Optical focusing through/inside scattering media, like multimode fiber and biological tissues, has significant impact in biomedicine yet considered challenging due to strong scattering nature of light. Previously, promising progress has been made, benefiting from the iterative optical wavefront shaping, with which deep-tissue high-resolution optical focusing becomes possible. Most of iterative algorithms can overcome noise perturbations but fail to effectively adapt beyond the noise, e.g. sudden strong perturbations. Re-optimizations are usually needed for significant decorrelated medium since these algorithms heavily rely on the optimization 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, dynamic mutation algorithm, with high adaptability against perturbations by probing how far the optimization has gone toward the theoretically optimum. The diminished focus of scattered light can be effectively recovered when perturbations to the medium cause significant drop of the focusing performance, which no existing algorithms can achieve due to their inherent strong dependence on previous optimizations. With further improvement, this study may boost or inspire many applications, like high-resolution imaging and stimulation, in instable scattering environments.
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