A Semi-Analytical Angular Spectrum Method (SAASM) is introduced for the reconstruction process of lensless digital in-line holography with spherical wave illumination. This approach solves a distortion issue in the reconstructed field that emerges when the conventional, Angular Spectrum Method with planar reconstruction wave (ASM-PRW), method is used for high numerical aperture setups. The performance of the proposed approach is compared against ASM-PRW. The benefits of SAASM in terms of resolved limit and detection efficiency of small particles near the detection limit are shown using holograms containing simulated particles, suspended glass beams of known diameter and dry pollens.
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