Removal of defocused images using three-dimensional nonlinear diffusion based on digital holography

We combine the 3D hybrid-Weickert nonlinear diffusion regularizer with digital holography, which can distinguish the locations of certain small-sized particles that are overlapped along the z-axis, to realize autofocusing of multiple micro-objects and simultaneously remove the defocused images. The proposed method is applied to all the reconstruction slices generated from the hologram after each back-propagation. After applying the proposed scheme for certain small-sized particles, the reconstructed image at the ground truth z position is retained, the defocused images are diffused out when the reconstruction range along the z-axis is sufficiently long and the reconstruction depth spacing is sufficiently fine. The results demonstrated that the proposed scheme can diffuse out the defocused images that are 20 μm from the ground truth z position, despite several scattering particles of different diameters being completely overlapped along the z-axis with a distance of 800 μm when the hologram pixel pitch is 2 μm. In addition, the results revealed that the sparsity distribution of the ground truth z slice is not affected by the sparsity distribution of the corresponding defocused images when the diameter of the particle is less than 35 μm and the reconstruction depth spacing is more than 20 μm.