By what I understand, a "standard" slc from a SAR has complex values for each pixel. Here the phasor consists of the magnitude and the relative phase. What I don't understand is the complex nature of an interferogram and how this relates to the coherence. Am I right in that in an interferogram the complex value consists of the phase-difference between the two SLCs and the coherence or this working completely different?

1 Answer 1


It's not completely different, but not entirely correct:

Say you have two SLC's, each with an amplitude and a phase. When you cross-multiply SLC1 and SLC2*, the amplitude of the resulting interferogram at each point will just be the product of the two SLC amplitudes. The interferogram phase at each pixel will be the phase difference between the two SLC's at that pixel.

SAR images contain speckle and other noise sources, so they are often spatially averaged to reduce the noise. The complex values of the interferogram are averaged over some box of several pixels by several pixels in a process called multilooking. The phase that results from this average is the multilooked interferogram phase, and tells you an averaged phase difference of the SLCs. The amplitude that results from the multilooked interferogram, scaled by the amplitudes of each individual SLC, gives the coherence:

Equation for SAR Coherence

where gamma is the coherence, the brackets denote averaging over some sample, the asterisk denotes a complex conjugate, and z1 and z2 are the complex values of SLC1 and SLC2. So the coherence is the averaged interferogram magnitude, divided by the square root of the magnitude of SLC1 times SLC2.

The coherence tells us how well pixels in an area are in phase, or coherent, with one another. For this reason, there is no value of coherence for an individual single-look pixel, because it is not being compared to anything.

Equation from this paper, though many other sources use this equation.

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