Imaging through an opaque layer has been a longstanding problem, which has typically been addressed by separating the extremely weak light field that is not scattered from the overwhelming amount of background light that has scattered multiple times such as in optical coherence tomography. A recent paradigm shift is harnessing spatial information from the multiply-scattered or diffused light for imaging applications. The key to harnessing spatial information from multiply-scattered light is the hidden correlations of random speckles formed by the interference of scattered light. The most celebrated one of such hidden correlations is known as the angular “memory effect”: when the incident wavefront of a coherent beam on a diffusive medium is tilted by a small angle, the transmitted wavefront is tilted in the same direction by the same amount. However, it has certain constraints such as finite angular correlation range and predetermined direction that correlations are observed. Here, we propose and experimentally demonstrate a general approach to arbitrarily modify the angular memory effect in opaque scattering media. Introducing an angular memory operator by applying a certain transformation to the field transmission matrix, we show that the eigenvectors of such an operator have perfect “memory” for arbitrarily chosen angles and tilt directions of input and output wavefronts. Our work paves the way to customize the memory effect of both classical and quantum waves for imaging, metrology, and communication applications in complex scattering systems.
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