In optical tomography, there exist certain spatial frequency components that cannot be measured due to the limited projection angles imposed by the numerical aperture of objective lenses. This limitation, often called as the missing cone problem, causes the under-estimation of refractive index (RI) values in tomograms and results in severe elongations of RI distributions along the optical axis. To address this missing cone problem, several iterative reconstruction algorithms have been introduced exploiting prior knowledge such as positivity in RI differences or edges of samples. In this paper, various existing iterative reconstruction algorithms are systematically compared for mitigating the missing cone problem in optical diffraction tomography. In particular, three representative regularization schemes, edge preserving, total variation regularization, and the Gerchberg-Papoulis algorithm, were numerically and experimentally evaluated using spherical beads as well as real biological samples; human red blood cells, and hepatocyte cells. Our work will provide important guidelines for choosing the appropriate regularization in ODT.
Besides missing cone problem, the non-linearity of ODT is another challenging issue. The system equation of ODT is non-linear. Therefore, there are two representative approximations to linearize the problem; Born and Rytov approximation. These approximations are valid under the assumption of weakly scatterers. However, even in case each scatterer is weak scatterer so that approximations are valid, multiple scattering that occurs among these individual scatterers could cause severe distortions in reconstructed RI tomograms. In this paper, we proposed a new reconstruction algorithm for ODT using the joint sparsity of supports of samples during multiple illuminations. The algorithm is implemented using Fourier transform combined with ADMM optimization technique resulting efficient algorithm in terms of computation. We evaluated the proposed algorithm using various samples such as spherical beads, human red blood cells, hepatocyte cells, and multiple microspheres. The proposed method not only resolve the missing cone problem but also improve the resolution of RI tomograms revealing structures that are not observable under approximations.