Sparsity-constrained wavefront optimization by leveraging complex media

Wavefront shaping gains increasing importance in complex photonics, which can manipulate light spatially and temporally to counter the scattering effect. Important applications include deep-tissue imaging, microendoscopy, optical communications, nanofabrication, and remote sensing. However, high-speed and high-fidelity wavefront shaping is fundamentally hindered by the dimensionality limitation of hardware devices, evinced by the competition between the frame rate, pixel count, and modulation depth. To overcome the speed-fidelity tradeoff, we leverage complex media (e.g., diffusers or multimode fibers) as analogue random multiplexers for pattern compression to address the demand for high-dimensional spatiotemporal control. Sparsity-constrained wavefront optimization is designed to solve the problem by seeking a low-dimensional, robust representation of wavefronts with a carefully designed sparsity constraint. This optimization framework can achieve high-fidelity wavefront shaping through complex media using high-speed, yet relatively low-precision spatial light modulation devices (e.g., digital micromirror devices) without compromising the frame rate.

Methods
The dataset contains an experimentally calibrated complex-field transmission matrix of a graded-index multimode fiber (GIF50C, Thorlabs) and 1000 preprocessed test images extracted from the Fashion-MNIST dataset. The script takes the preprocessed test images as the ground truth. It carries out the sparsity-constrained wavefront optimization to solve for the wavefront to generate those test images through the multimode fiber given its transmission matrix.  

In brief, the transmission matrix was measured by raster scanning the proximal end of the multimode fiber using a DMD and recording the corresponding speckles at the distal end using off-axis holography. The test images were first downsampled and interpolated to match the coordinate of the distal end of the multimode fiber. Then, they were vectorized to a one-dimensional vector to comply with the format of the transmission matrix. The initial guesses were obtained by performing the Gerchberg-Saxton algorithm with 10 iterations. All the implementation details can be found in Section 4.3 of our paper https://arxiv.org/abs/2302.10254.