Tight focusing through scattering media via a Bessel basis transmission matrix.

The transmission matrix (TM) is a powerful tool for focusing light through scattering media. Here, we demonstrate a Bessel-basis TM that enables tight focusing through the scattering media and reduces the full width at half maximum of the focus by 23% on average, as compared to the normally used Hadamard-basis TM. To measure the Bessel-basis TM, we establish a common-path inter-mode interferometer (IMI), which can fully utilize the pixels of the spatial light modulator, leading to an enhancement in the peak-to-background intensity ratio (PBR) of the focus. Experimental results suggest that the Bessel-basis TM can achieve a tighter focus behind the scattering media, and the PBR of the focus obtained by the IMI is around 14.3% higher than that achieved using the normal peripheral reference interferometry.