Reference-free transmission matrix retrieval and rapid focusing through scattering media via self-correcting goal optimization method

Wavefront shaping through scattering media using the transmission matrix (TM) is currently limited by the computation speed of TM. To overcome this limitation, we propose a self-correcting goal optimization algorithm (SCGOA) that reduces complexity via weighted subspace optimization and demonstrates high tolerance for coarse phase quantization. This feature renders the algorithm fully compatible with high-refresh-rate MEMS Phase Light Modulators (PLMs). By integrating SCGOA with such hardware, we enable rapid reference-free TM retrieval. Experimental results validate that this method achieves accurate transmission matrix retrieval under low phase quantization, yielding a 57.44% enhancement in theoretical focusing efficiency and enabling a 10-point scan within 0.27 seconds.