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We present the computational technique for automatic numerical refocusing in coherent lensless Gabor microscopy (digital in-line holographic microscopy). It is based on the adaptive filtering of the recorded on-axis Gabor hologram to eliminate its incoherent background term and extract interference fringes determined by the light scattered on the sample. Numerical propagation of such filtered hologram, based on the angular spectrum method, yields the computationally generated dark-field imaging realized in amplitude channel of the complex propagated f ield. As the focus metric we calculate the variance of the dark-field gradient - it attains maximum value in the focal planes for all types of objects (phase, amplitude and mixed phase-amplitude). Demonstrated autofocusing technique is positively validated using experimental data exhibiting significant variation of the confluence for double focal plane scenarios (two closely located sample planes filled with microbeads). Described technique compares favorably with other well-established automatic numerical refocusing methods (e.g., based on the high-pass filtered complex amplitude and edge sparsity) mainly in terms of higher axial resolution and better robustness to hologram low signal-to-noise ratio and object non-uniformity.
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M. Trusiak, M. Rogalski, P. Zdańkowski, Jose Angel Picazo-Bueno, Vicente Micó, "Numerical autofocusing in Gabor lensless microscopy employing computational dark-field imaging," Proc. SPIE 11774, Holography: Advances and Modern Trends VII, 117740G (18 April 2021); https://doi.org/10.1117/12.2589122