Abstract
Transmission matrices (TMs) have become a powerful and widely used tool to describe and control wave propagation in complex media. In certain scenarios the TM is partially uncontrollable, complicating its identification and use. In standard optical wavefront shaping experiments, uncontrollable reflections or imperfect illumination may be the cause; in reverberating cavities, uncontrollable reflections off the walls have that effect. Here we employ phase retrieval techniques to identify such a partially uncontrollable TM solely based on random intensity-only reference measurements. We demonstrate the feasibility of our method by focusing both on a single target as well as on multiple targets in a microwave cavity, using a phase-binary Spatial-Microwave-Modulator.
Highlights
IntroductionThe control of wave propagation in complex media has received a lot of attention, being crucial to improve information transfer in a wide range of domains, including imaging, medical therapies and telecommunication amongst others [1, 2, 3, 4]
In recent years, the control of wave propagation in complex media has received a lot of attention, being crucial to improve information transfer in a wide range of domains, including imaging, medical therapies and telecommunication amongst others [1, 2, 3, 4]
This paper shows that even in complex media with a partially uncontrollable transmission matrix, the complex-valued transmission matrix can be estimated, up to a global phase factor on each of its rows, purely based on intensity-only output measurements corresponding to random, phase-binary input patterns
Summary
The control of wave propagation in complex media has received a lot of attention, being crucial to improve information transfer in a wide range of domains, including imaging, medical therapies and telecommunication amongst others [1, 2, 3, 4]. It was later refined in terms of speed and technical requirements to increase its applicability in practical contexts [22] Without resorting to such indirect phase measurements, signal processing techniques known as phase retrieval (PR) can recover the full complex-valued TM only from the knowledge of the magnitudes of projections of known patterns through the medium. To maximize |Yi|2 the controllable (blue) phasors have to be aligned in a specific radial direction, namely that of the sum of the uncontrollable phasors; this angle θ (Yi) is indicated in Fig. 1(g) and varies randomly with the output position i This is the challenge we tackle in this paper, first for a single receiver and later for multiple receivers, with a TM approach
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