Refocusing criterion via sparsity measurements in digital holography

Several automatic approaches have been proposed in the past to compute the refocus distance in digital holography (DH). However most of them are based on a maximization or minimization of a suitable amplitude image contrast measure, regarded as a function of the reconstruction distance parameter. Here we show that, by using the sparsity measure coefficient regarded as a refocusing criterion in the holographic reconstruction, it is possible to recover the focus plane and, at the same time, establish the degree of sparsity of digital holograms, when samples of the diffraction Fresnel propagation integral are used as a sparse signal representation. We employ a sparsity measurement coefficient known as Gini's index thus showing for the first time, to the best of our knowledge, its application in DH, as an effective refocusing criterion. Demonstration is provided for different holographic configurations (i.e., lens and lensless apparatus) and for completely different objects (i.e., a thin pure phase microscopic object as an in vitro cell, and macroscopic puppets) preparation.