Sub-Nyquist sampling boosts targeted light transport through opaque scattering media

Optical time-reversal techniques are being actively developed to focus light through or inside opaque scattering media. When applied to biological tissue, these techniques promise to revolutionize biophotonics by enabling deep-tissue non-invasive optical imaging, optogenetics, optical tweezing, and phototherapy. In all previous optical time-reversal experiments, the scattered light field was well-sampled during wavefront measurement and wavefront reconstruction, following the Nyquist sampling criterion. Here, we overturn this conventional practice by demonstrating that even when the scattered field is under-sampled, light can still be focused through or inside scattering media. Even more surprisingly, we show both theoretically and experimentally that the focus achieved by under-sampling can be one order of magnitude brighter than that achieved under the well-sampling conditions used in previous works, where 3 × 3 to 5 × 5 pixels were used to sample one speckle grain on average. Moreover, sub-Nyquist sampling improves the signal-to-noise ratio and the collection efficiency of the scattered light. We anticipate that this newly explored undersampling scheme will transform the understanding of optical time reversal and boost the performance of optical imaging, manipulation, and communication through opaque scattering media.