Several themes mentioned in this blog are colliding in the following preprint. First thanks to the Moore's law we have the ability to do high resolution imagery with smartphone cameras like the Lumia 1020. Then there is this imaging with nature theme and then there is the sparse phase retrieval problem. I say sparse but there is no connection to that in this preprint and much like FROG (see here and here also), time will tell. What is so interesting here is that there is no need to know the transmission matrix or even the need for a time of flight cameras to see around the corners: A smartphone camera is all you need.
On a more general note, those quantum optic problems seem to have solutions for sparse imaging but there isn't much of a literature on the subject, in particular, since everybody is focused on correlation type of imaging, other types of nonlinearities such as triple correlation interferometry seem to be left on their own device (see the vocabulary used here and here). Anyway, enjoy!
[ and by the way, no, the speckle is not the problem, it was, and continues to be the solution ]
Non-invasive real-time imaging through scattering layers and around corners via speckle correlations by Ori Katz, Pierre Heidmann, Mathias Fink, Sylvain Gigan
Imaging with optical resolution through and inside complex samples is a difficult challenge with important applications in many fields. The fundamental problem is that inhomogeneous samples, such as biological tissues, randomly scatter and diffuse light, impeding conventional image formation. Despite many advancements, no current method enables to noninvasively image in real-time using diffused light. Here, we show that owing to the memory-effect for speckle correlations, a single image of the scattered light, captured with a standard high-resolution camera, encodes all the information that is required to image through the medium or around a corner. We experimentally demonstrate single-shot imaging through scattering media and around corners using incoherent light and various samples, from white paint to dynamic biological samples. Our lensless technique is simple, does not require laser sources, wavefront-shaping, nor time-gated detection, and is realized here using a camera-phone. It has the potential to enable imaging in currently inaccessible scenarios.
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