Influence of the limited detector size on spatial variations of the reconstruction accuracy in holographic tomography

Holographic tomography (HT) allows noninvasive, quantitative, 3D imaging of transparent microobjects, such as living biological cells and fiber optics elements. The technique is based on acquisition of multiple scattered fields for various sample perspectives using digital holographic microscopy. Then, the captured data is processed with one of the tomographic reconstruction algorithms, which enables 3D reconstruction of refractive index distribution. In our recent works we addressed the issue of spatially variant accuracy of the HT reconstructions, which results from the insufficient model of diffraction that is applied in the widely-used tomographic reconstruction algorithms basing on the Rytov approximation. In the present study, we continue investigating the spatially variant properties of the HT imaging, however, we are now focusing on the limited spatial size of holograms as a source of this problem. Using the Wigner distribution representation and the Ewald sphere approach, we show that the limited size of the holograms results in a decreased quality of tomographic imaging in off-center regions of the HT reconstructions. This is because the finite detector extent becomes a limiting aperture that prohibits acquisition of full information about diffracted fields coming from the out-of-focus structures of a sample. The incompleteness of the data results in an effective truncation of the tomographic transfer function for the out-of-center regions of the tomographic image. In this paper, the described effect is quantitatively characterized for three types of the tomographic systems: the configuration with 1) object rotation, 2) scanning of the illumination direction, 3) the hybrid HT solution combing both previous approaches.