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We propose a three-dimensional nonlinear diffusion method to implement thesimilar autofocusing function of multiple micro-objects and simultaneouslyremove the defocused images, which can distinguish the locations of certainsized scattering particles that are overlapping along z-axis. It is applied toall of the reconstruction slices that are generated from the captured hologramafter each back propagation. For certain small sized particles, the maxima ofmaximum gradient magnitude of each reconstruction slice appears at the groundtruth z position after applying the proposed scheme when the reconstructionrange along z-axis is sufficiently long and the reconstruction depth spacing issufficiently fine. Therefore, the reconstructed image at ground truth zposition is remained, while the defocused images are diffused out. The resultsdemonstrated that the proposed scheme can diffuse out the defocused imageswhich are 20 um away from the ground truth z position in spite of that severalscattering particles with different diameters are completely overlapping alongz-axis with a distance of 800 um when the hologram pixel pitch is 2 um. It alsodemonstrated that the sparsity distribution of the ground truth z slice cannotbe affected by the sparsity distribution of corresponding defocused images whenthe diameter of the particle is not more than 35um and the reconstruction depthspacing is not less than 20 um.

Defocused images removal of axial overlapping scattering particles by using three-dimensional nonlinear diffusion based on digital holography