Light propagation in turbid media: an approach of interpolation in the optimal phase matrix

Abstract

To control the light propagation in turbid media, it is necessary to reconstruct the output wavefront. In 2007 Vellekoop et al. 1 , developed an iterative algorithm that divides the input wavefront in N x N channels called segments, after passing through turbid media, the output wavefront is reconstructed by measuring the intensity at a desired point, and then the phase of each channel is updated, the final N x N phase is called optimal phase matrix. The interpolation technique is capable of transforming a N x N matrix into a second 2 N x 2 N matrix, where, the 50 percent of the resulting matrix elements correspond to the homogeneous distribution of the original matrix values and the remain values are generated by interpolating the neighbors. Our proposal uses the optimal phase matrix obtained by an iterative algorithm, and then the number of segments is increased by interpolation. We analyze the circularity, the signal to noise ratio (SNR), the Full Width at Half Maximum (FWHM) and the correlation for different output wavefronts obtained by the optimal phase matrix and the interpolation optimal phase matrix. Our results show that, Circularity, SNR, and FWHM parameters do not change significantly and the acquisition time of the optimal phase matrix decreases compared with a similar matrix obtained by the iterative algorithm; therefore, our proposed technique that consists in the combination of interpolation and iterative algorithm is useful to study the light transmission in turbid media when a high resolution is needed in the transmission matrix, for example, phase holograms transmission through turbid media.