Rapid measurement of transmission matrix with the sequential semi-definite programming method**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFB1104500), the Natural Science Foundation of Beijing (Grant No. 7182091), and the National Natural Science Foundation of China (Grant No. 21627813).

Abstract

This paper puts forward for the first time a combined transmission matrix (TM) method to measure the monochromatic TM of scattering media without a reference beam. This method can be named a sequential semi-definite programming method which combines the sequential algorithm and the semi-definite programming method. Firstly, each part of the TM is calculated respectively in proper sequence. Then every part of TM is combined to form a complete TM in accordance with a certain rule. The phase modulation of the incident light is achieved by using a high speed digital mirror device with the superpixel method. We have experimentally demonstrated that the incident light field is focused at the target through scattering media using the measured TM to optimize the wavefront of the incident light. Compared with the semi-definite programming method, our method takes less computational time and occupies less memory space. The sequential semi-definite programming method shows potential applications in imaging through biological tissues.