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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
deformation. If we can subtract phase gradients resulted from 1) 
and 2) on interferograms, then the information of residual phase 
gradients can be used to monitoring dynamic change of earth 
surface (Gabriel A. K, Goldstein R. M,1989). According to the 
different methods of removing topographic effects, we can 
basically classify the technique into two categories: differential 
interferometry based on DEM simulated interferogram and 
differential interferometry based on unprimed SAR 
interferogram, but as to principles related to the two methods, 
there is no evident difference. 
Consider the condition of no existence of surface deformation 
during SAR imaging period, the general geometry of SAR 
interferometry is illustrated in figure 1. Two radar antennas A, 
and A, simultaneously viewing the same surface and separated 
by a baseline vector B with length B and angle a with respect 
to horizontal. A; is located at height h above some reference 
surface. The distance between A, and the point on the ground 
being imaged is the range p , while p * óp is the distance 
between A, and the same point. If À is the wavelength of the 
radar and óp is the range difference between the reference and 
repeat passes of the satellite, the phase difference Q between 
the signals received from the same surface element at the two 
antenna positions is: 
47x 
SU 
ó 7 (1) 
Recalling the law of cosine, Eq. (2) can be easily obtained 
according to the imaging geometry. 
(o+ àpy =p’ +B? -2pBsin(0 - a) (2) 
A; 
  
  
  
  
Figure 1. Imaging geometry of repeat-pass SAR ınterferometry 
Where 0 is the look angle of the imaging radar. For space- 
borne geometries, we can make the parallel-ray approximation 
and rearrange the above equation by ignoring the second term 
(6p) on the right-hand side of Eq. (2), thus we obtain: 
731 
2 
. B 
op ~ Bsin(0 — a )+ — (3) 
2p 
B? 
Because of p>>B /|we can discard the term of ST for 
<p 
simplicity of analysis, thus we have another equation: 
op ~ Bsin(0 - a) = B, (4) 
where B, is the component of baseline parallel to the look 
direction. 
Combining with Eq. (4), we can rearrange Eq. (1) as: 
gins l (5) 
From equation (5), we know that the measured quantity of 
phase difference @ is directly proportional to B, and wave 
numbers (2TT/\), with constant of proportionality 2. 
On the assumption that we have the second interferogram 
(primed interferogram) over the same region with the same p 
and 0 as the first interferogram (unprimed interferogram), but 
having a baseline length B’ and angle @' with respect to 
horizontal, we can obtain the equation Bj = B'sin(0 - a") 
similar to Eq. (4). Similarly, we can obtain Eq. (6) similar to 
Eq. (5) on the condition that no factors other than topography 
generate phase effects. 
4x 
, = — H' 
ó =" (6) 
Combining Eq. (5) with (6), when radar wavelength is constant 
we obtain: 
à B 
eR 7 
ó / i 
= 
- 
Which means that, the ratio of the two phases is just equaled to 
the ratio of the two parallel components of the baseline, i.e., 
independent of topography. 
Now consider the second interferogram acquired over the same 
region as before but at different time, so that ground 
deformation (due to an earthquake) has displaced many of the 
resolution elements for the primed interferogram in a coherent 
manner. In addition to the phase dependence on topography, 
this time there is an additional phase change due to the radar 
line-of-sight component of displacement Ap .