Phase unwrapping in interferometry I observed that in "interferometry" is used a process called phase unwrapped. This process can be done by using complicated algorithms but I was not able to found an example more simplistic. If somone could help or provide some examples in this direction will be nice. 
Thank you :) !
 A: Suppose you want to use interferometric synthetic aperture radar (InSAR) to make a map of the surface of the Earth. To do that, you'd put a C-band SAR ($\lambda = 5.6\,$cm) on the Space Shuttle, with two receive antennas:

Before you make a map of the globe, you need to make local maps under the shuttle orbit. For that, you are trying to measure the terrain height field:
$$ h_t(x, y)$$
where $(x, y)$ are some suitable surface coordinates.
The receive antennas, each at the end of the baseline ${\bf B}$ measure complex radar amplitudes, $A$, that are a product of a magnitude, $M$, and a phase, $\phi$:
$$ A_i(x, y)=M_i(x, y)e^{i\phi_i(x, y)}\ \ {i \in (1, 2)} $$
The measured phase difference:
$$\Delta\phi_M(x, y) \equiv \phi_2(x, y)-\phi_1(x, y) $$
can be extracted from:
$$ \frac{A_1^*(x, y)A_2(x, y)}{M_1(x, y)M_2(x, y)} = e^{i(\phi_2(x, y)-\phi_1(x, y))}$$
From the diagram, you can show that the target height is:
$$h_t(x, y) = h_p - \rho(x, y)\cos{\big[\sin^{-1}{\big(\frac{\lambda\Delta\phi(x, y)}{2\pi B}\big)+\alpha} \big]} $$
where the range, $\rho$ is measured by the radar.
The problem arises because the radar does not measure $\Delta\phi(x, y)$ because of phase wrapping. The radar measures:
$$ \Delta\phi_M(x, y) = [\Delta\phi(x, y)\,{\rm mod}\,2\pi] + n(x,y) $$
where $n(x,y)$ is phase noise.
For SRTM, the terrain height for a phase wrap was several hundreds of meters, so a scene with 3000m of elevation difference can be wrapped 10 times.
The problem of phase unwrapping refers to the process of recovering the true phase difference $\Delta\phi(x, y)$ from the measured, wrapped phase, $\Delta\phi_M(x, y)$, in the presence of noise, $n(x,y)$, and voids (missing data), and other problems.
Data may look something like this:

where 1 color wrap is a two-pi phase wrap. Or

Note the regions of high noise, missing data, possibly disconnected regions, and in these data, which are time-series InSAR, complete decorrelation because of surface changes (such as crop growth). 
One of the difficulties, that is not obvious from either of figures, is that the phase unwrap between two posts in the image can be path dependent. Of course, any closed loop should have zero total phase change from start to finish; however, that doesn't always happen in the data because of noise. There is also the problem of data gaps, across which phase unwrapping is not possible.
