Interesting paper by people at Rice and Northwestern universities about different phase retrieval algorithms for measuring transmission matrices without using interferometric techniques. The thing with interferometers is that they provide you lots of cool stuff (high sensibility, phase information, etc.), but also involve quite a lot of technical problems that you do not want to face every day in the lab: they are so sensitive that it is a pain in the ass to calibrate and measure without vibrations messing everything up.
Using only intensity measurements (provided by a common sensor such as a CCD) and algorithmic approaches can provide the phase information, but at a computational cost that sometimes makes things not very useful. There is more info about all of this (for the coherent illumination case) in the Rice webpage (including a dataset and an implementation of some of the codes).
Inverse Scattering via Transmission Matrices: Broadband Illumination and Fast Phase Retrieval Algorithms
by Sharma, M. et al., at IEEE Transactions on Computational Imaging
Abstract:
When a narrowband coherent wavefront passes through or reflects off of a scattering medium, the input and output relationship of the incident field is linear and so can be described by a transmission matrix (TM). If the TM for a given scattering medium is known, one can computationally “invert” the scattering process and image through the medium. In this work, we investigate the effect of broadband illumination, i.e., what happens when the wavefront is only partially coherent? Can one still measure a TM and “invert” the scattering? To accomplish this task, we measure TMs using the double phase retrieval technique, a method which uses phase retrieval algorithms to avoid difficult-to-capture interferometric measurements. Generally, using the double phase retrieval method re- quires performing massive amounts of computation. We alleviate this burden by developing a fast, GPU-accelerated algorithm, prVAMP, which lets us reconstruct 256^2×64^2 TMs in under five hours.
After reconstructing several TMs using this method, we find that, as expected, reducing the coherence of the illumination significantly restricts our ability to invert the scattering process. Moreover, we find that past a certain bandwidth an incoherent, intensity-based scattering model better describes the scattering process and is easier to invert.
F. Soldevila 