Multimode fibers (MMFs) are a promising solution for high-throughput signal transmission in the time domain. However, crosstalk among different optical modes within the MMF scrambles input information and creates seemingly random speckle patterns at the output. To characterize this process, a transmission matrix (TM) can be used to relate input and output fields. Recent innovations use TMs to manipulate the output field by shaping the input wavefront for exciting advances in deep-brain imaging, neuron stimulation, quantum networks, and analog operators. However, these approaches consider input/output segments as independent, limiting their use for separate signal processing, such as logic operations. Our proposed method, which makes input/output segments as interdependent, adjusts the phase of corresponding output fields using phase bias maps superimposed on input segments. Coherent superposition enables signal logic operations through a 15-m-long MMF. In experiments, a single optical logic gate containing three basic logic functions and cascading multiple logic gates to handle binary operands is demonstrated. Bitwise operations are performed for multi-bit logic operations, and multiple optical logic gates are reconstructed simultaneously in a single logic gate with polarization multiplexing. The proposed method may open new avenues for long-range logic signal processing and transmission via MMFs.

Transmission matrix (TM) allows light control through complex media, such as multimode fibers (MMFs), gaining great attention in areas, such as biophotonics, over the past decade. Efforts have been taken to retrieve a complex-valued TM directly from intensity measurements with several representative phase-retrieval algorithms, which still see limitations of slow or suboptimum recovery, especially under noisy environments. Here, we propose a modified nonconvex optimization approach. Through numerical evaluations, it shows that the optimum focusing efficiency is approached with less running time or sampling ratio. The comparative tests under different signal-to-noise levels further indicate its improved robustness. Experimentally, the superior focusing performance of our algorithm is collectively validated by single- and multispot focusing; especially with a sampling ratio of 8, it achieves a 93.6% efficiency of the gold-standard holography method. Based on the recovered TM, image transmission through an MMF is realized with high fidelity. Due to parallel operation and GPU acceleration, our nonconvex approach retrieves a 8685 × 1024 TM (sampling ratio is 8) with 42.3 s on average on a regular computer. The proposed method provides optimum efficiency and fast execution for TM retrieval that avoids the need for an external reference beam, which will facilitate applications of deep-tissue optical imaging, manipulation, and treatment.

Controllable optical propagation, such as forming diffraction-limited optical focusing, beyond the diffusion limit in biological tissue or tissue-like scattering media, has been desired for long yet considered challenging. In the past two decades, optical wavefront shaping (WFS) has been proposed and has progressed, demonstrating its remarkable potential. That said, inherent tradeoffs still exist among optimization speed, control degree of freedom, and energy gain, which has hindered wide applications of the technology. Most recently, an analogue optical phase conjugation system was developed, equipped with stimulated emission light amplification that effectively achieves the least tradeoff ever, yielding high-gain and high-speed performance of optical focusing through dynamic thick media.

Information retrieval from visually random optical speckle patterns is desired in many scenarios yet considered challenging. It requires accurate understanding or mapping of the multiple scattering process, or reliable capability to reverse or compensate for the scattering-induced phase distortions. In whatever situation, effective resolving and digitization of speckle patterns are necessary. Nevertheless, on some occasions, to increase the acquisition speed and/or signal-to-noise ratio (SNR), speckles captured by cameras are inevitably sampled in the sub-Nyquist domain via pixel binning (one camera pixel contains multiple speckle grains) due to finite size or limited bandwidth of photosensors. Such a down-sampling process is irreversible; it undermines the fine structures of speckle grains and hence the encoded information, preventing successful information extraction. To retrace the lost information, super-resolution interpolation for such sub-Nyquist sampled speckles is needed. In this work, a deep neural network, namely SpkSRNet, is proposed to effectively up sample speckles that are sampled below 1/10 of the Nyquist criterion to well-resolved ones that not only resemble the comprehensive morphology of original speckles (decompose multiple speckle grains from one camera pixel) but also recover the lost complex information (human face in this study) with high fidelity under normal- and low-light conditions, which is impossible with classic interpolation methods. These successful speckle super-resolution interpolation demonstrations are essentially enabled by the strong implicit correlation among speckle grains, which is non-quantifiable but could be discovered by the well-trained network. With further engineering, the proposed learning platform may benefit many scenarios that are physically inaccessible, enabling fast acquisition of speckles with sufficient SNR and opening up new avenues for seeing big and seeing clearly simultaneously in complex scenarios.

Optical imaging through or inside scattering media, such as multimode fiber and biological tissues, has a significant impact in biomedicine yet is considered challenging due to the strong scattering nature of light. In the past decade, promising progress has been made in the field, largely benefiting from the invention of iterative optical wavefront shaping, with which deep-tissue high-resolution optical focusing and hence imaging becomes possible. Most of the reported iterative algorithms can overcome small perturbations on the noise level but fail to effectively adapt beyond the noise level, e.g., sudden strong perturbations. Reoptimizations are usually needed for significant decorrelation to the medium since these algorithms heavily rely on the optimization performance in the previous iterations. Such ineffectiveness is probably due to the absence of a metric that can gauge the deviation of the instant wavefront from the optimum compensation based on the concurrently measured optical focusing. In this study, a square rule of binary-amplitude modulation, directly relating the measured focusing performance with the error in the optimized wavefront, is theoretically proved and experimentally validated. With this simple rule, it is feasible to quantify how many pixels on the spatial light modulator incorrectly modulate the wavefront for the instant status of the medium or the whole system. As an example of application, we propose a novel algorithm, the dynamic mutation algorithm, which has high adaptability against perturbations by probing how far the optimization has gone toward the theoretically optimal performance. The diminished focus of scattered light can be effectively recovered when perturbations to the medium cause a significant drop in the focusing performance, which no existing algorithms can achieve due to their inherent strong dependence on previous optimizations. With further improvement, the square rule and the new algorithm may boost or inspire many applications, such as high-resolution optical imaging and stimulation, in instable or dynamic scattering environments.

Edge enhancement is a fundamental and important topic in imaging and image processing, as perception of edge is one of the keys to identify and comprehend the contents of an image. Edge enhancement can be performed in many ways, through hardware or computation. Existing methods, however, have been limited in free space or clear media for optical applications; in scattering media such as biological tissue, light is multiple scattered, and information is scrambled to a form of seemingly random speckles. Although desired, it is challenging to accomplish edge enhancement in the presence of multiple scattering. In this work, we introduce an implementation of optical wavefront shaping to achieve efficient edge enhancement through scattering media by a two-step operation. The first step is to acquire a hologram after the scattering medium, where information of the edge region is accurately encoded, while that of the nonedge region is intentionally encoded with inadequate accuracy. The second step is to decode the edge information by time-reversing the scattered light. The capability is demonstrated experimentally, and, further, the performance, as measured by the edge enhancement index (EI) and enhancement-to-noise ratio (ENR), can be controlled easily through tuning the beam ratio. EI and ENR can be reinforced by ～8.5 and ～263 folds, respectively. To the best of our knowledge, this is the first demonstration that edge information of a spatial pattern can be extracted through strong turbidity, which can potentially enrich the comprehension of actual images obtained from a complex environment.