Diffraction microtomography with sample rotation : effect of the missing apple core on the reconstruction of the sample

The observation of non-fluorescent transparent objects poses a real challenge in transmission microscopy due to their inherent low contrast in refractive index (RI). A solution for weakly diffractive samples would be using coherent light and multiple views. Indeed the 3-D distribution of the complex RI can be reconstructed from the knowledge of the scattered fields sampled under various view angles. Diffraction microtomographic imaging realized by rotating the sample using a fixed illumination was studied and the issue of the "missing cone", which results in a deformation along the optical axis, was also addressed. For this approach, the reconstruction is often based on an inverse Radon transform leading to an isotropic spatial resolution. But neglecting diffraction may result in reconstruction artifacts. We studied the reconstruction process in tomographic microscopy with sample rotation and non-negligible weak diffraction. We found that, contrary to first thought, the Optical Transfer Function still lacks some frequencies along the rotational axis. We have then investigated numerically the influence of these missing frequencies on the precision of the reconstruction.