Rob Dekker 
  
5 INTERFEROMETRY 
SAR across-track interferometry (Li and Goldstein 1990) is a technique, like stereoscopy in optical imagery, that can 
provide a Digital Elevation Model (DEM). In the case of repeat-pass across-track interferometry, two single look 
complex images must be acquired. The terrain height information can be derived from their phase difference by: 
d Arsin 0 A 
4z(B. sinO B, cos 0) 
  
(I) 
Here h stands for the terrain height, 7 for the range (i.e. the distance between the illuminated object and the radar), À for 
the radar wavelength, © for the incidence angle and Ag for the phase difference between the images, corrected for the 
phase difference of the reference earth model that is applied. B, and B. are respectively the horizontal and vertical 
components of the baseline (i.e. the distance between the two flight paths of the platform). The main requirements of 
repeat-pass interferometry are (1) that the baseline perpendicular component must generally fit in between 150m and 
300m (van Genderen and Gens 1996), and (2) that the time interval between the acquisitions must be as short as 
possible. The first requirement is associated with the spatial or baseline decorrelation between the images, defined by 
Zebker and Villasenor (1992): 
2B,0, cos? 0 
p spatial = 1 Ar (2) 
Here 6, stands for the ground-range resolution. The spatial decorrelation (range 0 to 1) is an overall measure for the 
reliability of the phase difference, which directly relates to the reliability of the extracted terrain height in equation (1). 
The second requirement is associated with the temporal decorrelation, which is dependent on the stability of the 
illuminated surface. The temporal decorrelation is more a local measure for the reliability of the phase difference, 
because most images contain different surfaces with different natures. For example, urban and rock areas are generally 
more stable than surfaces like range land and wood. Water surfaces change very fast. The total correlation of a surface, 
including the spatial and temporal decorrelation, is also denominated as the coherence. 
To generate a DEM the following procedure must be followed: 
(1) co-registration 
(2) calculation of the phase difference image, including correction for phase difference of the reference earth model 
(3) phase unwrapping 
(4) calculation of the local terrain height using equation (1) 
(5) possible subtraction of an elevation trend or offset 
Step 3 is an important step in interferometric processing. Because the range of the phase is 0 to 2x (meaning it is 
wrapped), the phase difference image has to be unwrapped. In practice, this is a difficult problem. Its success is 
dependent on the reliability of the phase (coherence) and the robustness of the algorithm. Therefore, most algorithms 
temporary stop unwrapping if the coherence is too low, and interpolate the missing parts. After unwrapping, the DEM 
can be calculated using equation (1). Sometimes it is necessary to subtract an overall trend or offset (step 5), due to 
errors in the reference phase. To calculate a possible trend or offset, the differences in elevation have to be small 
compared to the dimensions of the image. Another method is locating reference points in the image of which the height 
is known. 
The tandem pair that was used was 32516-12843, acquired on 3-4 October 1997, see table 2. The baseline of this image 
pair is not ideal for interferometric processing, because it leads to a maximum coherence of 0.685, see table 6. This will 
have an effect on the phase unwrapping (step 3). Other suitable tandem pairs were unfortunately not available at the 
moment of this study. The procedure did not give any problems, except for step 3, as expected. An elevation trend was 
found so step 5 was performed. After processing, the DEM was compared with a photogrammetric DEM with a vertical 
accuracy better than 2 m (Sliuzas and Brussel 2000b). The analysis showed differences up to 380m. The histogram of 
the differences in height between both DEMs, also showed three major Gaussian distributions at an in-between distance 
of 36 m. This indicates phase unwrapping errors because it corresponds to one phase cycle (2x). The RMS of the single 
Gaussian distributions measured about 16 m, which is not extreme for an interferometrically obtained DEM (Small and 
Nuesch 1996). But it is larger than that of the photogrammetric DEM. The main reason for this is the low coherence. 
  
66 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
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