Thus, severely limiting its practical use for non-invasive imaging inside complex samples, where the goal is to perform imaging without direct access to the target plane. However, while such experimentally measured TM allowed focusing and imaging, this could only be done at the camera output plane, located outside the scattering sample. Experimental access to the optical TM was first made possible by measuring the response from each pixel of an SLM placed at a chosen input plane to each pixel of a camera placed at a desired output plane 6.
The TM essentially contains the medium’s response at every output spatial mode to excitation by any input spatial mode, i.e., the medium’s set of Green functions. A generalized theoretical framework underlying all experiments involving light propagation in complex media is the reflection/transmission matrix (TM) formalism 6, 15, 16, 17. Following the pioneering work of Vellekoop and Mosk 5, wavefront optimization was used for correcting spatial 6, 7, 8, 9, temporal 10, 11, spectral 12, and polarization 13 distortions, and to optimize transmission 14 through multiply-scattering media. The ability to digitally control optical interference in multiply-scattering media using spatial light modulators (SLMs) has recently given rise to new focusing and imaging techniques 3, 4. However, the complex wavefront distortions, even deep inside diffusive samples, can be effectively reversed by high-resolution shaping of the input optical wavefront 1, in a fashion analogous to time-reversal experiments in ultrasound 2. We experimentally demonstrate complex light control using the AOTM singular vectors, and utilize the AOTM framework to analyze the resolution limitation of acousto-optic guided focusing approaches.Ĭonventional optical focusing and imaging techniques fail in strongly scattering media because of the multiple-scattering events that any incident optical beam undergoes in its propagation inside them. The AOTM provides both a generalized framework to describe any acousto-optic based technique, and a tool for light control and focusing beyond the acoustic diffraction-limit inside complex samples. Here, we introduce the acousto-optic transmission matrix (AOTM), which is an ultrasonically-encoded, spatially-resolved, optical scattering-matrix. To overcome this limitation, the current state-of-the-art approaches utilize focused ultrasound for generating acousto-optic guide-stars, in a variety of different techniques. While the complex optical distortions induced by scattering can be effectively undone if the medium’s scattering-matrix is known, this matrix generally cannot be retrieved without the presence of an invasive detector or guide-star at the target points of interest. Studying the internal structure of complex samples with light is an important task but a difficult challenge due to light scattering.
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