Detailed study on ill-conditioned transmission matrices when focusing light through scattering media based on wavefront shaping

Recent advances in wavefront shaping, i.e., wavefront modulated by a spatial light modulator, have opened hopeful venues to focus light through scattering media in particular and unparalleled ways, by means of codifying the values of pixels of the modulator. The transmission matrix approach is one of the most exciting recent advances to obtain optimal phase distributions, due to the consent of enabling turbidity suppression, in both transmitted and reflected waves, with high resolution and large efficiency. However, the transmission matrix is ill-conditioned, which seriously affects the precision of phase distributions. In this paper, we study the ill-condition of the transmission matrix in detail. An idea of optimizing the singular values of the transmission matrix is proposed, which improves the accuracy and stability of the phase distribution. Experiments verify this idea.