Fast compensation for arbitrary focusing through scattering media

We introduce a fast compensation scheme to realize arbitrary focusing after propagation through a scattering sample. Theoretical analysis of the effect of cross terms on multi-point focusing is conducted based on the transmission matrix theory. The results show that the cross-term influence is very significant, which needs to be considered. The Multi-Population Genetic Algorithm is adopted to retrieve the input mode for the suppression of the cross-term effect. In order to realize fast compensation and reduce measurement noise, the off-axis holographic method is used to measure the large transmission matrix, which reduces the number of measurements compared with the traditional method. In the experiment, after retrieving the input phase, we obtain a high-quality focal output, and the signal-to-noise ratio is increased by 13.6 dB.