Inverse Scattering via Transmission Matrices: Broadband Illumination and Fast Phase Retrieval Algorithms

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.

Focusing light through dynamical samples using fast continuous wavefront optimization

The guys at LKB keep going inside turbid media. This time, they have done it really fast. By using a phase spatial light modulator and with the help of a FPGA card, they were able to focus light through a scattering medium at a rate of ~4 kHz.

This is trying to solve a common problem in biological systems when you use the Transmission Matrix approach: live systems evolve, and thus the matrix that you measure is not valid after a really short time.

For me, this is a really nice technical implementation (and not an easy one to do) merging electronics, computer science, and optics to tackle a well defined biological problem.

Focusing light through dynamical samples using fast continuous wavefront optimization,

B. Blochet et al, at Optics Letters

(featured image extracted from Fig. 1 of the manuscript)

Abstract:

We describe a fast continuous optimization wavefront shaping system able to focus light through dynamic scattering media. A micro-electro-mechanical system-based spatial light modulator, a fast photodetector, and field programmable gate array electronics are combined to implement a continuous optimization of a wavefront with a single-mode optimization rate of 4.1 kHz. The system performances are demonstrated by focusing light through colloidal solutions of TiO2 particles in glycerol with tunable temporal stability.