Marc Honikel 
  
Applying (14) to the optical DEM points after a slant range conversion derives the second, independent interferometric 
data source, the synthetic interferogram. The baseline and sensor information, necessary for height to phase and slant. 
range conversion, and is obtained from the SAR sensor specification and ephemeris data. The result of the smulation is 
an unwrapped phase image is wrapped in a range between -x and x through a modulo 2 operation (Fig. 4). 
3.2.2 Signal-to-noise ratio. As the SNR decides about the filter behavior, the correct determination of the SNR is 
inevitable for the successful phase restoration. In the InSAR case, determination of the SNR becomes a straightforward 
task, as this information is directly retrievable from the interferometric processing by computing the local coherencep 
from the complex SAR images X1 and X2 
s EL X1-X2*) 
JE XI- X LE(X2- X2) 
  
(15) 
  
High coherence indicates those areas, where phase estimation for DEM generation is reasonable (Fig. 3). The SNR can 
be expressed as a function of the coherence with 
SNR = ——— (16) 
1-p 
Note that a coherence estimate is computed within an estimator window from the flattened interferogram (Small, 1994), 
therefore the estimated phase noise depends on the size of the estimator window (Prati, 1994). Still, the estimated 
coherence is a very good measure for the local SNR. 
3.2.3 Point spread function. Referring to Fig. 1, B(k,]) relates the ideal image F(k,l) to the output of the blurring 
Gy(k,l) before the noise addition. Both the ideal image f and the blurring are determined from the given data for the 
computation of B(k,l). 
Though the simulated phases may give a good approximation of the ideal phase course, measures have to be taken in 
order to avoid the introduction of optical DEM errors into the interferometric processing chain. A weighting of the 
simulated phases with respect to their expected error is performed using their cross-correlation coefficient, originating 
from the SPOT image matching (Fig. 5). High cross-correlation indicates the similarity between stereo images to be 
matched, and therefore is a measure of reliability of the detection of conjugate points. Erroneous matching still occurs 
even if the correlation is high, often causing spikes i.e. points with high height deviation compared to the surrounding 
mean. These spikes are interpreted as uncorrelated random noise in the DEM adding to the local height variance. 
Therefore, points showing extreme height variance are excluded from the phase simulation, by giving them zero weight. 
In order to increase the number of valid phase measurements, thus minimizing holes in the ideal interferogram through 
the weighting, also highly coherent interferometric phase values (p > 0.6) are used in the computation of F(k.l). 
A blurred interferogram is approximated by phase subsampling in azimuth direction by factor 6 followed by phase 
averaging for noise reduction. Although the resulting image g, has a lower resolution, the noise level is massively 
reduced, hence it serves for the estimation of the point spread function, which is finally computed in the Fourier domain 
by 
B(k,) 9 Gy(k,DF (kl) (17) 
     
  
8 i ; E = 
Figure 2. ERS-1, 3day-pass — Figure 3. Phase coherence Figure 4. Interferogram, ^ Figure 5. Cross-Correlation, 
interferogram (~1 50km”). indicates the noise of Fig. 2. — simulated a SPOT DEM. from the point matching. 
   
          
  
152 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 
4.1 
The 
ath 
set: 
The 
al: 
as I 
The 
wh 
cor 
figi 
The 
als 
resi 
exa 
hav 
Du 
bas 
sim 
tie- 
4.2 
The 
me 
inte 
uny 
frin 
col 
for 
of : 
hay 
The 
sec