303 
but this model needs high-precision attitudes parameters of plat; 
the equivalent collinearity equation considered the 
characteristics of range projection and influence factors of 
image deformations which is equivalent to express by attitude 
angles, but this model is not considered the SAR imaging 
principles and the parameters needed to solute are much more; 
the parallax and elevation relation model is often seen in 
documents, but this method has few expressions. 
This paper described the method which solutes the three- 
dimensional coordinates may be one of them. In this model, 
firstly, image distortion caused by factors other than elevation is 
corrected by range formulation. Secondly, polynomial 
parameters could be calculated by control points. Finally, the 
model formulations could be established by correspondence 
points on stereo image pairs, and the three-dimensional 
coordinates can be got by iterative computation. 
3. STUDY METHOD AND IMPROVEMENT OF 
CALCULATION FLOW 
Researcher G.M Huang of CASM(Chinese Academy of 
Surveying and mapping) has used the correction of projection 
difference of photogrammetry to the fields of SAR image 
correction and DEM generation txl[10] .This method can be called 
polynomial orthorectification model. The study method and 
improvement of calculation flow are given based on this theory. 
Displacement of radar image caused by terrain can be displayed 
in Fig.l. The altitude of ground point P is h , and P' is a 
plotted point of P on the reference surface. So, displacement of 
images Ax caused by topographic relief can be approximately 
described as following equation 1101 : 
Ax*-h(H-h)/R/s (1) 
Where h — altitude of ground point 
H = height of SAR platform 
R = distance between radar and ground point 
5 = slant range resolution 
SAR adopts side-looking imaging mode. In this paper, x axis is 
arranged to point to the side-looking direction, so height 
displacement influence only x, and there is no difference from 
the normal polynomial function in direction y. So, when we use 
stereo image pairs to generate DEM, there are two polynomial 
orthorectification models for each group of correspondence 
points, and the functions can be expressed as follows: 
x, =a l0 + a n X+a l2 Y+a n X 2 + a l4 XY+a, 5 Y 2 +(H, -h-h 2 )/R, /s, 
y, =b l0 +b n X+b n Y+b n X 2 +b l4 XY+b, 5 Y 2 
x r =a r0 +a rl X + a r2 Y+a ri X 2 +a r4 XY+a r5 Y 2 +(H r • h-h 2 )/R r /s r 
y r ~b r o +b rl X+b r2 Y+b ri X 2 +b r4 XY+b r5 Y 2 
(2) 
An calculation flow of (2) had been designed in the literature 181 , 
and an experiment of this model had been done by Radarsat 
images. However, that calculation flow is much more complex, 
and residual error was considered in projection difference due 
to doing iterative calculation of two images separately. So, 
when it is used in airborne SAR images, the result is not 
convergent. Thus, an improvement of the calculation flow has 
been done in this paper, and the ground point coordinates (X, 
Y , h ) of correspondence points can be got by unite 
adjustment method. The details of process steps can be 
described as follows: 
(D Confirm the initial values ( X° , Y° , h° ) of three 
unknowns (X, Y, h). The barycentric coordinates of all control 
points are regarded as the initial values in this paper. 
® According to principle of indirect adjustment method, 
error equations can be established by image coordinates of 
correspondence points and approximate coordinates of ground 
points. 
(D The correction values (dX , dY ,dh) of unknowns can 
be calculated according to least square method, and then adding 
the iterative correction values of this time to iterative 
approximate values of last time to get new values of unknowns. 
(D Comparing correction values of unknowns with tolerance, 
if they are smaller than tolerance, iterate calculation should be 
finished; or new values of unknowns should be regarded as 
approximate values, and repeat the process steps (2)—(3) until 
meeting tolerance. The tolerance can be 0.1 time of SAR image 
resolution. 
4. STUDY AREA AND EXPERIMENT RESULTS 
Image data used for the study are offered by the No. 704th 
Research Institute of China Aeprospace Times Electronics 
Corporation. The experimental area is located in ShanXi 
province, where the relief is loessial plateau and the height 
difference is about 450 m. 
According to experimental necessary, there are totally 7 flight 
lines. The images obtained by flight lines 5, 9, 14 are adopted in 
this paper, whose initial slants are 10500 m, 10000 m, and 
10750 m. The height of platform is about 4000 m and the 
resolution of images is 1 m. Flight lines 5 and 9 are planed from 
west to east and side-looking direction is north; Flight line 14 is 
planed from east to west and side-looking direction is south. In 
this experiment, same side stereo pairs are composed by images 
obtained by flight lines 5 and 9; opposite side stereo pairs are 
composed by images obtained by flight lines 9 and 14. 
The hue and distortion between the same side stereo image 
pairs are similar, so it is easy to select the correspondence 
points. However, the hue and distortion between opposite side 
stereo image pairs are different, because the direction of 
shadow of the two image pairs is opposite (Figure2).