Wavefront shaping unlocked many exciting applications related to imaging through scattering media. However, they usually require to have some feedback from the object to observe, typically a guide-star generated by physically labeling the sample or by using ultrasound (that reduced the resolution). Other computer-based approaches recently developed relied on the memory-effect, which drastically limits the field of view, or requires a coherent illumination. In the present paper, T. Yeminy and O. Katz present a very simple approach that allows the reconstruction of an object hidden behind a scattering medium under incoherent illumination. It uses wavefront shaping of the scattered light together with an optimization procedure based on some assumptions about the object.
The idea is simple and quite generic. After undergoing the mixing due to the propagation through the scattering medium, the image undergoes another transformation, that we can control using a spatial light modulator (see Figure 1.).
Figure 1. Schematic of the experimental setup. Image from [T. Eminy and O. Katz., arxiv, 2007.03956 (2020)].
Ideally, we want this transformation to undo the one generated by the turbid medium. To find an approximate solution to that problem, the authors then run an optimization procedure based on a genetic algorithm. To know where to go, one needs to define a cost function. Because the illumination is incoherent, the initial image has low contrast and random features. They run two optimizations with different cost functions. The first one is based on a measure of the entropy of the image. Typically, the entropy of a signal looks like this:
$$ E = -\sum_i x_i \log(x_i) $$
The entropy can be seen as a measure of the randomness of the signal. Minimizing it also increases sparsity. So, by choosing the entropy as a cost function, we implicitly use assumptions about the image we want to recover; it is sparse and not random. It is a fair assumption for any natural image. As we see in Figure 2., the result is not perfect with some replica visible. The authors then run a second optimization using the variance of the image, this favors results with sharp edges. Again, we do an implicit assumption, the image has quite sharp edges.
Figure 2. Images before and after the two steps of the optimization. Image from [T. Eminy and O. Katz., arxiv, 2007.03956 (2020)].
Under these assumptions, the procedure allows the reconstruction of unknown images hidden behind a scattering medium. The key advantages are that it uses incoherent light, it requires no calibration or labeling and the field of view is claimed to be larger than the range memory effect. To my best knowledge, such a combination was not previously reported.