强散射过程中基于奇异值分解的光学传输矩阵优化方法

Transmission matrix optimization based on singular value decomposition in strong scattering process

通过测量散射介质的传输矩阵能够控制光在此介质中的传输,但目前没有通过优化传输矩阵(即搜索介质本征传输矩阵)来提高光传输效率的研究.通过测量介质的传输矩阵进行奇异值分解与背景滤波,初步优化了传输矩阵后,提出通过遗传算法再次优化传输矩阵,实现了进一步优化传输矩阵,提高了聚焦效率和信噪比.所提方法为可见光在生物组织中的成像提供了一种新的思路和方法.

In the last decade, the scattering medium has been gradually attacking attention from researchers. Among the proposed approaches, the transmission matrix（TM） is considered as an effect way to describe the scattering properties which relate to input optical and output optical fields. However, the acquired transmission matrix and its eigenvalues strongly depend on the experimental conditions, such as the numbers of input channels（limited numerical aperture and illumination area, or the pixel number of the spatial light modulator） and output channels. In other words, the actual transmission matrix of the scattering medium is the acquired transmission matrix with infinite numbers of the input and output channels. We propose an approach to obtaining the actual matrix by evaluating its eigenvalues. First, the matrix is expressed by the singular value decomposition to obtain its inverse matrix. Then first level optimization is to dispose of some extreme singular values to remove the ill-conditioned problem of the matrix, and then, as a second level optimization, the genetic algorithm is to remove the eigenvalues which have the negative contributions to the intensity of the selected focal point. Our experiments show that the gray value of the intensity and the signal-to-noise ratio（SNR） of the focal point after employing the phase pattern are 129 and 7.54, respectively. After the first level optimization, the gray value of the intensity and the SNR rise to 172 and 9.73, respectively. Then, they reach to 192 and 10.29, respectively, after adopting the genetic algorithm. After the second level optimizations, the intensity at the focal point increases 48.8% compared with the case with just the optimized phase pattern from the acquired TM, and the SNR increases by nearly 36.5%. The reason behind the increase of the intensity after the optimizations, we believe,is that the transmission matrix of the scattering medium reaches its actual matrix in certain conditions. The proposed approach opens the way to obtaining the actual transmission matrix by mathematic optimizations without increasing the experimental levels.