Abstract
Wavefront shaping techniques are being actively developed to achieve optical focusing through and inside opaque scattering media. These techniques promise to revolutionize biophotonics by enabling deep-tissue non-invasive optical imaging, optogenetics, optical tweezing, and light-based therapy. Among the existing wavefront shaping techniques, optical time-reversal-based techniques determine the optimum wavefront globally based on the principle of time reversal, without the need to perform time-consuming iterations to optimize each mode in sequence. In all previous optical time-reversal-based wavefront shaping experiments, Nyquist sampling criterion was followed so that the scattered light field was well-sampled during wavefront measurement and wavefront reconstruction. In this work, we overturn this conventional practice by demonstrating that a high-quality optical focus can still be achieved even when the scattered light field is under-sampled. Even more strikingly, we show both theoretically and experimentally that the focus achieved by the under-sampling scheme can be one order of magnitude brighter than that achieved by the well-sampling schemes used in previous works, where 3×3 to 5×5 pixels sampled one speckle grain on average. Moreover, since neighboring pixels were uncorrelated in feedback-based wavefront shaping, introducing the concept of sub-Nyquist sampling in time-reversal-based wavefront shaping makes the optimal phase maps obtained using these two different methods consistent. We anticipate that this newly explored under-sampling scheme will transform the understanding of optical time reversal and boost the performance of optical imaging, manipulation, and communication through opaque scattering media.
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