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Holographic tomography (HT) enables nondestructive, quantitative measurement of three-dimensional refractive index distribution of transparent, weakly-scattering micro-samples. The method has been successfully applied for inspection of technical objects, as well as biomedical specimens. The key element of the HT measurement is acquisition of multiple holograms corresponding to various projection directions. In the conventional configuration of HT, this is achieved by rotating a sample, which provides high and almost isotropic resolution of tomographic imaging. However, the major disadvantages of this configuration is degradation of the reconstruction quality due to inaccuracies of the sample rotation. In this paper, we propose a novel autofocusing solution, which enables compensation of the rotation errors in HT. The method utilizes cross-analysis of two optical fields that were registered for special combination of the illumination and rotation angles. The proper selection of these parameters ensures redundancy of information in the fields, which here is used for quantitative evaluation of the misalignment error. Notably, the proposed solution is fundamentally different than other alignment methods for HT. Those methods utilize autofocusing algorithms that assume a single in-focus plane of a sample. Contrarily, our solution does not disregard the 3D character of a sample and thus is compatible with tomographic measurements. The utility of the proposed alignment method is validated with numerical simulations using two examples of complex samples with large axial thickness: a set of beads and Shepp-Logan phantom.
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