  We propose a three-dimensional nonlinear diffusion method to implement the
similar autofocusing function of multiple micro-objects and simultaneously
remove the defocused images, which can distinguish the locations of certain
sized scattering particles that are overlapping along z-axis. It is 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 after applying the proposed scheme when the reconstruction
range along z-axis is sufficiently long and the reconstruction depth spacing is
sufficiently fine. Therefore, the reconstructed image at ground truth z
position is remained, while the defocused images are diffused out. The results
demonstrated that the proposed scheme can diffuse out the defocused images
which are 20 um away from the ground truth z position in spite of that several
scattering particles with different diameters are completely overlapping along
z-axis with a distance of 800 um when the hologram pixel pitch is 2 um. It also
demonstrated that the sparsity distribution of the ground truth z slice cannot
be affected by the sparsity distribution of corresponding defocused images when
the diameter of the particle is not more than 35um and the reconstruction depth
spacing is not less than 20 um.
