometric positioning accuracy of satellite remote sensing image without ground control points can be improved. Since DMC3/TripleSat constellation was launched on 10 July 2015, this study has been continually experimenting with the three 1 m resolution optical satellites. The atmospheric refraction correction algorithm has been integrated into the DMC3/TripleSat rigorous geometric model, which is used to produce the Level-1A basic image products.

Atmospheric Refraction Geolocation Error The stratified Earth’s atmosphere comprises mainly gas molecules, water vapor, and aerosols. When the Sun’s ray is reflect- ed by ground objects through the atmosphere to the imaging detectors in-orbit, the propagation direction of reflection rays shall be deviated due to atmospheric refraction. Conversely, from the view of detectors of imaging payload, the atmospheric refraction results in a deviation of LOS from its original propagation direction and lead to an atmospheric refraction geolocation error. In the following, we will model the geolocation error with rigorous mathematic formulas. In Figure 1, suppose atmospheric refraction does not exist, the line dSP represents the LOS of one detector with view angle α, where Point d refers to the detector (the distance from the imaging detector to the linear array principal Point o is also expressed as d), Point S is the perspective center of optical imaging payload, and Point P is the intersection of LOS and the Earth’s ellipsoid. This line dSP also contains Point P0, which is the intersection of LOS and the top atmosphere. In order to describe the ray trackingDelivered by Ingenta geometric algorithm of LOS vector, it is assumedIP: 192.168.39.211 the Earth’s at- On: Fri, 24 Sep 2021 20:01:12 mosphere is a single layer homogeneousCopyright: sphericalAmerican atmosphere Society for Photogrammetry and Remote Sensing only consisting of gas molecules and water vapor: h is the atmosphere thickness and n is the atmospheric refraction index (n >1). Point P1 is the intersection of LOS deviated by atmospheric refraction and the Earth ellipsoid. The line of d1SP1 (dashed line) is the atmospheric refraction bias compensated LOS. Also, in Figure 1, we define f as the focal length, H as satellite platform height, and R as the Earth’s mean radius. The ground surface distance between point P and P1 is the atmospheric refraction geolocation error that would exist in rigorous Figure 1. LOS propagated in single layer spherical atmosphere. geometric model if atmospheric refraction is not considered. Next, we will calculate the atmospheric refraction geoloca- nrsins= in i (4) tion error with a rigorous mathematic formula using symbols predefined in Figure 1. According to the sine law we have the  sin i  r arcsin (5) following formulas: ⇒=    n  RR+ H where n is the refraction index, i is the incident angle, and r is = (1) sinsαβin()180 − the refraction angle. We defineθ as ∠SOP, θ0 as ∠SOP0 as ∠P0OP1 and ∆θ as  RH+  ∠P1OP. Since OP0 = R + h, OP = R, and the refraction angle r ⇒=βαarcsin  sin  (2)  R  is known in ∆P0OP1, and θ1 can be calculated: ()Rhsin i where α is the off-view angle, and β is the incident angle of  +  θ1 = arcsin   − r (6) LOS to the earth ellipsoid without considering the atmospher-  R  ic refraction error. In the same way, the incident angle of LOS to the top atmosphere can be calculated: Known as the off-view angle α, the incident angle i and β in ∆SOP0, θ0 can be calculated:  RH+  (3) i = arcsin  sin α  θβ=−α (7)  Rh+  θα0 =−i (8) where h is the atmosphere thickness. Combining the above equations, angle ∆θ (radian) and arc According to the Snell refraction law, the refraction angle r length are calculated. is as follows:

428 June 2016 Photogrammetric Engineering & Remote Sensing

05-16 June Peer Reviewed.indd 428 5/16/2016 10:28:51 AM   2..23366 710 79227.75141× 104   P Δθ=−θθ01− θ DP00..11 001137..10−−63P 2 37321 10 W (9) WW=+ ( +× W ) −×+−2 + 3   (14)   T TT  T PP1 =•R ∆θ (10) PPSa=−Pw If the characteristics of stratified Earth’s atmosphere and (15) the atmospheric refraction index are known, the refraction Tt=+273.15 (16) deviation angle of each layer can be calculated by the iterative σ = 1 (17) calculation of Equations 3, 5, and 6. Thus, the atmospheric λ

refraction deviation angle ∆θ is calculated: In the above equations, PS (Pascal) is dry air pressure after water vapor pressure removed, T is the absolute temperature Δθθ=−θθ01−− − θj (11) and σ is the wave number of monochromatic light with wavelength λ micron. where j is the number of layered atmosphere. Atmospheric Temperature (t) Atmospheric Refraction Index of Monochromatic Light The international standard atmosphere model (ISO 2533: 1975) The imager of a high resolution optical satellite is often com- is used to calculate the atmospheric temperature variation posed of blue (0.45 - 0.52 μm), green (0.53 - 0.60 μm), red (0.63 with altitude. The ISO 1975 atmosphere model defines that the - 0.69 μm), near-infrared (0.76 - 0.90 μm) multispectral bands mean temperature at sea level is 15 Celsius degree, the atmo- and 0.45 - 0.8 μm panchromatic band (Jacobsen, 2011; Yan et al., spheric pressure is 760 mm Hg and the Earth’s atmosphere is 2013). When the monochromatic light passes through the Earth’s divided into eight layers. The air temperature of each layer atmosphere, the refraction index depends on its wavelength. linearly changes with altitude as the following formula: The shorter the wavelength is, the larger the atmospheric refraction index is. In the astronomical observation, Lipcanu (2005)  15 − 65. h 0km ≤ h ≤ 11.019km and Stone (1996) adopted the Owens (1967) atmospheric refrac-  56.5 11..0192km h 0063km tion calculation algorithm to analyze the impact of atmospheric  − <≤ refraction on star observation. They found the atmospheric re-  −+56.(52h − 0.)063 20..0633km <≤h 2162km fraction result in a 57.5 micro-radian error of a viewed star at 45  t = −+44..5283()h − 2.162 32.1662km <≤h 47.35km (18) degrees zenith angle under the conditions of 15 Celsius degree  −25. 47..35km <≤h 51 413km environment temperature and 760 mm Hg atmospheric pressure.  When the atmospheric temperature t (Celsius), the atmo-  −−25..28(.h − 51 413).51 44137km <≤h 18. 02km  spheric pressure P (Pascal) and the water vapor pressure P  a w  −−58.(25 27hh−<1.)802 71.8028km ≤ 6km (Pascal) are known, the atmospheric refraction index is calculated according to the equations from 12 to 17: where t is the atmospheric temperature in Celsius degree. However, the mean temperature at sea level varies with 8  683939..7 4547 3  ()nD− 11×=0 2371.34 + 22+  S Delivered by geographicIngenta latitude, which makes the ISO 1975 standard  130 − σσ38.9 −  IP: 192.168.39.211 On:(12) Fri, atmosphere24 Sep 2021 model 20:01:12 to estimate temperature inaccurate in tro- + 66487..31+−58Copyright:058σσ2407.. 11American50+ 0885 Society1σ 6 D for Photogrammetryposphere. In andthe studyRemote of global Sensing precipitation with longitude ( ) W and latitude, Roper (2011) studied the earth surface mean air where temperature by averaging over all longitudes from 1948 to   9..325 × 10−4 0 25844  P DP00..11 001579. 10−8 S (13) 2009, which is shown in Figure 2. SS=+  ×− + 2     TT  T Some interesting conclusions can be drawn from Figure 2. Let angle φ be the latitude degree, the cos(φ) can be regarded as an independent variable linearly related to the Earth surface mean air temperature in the northern hemisphere when the latitude range is between 0 and 82 degrees. The same conclusion holds true for the southern hemisphere as the following formula shows:

78.c08 osφφ−−48.2820°≤ ≤ tL =  (19) 52.c07 osφφ−<26.40 ≤°82 

where tL is the Earth’s surface mean air temperature. Here we are only interested in air temperature in the troposphere of Equation 18 which depends on the Earth surface air tempera-

ture tL. Then, the troposphere air temperature at different altitude becomes:

()−−56.5 thL tt=+L 01km ≤≤h 1..019km (20) 11.019

Atmospheric Pressure (Pa) With the increase of altitude, atmospheric pressure smoothly decreases following an exponential function (Portland State Aerospace Society, 2004)):

Figure 2. Relationship between mean Earth surface air temperature with latitude.

Photogrammetric Engineering & Remote Sensing June 2016 429

05-16 June Peer Reviewed.indd 429 5/16/2016 10:28:55 AM Figure 3. Atmospheric pressure changes with altitude. Figure 4. Water vapor pressure changes with temperature.

gM  8  Ptw ≈+3386..39 ()0 00738 0..8072 −+0 000019 18..t 48 + 0 001316 (23)  Lh RLmol   PPa =−0 1  (21)  T  0 where Pw is water vapor pressure (Pascal), and t is Celsius where P is the atmospheric pressure (Pascal); degree. a Figure 4 illustrates how water vapor pressure changes from P0 is the atmospheric pressure at sea level (P0 = 101325 Pa); the Earth’s surface air temperature 30 Celsius degrees to the g is the earth surface gravity acceleration (g = 9.80665 m/s2); top mesosphere temperature −87 Celsius degrees. Delivered by Ingenta M is the molar mass of dry air (M = 0.0289644IP: 192.168.39.211 kg/mol); On: Fri,Atmospheric 24 Sep Refraction 2021 20:01:12 Index (n) Copyright: American Society for PhotogrammetrySuppose the atmospheric and Remote temperature Sensing is t, the air pressure is Rmol is the gas constant (Rmol = 8.31447 J/(mol·K)); Pa, the water vapor pressure is Pw and the central wavelength of spectral band is known, the atmospheric refraction index T0 is the standard temperature at sea level (T0 = 288.15 K); in the stratified atmosphere can be calculated by using Equa- L is the temperature lapse rate (such as: L = 0.0065 K/m in tions 12 to 17. For the object points located on the Equator, troposphere). latitude 30° and 60° in the northern hemisphere, and 30° in the southern hemisphere, Figure 5 shows the atmospheric The temperature of tropopause and stratopause is constant; atmospheric pressure at any altitude in these two layers is estimated according to the distance from the point to the bottom of each layer as the following equation:

 g  PPa =−1exp  ()hh− 1  (22)  RTkg 0   

where Rkg is the gas constant (Rkg = 287.05287 J/(kg·k)), h1 is the distance to the bottom of tropopause or strato-

pause and P1 (Pascal) is the atmospheric pressure at the altitude of h1. Figure 3 shows how the atmospheric pressure Pa changes with the altitude.

Water Vapor Pressure Pw Water vapor pressure is only related to the atmospheric temperature, and the change with temperature can be represented by the following equation (Bosen, 1960): Figure 5. Atmospheric refraction indexes change with altitude in the troposphere.

430 June 2016 Photogrammetric Engineering & Remote Sensing

05-16 June Peer Reviewed.indd 430 5/16/2016 10:28:55 AM refraction index of 0.5 μm blue light through the troposphere. Table 1. Atmospheric Refraction Indexes Change with Altitude at the Table 1 lists the atmospheric refraction index at intervals of Equator, N60°, N30° and S30° altitude from Earth’s surface to the stratopause. Altitude N60 N30 S30 From Table 1 and Figure 5, we can conclude that the (m) Degrees Degrees Equator Degrees atmospheric refraction index is 1 along LOS from payload in-orbit to the top of stratosphere at 47.35 km altitude. In the 1000 1.000268639 1.000250154 1.000242816 1.000249707 troposphere, tropopause and stratosphere, the atmospheric 3000 1.000221848 1.000209777 1.000204972 1.000209484 refraction index increases with the decreasing altitude. Under 5000 1.000184809 1.000178003 1.000175255 1.000177835 the same atmospheric pressure and water vapor pressure, the atmospheric refraction index is negatively correlated with the 7000 1.000155253 1.000152781 1.000151744 1.000152718 atmospheric temperature. The result is that the higher the lati- 9000 1.000131491 1.000132614 1.000133037 1.00013264 tude is, the larger the atmospheric refraction index is. The at- 11000 1.000112255 1.000116392 1.000118097 1.000116495 mospheric refraction index is almost unchanged for the same latitude regardless it is in the southern hemisphere or in the 15000 1.000044223 1.000044223 1.000044223 1.000044223 northern hemisphere. For example, the mean Earth surface air 20000 1.000020098 1.000020098 1.000020098 1.000020098 temperature at N60°, N30° and Equator is 0°, 20°, and 25° Cel- 30000 1.000003847 1.000003847 1.000003847 1.000003847 sius degrees, respectively, the atmospheric refraction indexes of N60° are larger than N30°, and N30° are larger than the 40000 1.000000753 1.000000753 1.000000753 1.000000753 Equator in troposphere. The atmospheric refraction indexes 50000 1.000000003 1.000000003 1.000000003 1.000000003 of N30° and S30° are almost equal. The atmospheric refrac- 60000 1.000000034 1.000000034 1.000000034 1.000000034 tion index at Equator has the minimum value in troposphere. Table 2 lists the distribution characteristics of atmospheric 70000 1.000000014 1.000000014 1.000000014 1.000000014 refraction with regard to the atmosphere layer and altitude. 80000 1.000000002 1.000000002 1.000000002 1.000000002 Therefore, the ISO eight layer atmosphere model can be simplified into two layers: 1. Troposphere layer: geometric altitude is between 0 and Table 2. Characteristics of Atmospheric Refraction Index 11,019 m; Base Top 2. Stratosphere layer (include tropopause): geometric Layer Altitude Altitude Atmospheric altitude is from 11,019 m to 47,350 m. Number Layer Name (m) (m) Refraction Index Varying with This simplification is based on the fact that the refraction 1 Troposphere 0 11019 latitude and index is 1 from the stratopause to mesopause. We will use altitude. the simplified two-layer atmosphere model to calculate the 2 Tropopause 11019 20063 Varying only with geolocation error as shown in Figure 6. 3 Stratosphere 20063 32162 Delivered by Ingenta altitude. The atmospheric refraction indexIP: in the192.168.39.211 troposphere and On: Fri, 24 4Sep 2021Stratosphere 20:01:1232162 47350 stratosphere are set to be Copyright:n1 and n2 respectively, American Society and i is for the Photogrammetry 5 Stratopause and Remote47350 Sensing51413 incident angle of LOS at the top of the stratosphere. D is the 6 Mesosphere 51413 71802 The refraction displacement on the ellipsoid surface because of LOS refracted 7 Mesosphere 71802 86000 index is 1. in the troposphere and stratosphere. A weighted average 8 Mesopause 86000 — algorithm is employed to calculate the atmospheric refraction index, which is calculated at each 1,000 m interval in the troposphere and 2,000 m interval in the stratosphere. The weighted average algorithm in the troposphere is described as follows:

Step 1: Calculate the difference (delta_atm_ref(i)) of two atmospheric refraction indexes at every 1,000 m interval.

Step 2: Calculate the difference (total_delta_atm_ref) of the atmospheric refraction index at the surface and top troposphere.

Step 3: Calculate the weight of each interval:

weight(i) = delta_atm_ref(i)/ total_delta_atm_ref

Step 4: Calculate mean atmospheric refraction index (mean_ atm_ref) of troposphere.

mean_atm_ref = sum[weight(i)·atm_ref(i)]

where atm_ref(i) is calculated by Equations 12 to 17 at any altitude increased 1,000 m interval in troposphere. For the 0.5 μm blue light, the atmospheric refraction index is 1.000014132 (n2) in the stratosphere at N60°, N30°, S30° and the Equator. The atmospheric refraction index in the Figure 6. Two layers atmospheric refraction model troposphere is 1.000199059 (n1) at N60° and 1.000187379 (n1) at the Equator. As for the atmospheric refraction index of different wavelength monochromatic light, Figure 7 shows

Photogrammetric Engineering & Remote Sensing June 2016 431

05-16 June Peer Reviewed.indd 431 5/16/2016 10:28:59 AM the atmospheric refraction index of blue (0.5 μm), green (0.55 μm), red (0.65 μm), and near-infrared (0.83 μm) monochromatic light through the troposphere at N30°. The shorter the wavelength, the larger of atmospheric refraction index value. In the following section, the atmospheric refraction geolocation error of the four monochromatic lights will be analyzed.

Atmospheric Refraction Geolocation Error When the satellite view angle α is known, we can calculate the atmospheric refraction geolocation error on the ellipsoid surface with zero altitude at any latitude. Suppose the mean Earth radius R is 6,371 km, the altitude of satellite orbit H is 650 km, Table 3 lists the atmospheric refraction geolocation error at N60°, N30° and the Equator of blue (0.5 μm), green (0.55 μm), red (0.65 μm) and near-infrared (0.83 μm) monochromatic light in different view angle of satellite in-orbit. In Table 3, α is the satellite off-pointing view angle, Figure 7. Atmospheric refraction index changes with different wavelength in tropo- Blu is blue band, Grn is green band, Red is sphere at N30 degrees. red band, and NIR is near-infrared band. Table 3. Atmospheric Refraction Geolocation Error (Unit: m) From Table 3, we can clearly observe N60 Degree N30 Degree Equator α that the atmospheric refraction geolocation Blu Grn Red NIR Blu Grn Red NIR Blu Grn Red NIR error increases nonlinearly with the increas- 5° 0.24 0.24 0.24 0.24 0.23 0.23 0.23 0.23 0.23 0.23 0.22 0.22 ing view angle. This conclusion is not only 10° 0.49 0.49 0.48 0.48 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.46 confirmed by our proposed method, but also 15° 0.78 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.75 0.75 0.75 0.74 verified by Noerdlinger (1999). Also, three 20° 1.14 1.14 1.13 1.12 1.11 1.11 1.10 1.10 1.10 1.10 1.09 1.09 other conclusions as follows: 25° 1.62 Delivered1.62 1.60 by Ingenta1.59 1.58 1.57 1.56 1.55 1.56 1.56 1.55 1.54 1. Atmospheric refraction geolocationIP: 192.168.39.21130° 2.28 2.27 On:2.25 Fri, 242.24 Sep2.22 2021 2.2120:01:122.20 2.19 2.20 2.19 2.18 2.17 error is increased fromCopyright: the Equator American 35° 3.26Society3.25 for Photogrammetry3.23 3.21 3.18 and3.17 Remote3.15 Sensing3.13 3.15 3.14 3.12 3.10 to South and North Poles. 40° 4.82 4.80 4.78 4.75 4.71 4.69 4.66 4.64 4.66 4.65 4.62 4.60 2. Atmospheric refraction geolocation 45° 7.56 7.53 7.49 7.45 7.38 7.35 7.31 7.27 7.31 7.28 7.24 7.20 error is increased with the shorter 50° 13.03 12.98 12.91 12.84 12.73 12.68 12.60 12.54 12.61 12.55 12.48 12.42 of monochromatic light wavelength in the same latitude. While, this value of the paper’s proposed method than Noerdlinger, Jae- difference between blue, green, red, and near-infrared hong and Jacobsen’s methods. bands are negligible. We will only use the green (0.55 μm) light to calculate the atmospheric refraction index for high resolution optical satellite images direct geore- Experiment on DMC3/TripleSat Constellation ferencing. The DMC3/TripleSat Constellation was launched on 10 July 3. Despite the fact that the atmospheric refraction geoloca- 2015 by a PSLV-XL launch vehicle from the Satish Dhawan tion error is not large, there is a need to correct this error Space Centre, Sriharikota launch site in India. The constella- for the state-of-the-art high resolution satellite, such as tion was successfully delivered into a sun-synchronous orbit WorldView-3 (GSD: 0.31 m), GeoEye-2 (GSD: 0.34 m), Geo- with the local time of the ascending node of 10:30 at 651 km Eye-1 (GSD: 0.46 m) and WorldView-1/2 (GSD: 0.46 m). altitude. The three satellites were phased 120 degrees apart around the same orbit using their on-board propulsion sys- Compared the atmospheric refraction geolocation error of tem. The DMC3/TripleSat Constellation satellites use the 450 the proposed method with the results of Noerdlinger (1999), kg SSTL-300S1 series platform, which provides 45 degrees Jaehong’s (Oh and Lee, 2011; Saastamoinen, 1972) and Ja- fast slew off-pointing and is capable of acquiring multiple cobsen’s (Jacobsen, 2004; Dowman et al., 2012) methods, the targets in one pass using multiple viewing modes. The high atmospheric refraction displacement is almost in the same resolution imager on board equipped with four Time-Delayed- when the satellite was imaging inside the core of 20 degrees Integration (TDI) CCD arrays provides 1 m ground sampling around nadir. When the off-pointing angle is over 20 degrees, distance (GSD) in panchromatic and 4 m GSD in blue, green, the results of these methods are different. The authors believe red and near-infrared multispectral mode with a swath width the Noerdlinger’s single layer spherically symmetrical atmo- of 24 km. The wide swath of the imager combined with agile sphere assumption will result in the atmospheric refraction off-pointing capability enable the DMC3/TripleSat Constella- index underestimated in the troposphere. And the Jaehong tion to target anywhere on earth at least once a day. Table 4 and Jacobsen’s methods took the satellite altitude and the lists the capability of DMC3/ TripleSat Constellation. object’s terrain elevation into account to calculate the atmo- The DMC3/TripleSat Constellation linear pushbroom im- spheric refraction constant. These three methods were all not ages are direct georeferenced by using the collinear rigorous considering the LOS path increased through the atmosphere geometric model. The rigorous geometric model fixes the rela- when optical satellite operated in off-pointing imaging mode. tionship between LOS vector in the camera coordinate system Therefore, the larger of satellite off-pointing angle, the larger with the ECEF coordinate system. The rigorous geolocation for

432 June 2016 Photogrammetric Engineering & Remote Sensing

05-16 June Peer Reviewed.indd 432 5/16/2016 10:28:59 AM T Table 4. DMC3/TripleSat Constellation Capability LOS vector [tan(ψy) – tan(ψx) 1] in camera coordinate system Sensor Panchromatic Multispectral is periodically calibrated by referencing the global geometric calibration sites. Blue: 0.44 – 0.51 From the analysis of atmospheric refraction effect on Green: 0.51 – 0.59 Band (μm) 0.45 to 0.65 geolocation, we draw the conclusion that the atmospheric Red: 0.60 – 0.67 refraction will change the direction of LOS and result in Near infrared: 0.76 – 0.91 the geolocation error on earth spheroid. In the procedure GSD (m) 1 4 of DMC3/TripleSat Constellation direct georeferencing, the detector’s LOS vector refractive deviation is subtracted from Swath (km) 24 24 the calibrated LOS vector in the camera coordinate system to Focal Length (m) 6.6667 6.6667 correct the atmospheric refraction geolocation error. When Detector the satellite operated in the roll and pitch imaging mode, the 10*10 40*10 Dimension (μm) collinear rigorous geometric model of Equation 24 is rewritten as below: Detector Number 6408*4 1602*4 Digitization (bit) 10 10 XX− 0   tan(ψψyp− itch _ atmoos ) Max Off-pointing     45 YY− 0 =−µM ECEF 2Camera tan()ψψxr− olla_ tmos (25) (degree)      ZZ  1   − 0 ECEF  Camera Stripe, Scene, Along track stereo, Imaging Mode Across track stereo and Area where MECEF2Camera = MOrbit2ECEF MBody2Orbit MCamera2Body. (ψx,ψy) is the interior orientation element in the camera coordinate sys-

tem, ψroll_atmos is the atmospheric refraction deviation angle represented in the camera coordinate system when the platform

rotation roll angle around the X axis, ψpitch_atmos is the atmospheric refraction deviation angle represented in the camera coordinate system when platform rotation pitch angle occurs around the Y axis. The definition of the interior orientation parameters is shown in Figure 8. OXYZ is the camera coordinate system and oxy is the image coordinate system. u is the LOS vector in Equation 24. u′ is the LOS vector in Equation 25 by subtracting the atmospheric refraction deviation angle in along and across track direction. In the DMC3/TripleSat Con- Delivered by stellationIngenta geometric model, the original points of the camera IP: 192.168.39.211 On: Fri, coordinate24 Sep 2021 system, 20:01:12 body coordinate system, and orbit coordi- Copyright: American Society for Photogrammetrynate system areand in Remote the same. Sensing The values of roll and pitch are interpolated from the exterior orientation attitude parameters. In the direct georeferencing of DMC3/TripleSat Constella- tion images, the atmospheric refraction geolocation error was transformed into the LOS deviation in the camera coordinate system. And the atmospheric refraction geolocation error correction procedure is divided into 10 steps: Figure 8. Definition of interior orientation parameters with atmospheric refraction geolocation error compensated. Step 1: Use Equation 24 to calculate the ECEF coordinate (X,Y,Z) of one pixel (x,y) by referencing WGS84 ellipsoid. each pixel is obtained by calculating the intersection point coordinate of the LOS with the earth ellipsoid in ECEF coordinate Step 2: Input the NASA Shuttle Radar Topographic Mission system, which can be described as follows without consider- (SRTM) global 90 m digital elevation data. ing the influence of atmospheric refraction. Step 3: Transform the object’s ECEF coordinate (X,Y, Z) into XX−   tan()ψ  0 y latitude and longitude. YY MMM  tan() (24)  − 0  = µ OrbitE22CEFBodyOrbit Camera2BBody − ψ x   ZZ  1  Step 4: Interpolate the roll and pitch value from exterior  − 0 ECEF  Camera orientation attitude parameters at the imaging instant. The

T roll and pitch values are considered as the view angle of the where [tan(ψy) – tan(ψx) 1] Camera represents the detectors LOS detector across and along track direction. vector in the camera coordinate system. MCamera2Body represents the bias matrix of the camera coordinate system to the Step 5: Use the simplified two layer atmosphere model and attitude control coordinate system. MBody2Orbit represents the terrain elevation to calculate the refraction index in strato- rotation matrix from the attitude control coordinate system sphere and troposphere. In the troposphere, there is a need to to satellite platform coordinate system. MOrbit2ECEF represents calculate the refraction index between the terrain elevation the rotation matrix from orbit coordinate system to ECEF T and the top of the troposphere. coordinate system. μ is a scalar. [X0 Y0 Z0] ECEF represents the satellite platform position interpolated by ephemeris at Step 6: Use the Equations 3 to 9 to calculate the Δθ and imaging instant. [X Y Z ]T ECEF represents the ECEF coordi- roll 0 0 0 Δθ across and along track direction on Earth’s surface. nate of the intersection point of LOS with the Earth ellipsoid. pitch During the in-orbit geometric calibration campaign, the preci- Step 7: Interpolate the spacecraft position (X0, Y0, Z0) by using sion instrument alignment angles in MCamera2Body matrix and ephemeris parameters at the imaging instant.

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING June 2016 433

05-16 June Peer Reviewed.indd 433 5/16/2016 10:47:59 AM Step 8: Calculate the distance from the imaged object (X,Y, Z) Table 5. Experiment Results of Four samples DMC3/TripleSat

and spacecraft position (X0, Y0, Z0). Constellation Images with the Atmospheric Refraction Geolocation Error Correction. The value of X_corr is the Atmospheric Refraction Geolocation

Step 9: Calculate the value of ψroll_atmos and ψpitch_atmos. An ex- Error Corresponding to the Pitch Off-pointing View, and the Value of Y_ ample of calculation (radian) as following: corr is the Atmospheric Refraction Geolocation Error Corresponding to the Roll Off-pointing View. ()Rh+ •∆θ ψ = demroll (26) Data Browse Image Geolocation Error (m): roll _ atmos 2 2 2 XX− +−YY +−ZZ ()0 ()0 ()0 Date: 23 Sep, 2015 X_corr: 0 Y_corr: 0.31 where, R is the mean Earth radius; hdem is the object’s terrain Image ID: D2000093VI elevation interpolated from SRTM 90 m digital elevation data. Location: Guildford, UK Off-pointing (degree): Step 10: Use Equation 25 to calculate the atmospheric refraction geolocation error corrected ECEF coordinate. Roll: -5.908 Pitch: 0 In the DMC3/TripleSat Constellation in-orbit commissioning and early operation phase, the studied method was used to di- Date: 2 Oct, 2015 X_corr: 0 rect georeferencing the DMC3/TripleSat 1 m resolution images. Image ID: D20000A3VI Y_corr: 0.82 Table 5 lists four sample DMC3/TripleSat Constellation images Location: Beijing, China with atmospheric refraction geolocation error correction. Since the spacecraft off-pointing limit in the early phase, the four Off-pointing (degree): sample images were all imaged in roll off-pointing mode. In Roll: -16.967 the future, we will investigate in the atmospheric refraction Pitch: 0 geolocation error in both roll and pitch off-pointing mode. Date: 13 Oct, 2015 X_corr: 0 Y_corr: -1.54 Conclusions Image ID: D20000BEVI As the propagation direction of LOS from satellite payload Location: Aden, Yemen in-orbit is deviated because of the atmospheric refraction, the Off-pointing (degree): points of the detector, projection center and ground object are Roll: 23.996 no longer in a line. This is one reason why there are geolocation errors in the collinear rigorous geometric model estima- Pitch: 0 tion. The paper describes how to use the LOS tracking geometry algorithm, ISO standard atmospheric model, and OwensDelivered Date: by Ingenta 16 Oct, 2015 X_corr: 0 atmospheric refraction index calculationIP: method 192.168.39.211 to estimate On: ImageFri, 24 ID: Sep D10000B1VI 2021 20:01:12 Y_corr: 0 the atmospheric refraction geolocationCopyright: error American and how Society to cor -for PhotogrammetryLocation: Zhaoyuan, and Remote Sensing rect this error in the collinear rigorous geometric model. Haerbin, China The proposed method is especially suitable for the high resolution agile optical satellite as images taken from a large Off-pointing (degree): off-pointing view angle is more susceptible to the atmospher- Roll: 0.001 ic refraction. We also have applied the proposed method in Pitch: 0 direct georeferencing DMC3/TripleSat Constellation 1 m resolution images to improve the geolocation accuracy without ground points. Crespi, M., F. Fratarcangeli, F. Giannone, and F. Pieralice, 2007. However, we have to admit that atmospheric refraction is SISAR: A rigorous orientation model for synchronous and one element that has made collinear geometric model non- asynchronous pushbroom sensors imagery, The International rigorous. Other elements, such as the light aberration and the Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XXXVI-1/W51, unpaginated CD-ROM. transmission delay of LOS, can also introduce geometric errors in the collinear geometric model. Only when all the causes Dowman, I., K. Jacobsen, G. Konecny, and R. Sandau, 2012. High that lead to inaccurate estimation of the interior orientation Resolution Optical Satellite Imagery, Whittles Publishing, 129 p. and exterior orientation parameters are calibrated, can we Fan, D.Z., C.B. Liu, and T. Wang, 2011. Building and Validation obtain a real accurate collinear rigorous geometric model. of rigorous geometric model of ALOS PRISM imagery, Acta Geodaetica et Cartographica Sinica, 40(5):569–574. Greslou, D., F. Lussy, and J. Montel, 2008. Light Aberration Effect Acknowledgments in HR Geometric Model, The International Archives of the This work was partly supported by the National High Tech- Photogrammetry, Remote Sensing and Spatial Information Sciences, XXXVII-B1:859–864. nology Research and Development Program of China (No. 2013AA12A303) and Major Project of High Resolution Earth Gruen, A., and S. Kocaman, 2008. Optical Sensors High Resolution: Geometry Validation Methodology, Technical report submitted to Observation System (Civilian Part) (No. 65-Y40B01-9001- ESA/ESRIN, 34 p. 13/15). The authors also thank the anonymous reviewers for Gyer, M., 1996. Methods for computing photogrammetric their construction comments and suggestions. refraction corrections for vertical and oblique photographs, Photogrammetric Engineering & Remote Sensing, References 62(3):301–310. Bosen, J., 1960. A formula for approximation of the saturation vapor Habib, A., S.W. Shin, K. Kim, C. Kim, K.I. Bang, E.M. Kim, pressure over water, Monthly Weather Review, pp. 275–276. and D.C. Lee, 2007. Comprehensive analysis of sensor modeling alternatives for high resolution imaging satellites, Photogrammetric Engineering & Remote Sensing, 73(11):1241– 1251.

434 June 2016 Photogrammetric Engineering & Remote Sensing

05-16 June Peer Reviewed.indd 434 5/16/2016 10:29:03 AM International Organization for Standardization, 1975. ISO 2533: 1975 Owens, J., 1967. Optical refractive index of air: Dependence on Standard Atmosphere, 108 p. pressure, temperature and composition, Applied Optics, Jacobsen, K., 2004. Issues and Methods for In-Flight and On-Orbit 6(1):51–59. Calibration, Post-Launch Calibration of Satellite Sensors, ISPRS Pan, H.B., G. Zhang, X.M. Tang, D.R. Li, X.Y. Zhu, P. Zhou, and Book Series, 2:83–92. Y.H. Jiang, 2013. Basic products of the ZiYuan-3 satellite and Jacobsen, K., 2011. Characteristics of very high resolution optical accuracy evaluation, Photogrammetric Engineering & Remote satellites for topographic mapping, Proceeding of the ISPRS Sensing, 79(11):1131–1145. Hannover Workshop - Commission I, WG I/4, unpaginated CD- Poli, D., and T. Toutin, 2012. Review of developments in geometric ROM. modelling for high resolution satellite pushbroom sensors, The Jeong, I.S., and J. Bethel, 2010. A study of trajectory models for Photogrammetric Record, 27(137):58–73. satellite image triangulation, Photogrammetric Engineering & Portland State Aerospace Society, 2004. A quick derivation Remote Sensing, 76(3):265–276. relating altitude to air pressure, URL: http://www.psas.pdx.edu Jeong, I.S., and J. Bethel, 2014. An automatic parameter selection (last data accessed: 26 April 2016). procedure for pushbroom sensor models on imaging satellites, Radhadevi, P.V., R. Müller, P. d'Angelo, and P. Reinartz, 2011. In-flight Photogrammetric Engineering & Remote Sensing, 80(2):171–178. geometric calibration and orientation of ALOS/PRISM imagery Jiang, Y.H., G. Zhang, and X.M. Tang, 2013. High accuracy geometric with a generic sensor model, Photogrammetric Engineering & calibration of ZY-3 three-line image, Acta Geodaetica et Remote Sensing, 77(5):531–538. Cartographica Sinica, 42(4):523–529. Roper, L., 2011. Precipitation rate versus latitude and longitude, Jiang, Y.H., G. Zhang, X.M. Tang, D.R. Li, W.C. Huang, and H.B. URL: http://www.roperld.com/science/ (last data accessed: 26 Pan, 2014. Geometric calibration and accuracy assessment of April 2016). ZiYuan-3 multispectral images, IEEE Transactions on Geoscience Saastamoinen, J., 1972. Atmospheric Correction for the Troposphere and Remote Sensing, 52(7):4161–4172. and Stratosphere in Radio Ranging of Satellites, The Use of Leprince, S., S. Barbot, F. Ayoub, and J.P. Avouac, 2007. Automatic Artificial Satellites for Geodesy, Geophysical Monograph Series and precise orthorectification, coregistration, and subpixel 15, 247–251. correlation of satellite images, application to ground deformation Stone, R., 1996. An accurate method for computing atmosphere measurements, IEEE Transactions on Geoscience and Remote refraction, Publications of the Astronomical Society of the Sensing, 45(6):1529–1558. Pacific, 108:1051–1058. Leprince, S., P. Musé, and J.P. Avouac, 2008. In-flight CCD distortion Tang, X.M., G. Zhang, and X.Y. Zhu, 2012. Triple linear-array calibration for pushbroom satellites based on subpixel Imaging geometry model of Ziyuan-3 surveying satellite and its correlation, IEEE Transactions on Geoscience and Remote validation, Acta Geodaetica et Cartographica Sinica, 41(2):191– Sensing, 46(9):2675–2683. 198. Lipcanu, M., 2005. A direct method for the calculation of Toutin, T., 2004. Review article: Geometric processing of remote astronomical refraction, The Proceedings of the Romanian sensing images: Models, algorithms and methods, International Academy, Series A, 6(2):1–7. Journal of Remote Sensing, 25(10):1893–1924. Lussy, F., and D. Greslou, 2012. Pleiades HR in flight geometric Wang, M., B. Yang, F. Hu, and X. Zang, 2014. On-orbit Geometric calibration: Location and mapping of the focal plane, Delivered by Ingentacalibration model and its applications for high-resolution optical International Archives of the Photogrammetry,IP: 192.168.39.211 Remote Sensing On: Fri, 24 Sepsatellite 2021 imagery, 20:01:12 Remote Sensing, 6:4391–4408. and Spatial InformationCopyright: Sciences, XXXIX-B1:519–523. American Society for PhotogrammetryWang, Z.Z., 2007. and Principles Remote of Sensing Photogrammetry, Wuhan University Mahapatra, A., R. Ramchandran, and R. Krishnan, 2004. Modeling Press, 237 p. the Uncertainty in orientation of IRS-1C/1D with a rigorous Wei, Z., F.C. Hu, and B. Zhang, 2006. The influence of atmospheric photogrammetric model, Photogrammetric Engineering & refraction on aerial digital remote sensing, Journal of Remote Remote Sensing, 70(8):939–946. Sensing, 10(5):651–655. Müller, R., T. Krauß, M. Schneider, and P. Reinartz, 2012. Automated Yan, M., B.Y. Yu, and Z.Y. Wang, 2013. Design of width of georeferencing of optical satellite data with integrated sensor panchromatic spectra of high resolution optical remote sensing model improvement, Photogrammetric Engineering & Remote camera based on pansharpening, Spacecraft Recovery & Remote Sensing, 78(1):61–74. Sensing, 34(3):1–8. Noerdlinger, P., 1999. Atmospheric refraction effects in Earth remote Yastikli, N., and K. Jacobsen, 2005. Influence of system calibration sensing, ISPRS Journal of Photogrammetry & Remote Sensing, on direct sensor orientation, Photogrammetric Engineering & 54:360–373. Remote Sensing, 71(5):629–633. Oh, J., and C. Lee, 2011. Atmospheric correction and velocity aberration for physical sensor modeling of high-resolution (Received 28 June 2015; accepted 10 December 2015; final satellite images, Journal of the Korean Society of Surveying Geodesy Photogrammetry & Cartography, 29(5):519–525. version 12 January 2016)

Photogrammetric Engineering & Remote Sensing June 2016 435

05-16 June Peer Reviewed.indd 435 5/16/2016 10:29:03 AM