Autofocusing of in-line holography based on compressive sensing

Holographic reconstruction is affected by the phase-conjugate wave arising from the symmetry of the complex field. Compressive sensing (CS) has been used in in-line digital holography (DH) to eliminate noise, especially the interference from twin images. Herein, CS with total variation regularization combining autofocusing is presented. It provides an autofocusing function from a single-exposure hologram and obtains reconstructed objects without twin image noise. A series of images at a fixed interval within a reconstruction distance are processed using a two-step iterative shrinkage/thresholding algorithm in CS. It can calculate the focus distance in a larger range around the focal plane using twin-image-free reconstruction, so it can achieve a higher focusing accuracy than traditional focusing methods, including the Laplace operator, absolute gradient operator, and Tamura coefficient. The proposed method is a simple combination of algorithms and a powerful extension that can effectively improve simulated and experimental image quality and handle difficult datasets, which existing algorithms cannot.