Comparative analysis of feedback methods in reconstruction algorithms for multiple-scattering holographic tomography

Holographic tomography (HT) enables measurement of three-dimensional refractive index distribution of transparent micro-objects by merging information from multiple transmitted waves corresponding to various illumination directions. HT has proven its great potential in technical inspection and biomedical studies; nonetheless, its further progress is hindered by inability of the standard reconstruction algorithms to account for multiple scattering. This limitation has been recently addressed with a few novel reconstruction approaches. In those techniques the tomographic reconstruction is iteratively improved by minimizing discrepancy between the experimentally acquired transmitted fields uE(x,y) and the analogical data uq(x,y) obtained via numerical propagation of the incident beams through the current refractive index estimate nq(x,y,z). The accuracy of these multiple-scattering reconstruction methods depends primarily on two features: (1) the forward model that allows computing the transmitted fields uq; (2) the feedback mechanism that converts uE - uq discrepancy into the reconstruction upgrade nq+1=nq+Δnq+1. In our work, we address the first issue with the wave propagation method that represents a reasonable trade-off between accuracy and time of computation. The paper focuses primary on the second issue, i.e. the feedback mechanism, that considerably influences the performance of the multiple-scattering reconstruction methods. In our work, we cross-analyze two feedback solutions, i.e. the gradient descent and the forward backward method. The performance of these solutions is tested via numerical simulations on different types of samples: step-objects representing technical samples and gradient structures emulating biological specimens. Our study investigates accuracy of the reconstruction, time of computation as well as stability and flexibility of the feedback method.