Image formation in holographic tomography: high-aperture imaging conditions

Three-dimensional (3D) imaging by holographic tomography can be performed for a fixed detector through rotation of either the object or the illumination beam. We have previously presented a paraxial treatment to distinguish between these two approaches using transfer function analysis. In particular, the cutoff of the transfer function when rotating the illumination about one axis was calculated analytically using one-dimensional Fourier integration of the defocused transfer function. However, high numerical aperture objectives are usually used in experimental arrangements, and the previous paraxial model is not accurate in this case. Hence, in this analysis, we utilize 3D analytical geometry to derive the imaging behavior for holographic tomography under high-aperture conditions. As expected, the cutoff of the new transfer function leads to a similar peanut shape, but we found that there was no line singularity as was previously observed in the paraxial case. We also present the theory of coherent transfer function for holographic tomography under object rotation while the detector is kept stationary. The derived coherent transfer functions offer quantitative insights into the image formation of a diffractive tomography system.