The International Archives of the Photoerammetry. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
1000 
2. RIGOROUS HiRLSE SENSOR MODEL 
2.1 Interior Orientation Modeling 
The HiRISE camera is characterized by high signal-to-noise ratio 
(SNR) and large image size in addition to high resolution. 
Fourteen CCD arrays are distributed on its focal plane (Figure 1). 
Each CCD array contains a 2048-pixel-wide line detector to 
build up an image in pushbroom mode, but with up to 128 lines 
of time delay and integration (TDI) to ensure a high SNR even in 
some extreme conditions. Ten of the 14 of the detectors, designed 
to accept only the red wavelengths, are overlapped one by one on 
the focal plane in the cross-track direction to provide continuous 
coverage of a 20,000-pixel-wide swath. The images provided by 
the red detectors mainly serve the purpose of morphologic 
studies. The other four detectors are sensitive to the blue-green 
and near-infrared (NIR) wavelengths. They allow for false-color 
imaging of the central 4000 pixels of the swath. The length of the 
along-track images that can be acquired depends on the number 
of CCDs used, pixel binning and data compression (Kirk, et al., 
2007). 
FPA Sur>sttate 
J*! IÜ 
Active Length of Red Array 
i 
CCD Active Area 
Figurel. HiRISE CCD structure on its focal plane (A. McEwen, 
et al., 2007) 
HiRISE interior orientations, describing the geometry inside the 
camera, are provided in the USGS ISIS 3 HiRISE Instrument 
Kernel. The physical position of a pixel with respect to the 
perspective center can be calculated using its row and column 
indices in three steps. First, the pixel position with respect to 
CCD center is calculated using the formulas below. 
ROW = TDI/2 - 64 - (BIN/2 - 0.5) ( i ^ 
COLUMN = (m- 0.5) x BIN - 1024 ; 
ROW and COLUMN are the indices with respect to CCD center; 
TDI and BIN are TDI and binning mode from the image header; 
“m” means the column index from image point measurement. 
Then, this row and column indices are converted to physical 
position with respect to the perspective center with Equation 2. 
x = tx i0 +t x tl xCOLUMN + t x j2 xROW 
y = ty i0 +ty n xCOLUMN+ty i2 xROW (2) 
z = ~f 
Where x, y and z are the physical coordinate of the pixel center 
with respect to the perspective center. tx j0 ... ty i2 are 
calibration parameters of the i th CCD array, /is the focal length 
of HiRISE which is calibrated as 11994.9988mm. The calibration 
data of the sensor is provided by R.L. Kirk from USGS. Finally a 
radial distortion needs correction for the best level of accuracy. 
The radial distortion is modeled as: 
2 2,2 
r =x +y m 
x p =x-(k 0 +r 2 k,+r 4 k 2 )x 
y P = y-( k o +T % +r \)y 
k Q , k, and k-, are distortion parameters; x, y are the coordinates 
from the previous step; x p ,y p and z are the final result of 
interior orientation that can be used in the procedure of bundle 
adjustment as measurements. 
2.2 Exterior Orientation Modeling 
Exterior Orientation (EO) parameters, which are the positions of 
the camera perspective center and bundle pointing angles at a 
specific time, are provided in SPICE kernels. The EO parameters 
of each image line can be retrieved by interpolating the 
spacecraft’s trajectory and pointing vectors. Previous researches 
prove that the change of EO parameters in short trajectories can 
be well modeled using polynomials (Yoon and Shan 2005). In 
this research, second-order polynomials are used to model this 
change 
X 1 1 ; = a 0 + a x t + a 2 t~ co L x = d a +d x t + d 2 t 
Y% =b 0 + b x t + b 2 t 2 (p\ = e 0 + e x t + e 2 t 2 
Z i ~ c o + c \t ^ i ~ fo f'f f’d 
whereX c ¡,Y C ¡,Z C x are the position of the perspective center of 
the sensor of the i’ h point; CO i , (p { , /O are the pointing angles 
of the i’ 1 ' point; a Q ... f 2 are the polynomial coefficients and t 
is the time-dependent image row index number. Modeled this 
way, EO parameters can be adjusted by modifying the 36 
polynomial coefficients of the stereo pair. The complexity of the 
adjustment is significantly reduced by this method. 
Since all 14 CCDs are fixed to the HiRISE frame, they share the 
same perspective center and focal plane. Therefore, changes of 
the EO parameters of all 14 CCDs yield one set of polynomial 
coefficients. This critical characteristic significantly reduces the 
complexity of the bundle adjustment on HiRISE stereo images. 
Images simultaneously generated by multiple CCD arrays can be 
processed together under a uniform rigorous camera model in the 
bundle adjustment instead of being processed strip by strip. 
To apply the strategy above, one reference CCD strip must be 
assigned; this strip could be arbitrarily chosen. Then the offsets 
between other CCD strips and the reference strip are calculated 
by comparing their EO data line by line. The row index of the