Yueqin Zhou 
  
The paper is organized as follows. Section 2 gives a brief description of the diffenential interferometric SAR. The errors 
involved in D-InSAR are analyzed in detail, and the model for error modelling in section 3. Some results are presented in 
section 4. 
2. DIFFERENTIAL SAR INTERFEROMETRY 
The differential SAR interferometry commonly involves the generation 
of two interferograms. One interferogram, which comes from two 
images spanning long time interval, is expected to contain fringes due 
to both topographic effects and surface movements. The other one, 
coming either from two SAR images spanning very short time interval, 
or an external Digital Elevation Model (DEM), contains topographic 
fringes only. By differencing the two interferograms, the topographic 
effects are removed from the surface movement fringes, leaving only 
the effects of surface movements, from which the surface movements 
can be derived. 
Figure 1 shows the geometry for repeat-pass SAR interferometry, in 
which only one SAR antenna was mounted on the platform. At one 
time, one SAR image was acquired. A second SAR image was acquired 
in a repeated pass some time later. Over the time interval between the 
two passes, a small height change occurred on the ground surface. Now 
take cell P as an example. Let Öh be the small height change occurred 
at cell P. Assume that the second pass exactly repeated the first, ie. 
  
  
Figure 1. Geometry for repeat-pass InSAR 
S, coincides with $ j» then the measured phase difference (interferometric phase) is related to the slant range change duo 
to the height change by: 
4 
$5. 1 = “or = 2 Shcos (1) 
Where, A is the wavelength, 0 is the off-nadir angle 6 of slant range 7, . But, if this is not the case, i.e. there is a baseline 
B between S, and S, , then the measured phase difference is related to both the topography and the height change: 
m 
ó de no 
2417 4 r À 
4n 
or = op asset) lease (2) 
From (1), the height change dh is derived: 
z À ($5. —@r7) .  À-dó 
dh = 
4 . cos 4r * cos 
  
(3) 
The topography-related phase @, can be obtained through using a reference DEM of the same area. The reference DEM 
can be obtained from two kinds of sources: one is through conventional mapping techniques such as optical stereo- 
photogrammetry, while the other is through InSAR topographic mapping using a second image pair. In the former case, 
only two pass images are involved. This is so-called two-pass D-InSAR. In the latter case, the second image pair may be 
independent of the first pair, or share one image with the first pair, leading to so -called four-pass method and three-pass 
method, respectively. By means of the reference DEM, the topography-related phase G, is calculated by: 
is 4r Bcos(0-a) Ps in: Bz, 
f i Poi reine 
Where, (€ is the incidence angle of the baseline B with respect to horizontal, B, is the perpendicular component of 
(4) 
baseline B, z p |s the height of cell P with respect to the reference plane. The resulting interferogram from any of the 
methods is called the double difference interferogram, which is independent of topography but contains only the small 
height change (concerning the case of subsidence). The interferometric phase values in the double difference interferogram 
are still wrapped by 277 . After phase unwrapping, the unwrapped phase values are then converted into the height change 
using (3). From (3), the height change error is easily d erived: 
À 
6,=——-G 
h 4xcos6 dé 
(5) 
  
354 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 
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