357 
MULTI-PHOTO COMBINED ADJUSTMENT WITH AIRBORNE SAR IMAGES BASED 
ON F.LEBERL ORTHO-RECTIFICATION MODEL 
X.J. Yue a ’ b ’*, G.M. Huang a ' b , Y. Zhang c , Z.Zhao b , L.Pang b 
a School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, 
Wuhan-(xijuanyue, huang.guoman) @163.com 
b Chinese Academy of Survey and Mapping, 16 Beitaiping Road, Beijing-zhengzhao@casm.ac.cn 
c National Earthquake Infrastructure Service, 63 Fuxing Road, Beijing-yzhang@gps.gov.cn 
KEY WORDS: Airborne SAR, F.Leberl Model, Ortho-rectification, GCPs, Pass Points, Multi-photo Combined Adjustment 
ABSTRACT: 
This paper introduces an ortho-rectification method of airborne SAR images which is multi-photo combined adjustment method 
based on F.Leberl imaging model. Multi-photo combined adjustment model of airborne SAR images is built. Multi-photo combined 
adjustment conditions are given in this paper. This method is applicable to multi-temporal, multi-side-looking-orientation, multi- 
flight-height, multi-resolution SAR Images. Two adjustment experiments have been done with one-meter resolution airborne SAR 
images in Chengdu study site. In the two experiments, the GCPs and the Pass Points are distributed rationally in each image. The 
two experimental results show that the coordinate accuracy of Pass Points is feasible for 1:10 000 scale ortho-image making and 
topographic map updating. There are four images in the first experiment, and nine GCPs and ten Pass Points are used. There are 
eleven images in the second experiment, and nine GCPs and thirty Pass Points are used. The second experimental result is better 
than the first one. Because the Pass Points are twice overlap in the first experiment and the most Pass Points are more than twice 
overlap in the second one. 
1. INTRODUCTIONS 
There are many perennially cloudy, misty and rainy regions in 
China. Therefore optical images are acquired very difficultly in 
these areas. A new approach to obtain mapping data in these 
areas is given by Synthetic Aperture Radar (SAR) which is all- 
weather and all-time. In these years, State Bureau of Surveying 
and Mapping of China have done airborne SAR mapping 
experiments in Zhengzhou Henan province and Zigong, 
Chengdu Sichuan province, in order to solve geometry 
rectification of high resolution airborne SAR images(Huang 
G.M. et al, 2008). In digital photogrammetry age, the formats 
of imaging models have not been difficulties of solution. F. 
Leberl imaging model accords with SAR imaging mechanism, 
and are independent from the attitude parameters of the sensor, 
only relates to the position, flight velocity and orientation of the 
sensor. So there are a few rectification parameters in F. Leberl 
imaging model(Zhu C.Y. et al, 2003). It is easy and effective to 
geometry rectification and object positioning of SAR images 
which are range projection. 
This paper introduces a geometry rectification method of 
airborne SAR images which is multi-photo combined 
adjustment method based on F. Leberl imaging model. Multi 
photo combined adjustment model of airborne SAR images is 
built. Multi-photo combined adjustment conditions are given. 
The influence of pass point accuracy due to the number and 
distribution of Ground Control Points (GCPs) and pass points is 
analyzed in this paper. 
2. MODEL AND SOLUTION 
2.1 Multi-photo Combined Adjustment Model Based on F. 
Leberl Imaging Equations 
F. Leberl imaging equations are mathematical equations that 
determine the position of image points in image space 
coordinate system based on geometric characters of SAR 
imaging. There are two geometric conditions used in SAR 
imaging. One is range condition in across-track, the other is 
Doppler condition in along-track(Franz Leberl, 1978; G. Domik, 
Franz Leberl, 1988). 
2.1.1 Range Condition: Function (1) is about it in slant 
range image. 
(X-X,) 2 +(Y-Y s ) 2 +(Z-z s f = (D, + m y ■ yf 
(1) 
where (X, Y, Z) = ground coordinate 
(X s ,Y s ,Z s ) = position of radar antenna in SAR 
imaging 
D s = scanning delay or initial slant range 
m v = resolution of SAR image in across-track 
y = image coordinate of SAR image in across-track 
2.1.2 Doppler Condition: Airborne SAR image covers a 
little area, so the effect of earth's rotation can be ignored. That 
is vertical between radar beam and aircraft flight track, and 
Doppler frequency is zero(Shu N., 2003; Wang D.H., Liu J., 
Zhang L., 2005). Function (2) is about it. 
u x (X-X s ) + u y (Y-Y s ) + u z (Z-Z s ) = 0 (2) 
where (U x ,U y ,U z ) = velocity vector of aircraft flight