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

摘要

Holographic tomography (HT) enables measurement of three-dimensional refractive index distribution of transparentmicro-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 ishindered by inability of the standard reconstruction algorithms to account for multiple scattering. This limitation hasbeen recently addressed with a few novel reconstruction approaches. In those techniques the tomographic reconstructionis iteratively improved by minimizing discrepancy between the experimentally acquired transmitted fields uE(x,y) and theanalogical data uq(x,y) obtained via numerical propagation of the incident beams through the current refractive indexestimate n~q(x,y,z).The accuracy of these multiple-scattering reconstruction methods depends primarily on two features: (1) the forwardmodel that allows computing the transmitted fields u_q; (2) the feedback mechanism that converts uE - u_q discrepancy intothe reconstruction upgrade n_(q+1)=n_q+Δn_(q+1). In our work, we address the first issue with the wave propagation method thatrepresents a reasonable trade-off between accuracy and time of computation. The paper focuses primary on the secondissue, i.e. the feedback mechanism, that considerably influences the performance of the multiple-scatteringreconstruction methods. In our work, we cross-analyze two feedback solutions, i.e. the gradient descent and the forwardbackwardmethod. 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 studyinvestigates accuracy of the reconstruction, time of computation as well as stability and flexibility of the feedbackmethod.