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.