[SciPy-User] 2D phase unwrapping

[Robert Kern]

On Sat, May 12, 2012 at 11:30 AM, Friedrich Romstedt
<friedrichromstedt at gmail.com> wrote:

> I worked pretty hard on an unwrapping algorithm for Fourier tranform results. By this I noticed the following points:
>
> • Phases are angles, so they are just identical, if their angle "value" is identical modulus 2 pi. There's nothing to tell them apart. The numerical value is just an insufficient model and we fight these insufficiencies when trying to "unwrap". They are already unwrapped. We just don't see it anymore.

Usually, the point of phase unwrapping is to try to recover an
underlying linear variable in the range (-inf, inf) that we are
observing through the lens of a complex phase. For example, when doing
Interferometric Synthetic Aperture RADAR (InSAR), the setup is to fly
a satellite doing SAR twice over a given area. SAR gives you a complex
image of the ground surface. The complex phase is related to the
two-way travel time of the RADAR signal. The phase of a single SAR
image is essentially meaningless because it depends on every little
detail on the surface, but if the surface did not change much in its
fine details (seriously, plants growing on just the order of
centimeters is a problem) but moved in the direction of the RADAR
signal due to seismic events, the difference in the phases
(interferometry!) is linearly related to the distance that the ground
moved. Except that the phase difference, the only thing we can
directly observe, gets wrapped. There *is* an underlying non-phase
linear variable here that we are trying to estimate via phase
unwrapping. When we're unwrapping phase, we're not really interested
in the phase itself. It's just the only thing that we can observe.
There are better and worse ways to unwrap phase in order to estimate
these underlying variables, but it's not a theoretically doomed
effort.

-- 
Robert Kern