Unfocused images removal of z-axis overlapping Mie scattering particles by using three-dimensional nonlinear diffusion based on digital holography

We propose a three-dimensional nonlinear diffusion method to remove the unfocused images of certain sized Mie scattering particles which are overlapping along z-axis. It is simultaneously applied to all of the reconstruction slices that are generated from the captured hologram after each back propagation. For certain small sized particles, the maxima of maximum gradient magnitude of each reconstruction slice appears at the ground truth z position when the reconstruction range along z-axis is sufficiently long and the reconstruction depth spacing is sufficiently fine after applying the proposed scheme, therefore, the reconstructed image at ground truth z position is remained, however, the unfocused images are diffused out. The results demonstrated that the proposed scheme can diffuse out the unfocused images which are 20um away from the ground truth z position in spite of that several Mie scattering particles were completely overlapping along z-axis with a distance 800um when the diameter is 15um and the hologram pixel pitch is 2um. It also demonstrates that the sparsity of the ground truth z slice cannot be affected by the sparsity of corresponding unfocused images when the particle is small enough as well when reconstruction depth spacing is higher than 20um