Numerical refocusing algorithm for in-line holography based on sparse regularization and physical constraints

In in-line holography, accurately reconstructing the complex amplitude of a target specimen often necessitates numerical refocusing to determine the exact propagation distance. However, twin images, scattering noise, and other disturbances can significantly impair the accuracy of focal plane detection. We propose a numerical refocusing method that first removes noise and then detects the focal plane. First, we construct a noise removal model by incorporating sparse and physical constraints into angular spectral diffraction. Next, we apply an iterative optimization algorithm to obtain noise-free reconstructed complex amplitude stacks within the search interval. Finally, we utilize an evaluation criterion to precisely locate the focal plane and simultaneously reconstruct the accurate complex amplitude. Simulation and experimental results demonstrate that the proposed method achieves higher focus detection accuracy and sensitivity compared to traditional methods. Moreover, the reconstructed complex amplitude, free from twin image disturbances, can be obtained directly from a single hologram. This approach is broadly applicable to the numerical refocusing of various sample types.