Edge sparsity criterion for robust holographic autofocusing

Autofocusing is essential to digital holographic imaging. Previously used autofocusing criteria exhibit challenges when applied to, e.g., connected objects with different optical properties. Furthermore, in some of the earlier autofocusing criteria, the polarity, i.e., whether to search for the peak or the valley as a function of depth, changes for different types of samples, which creates another challenge. Here, we propose a robust and accurate autofocusing criterion that is based on the edge sparsity of the complex optical wavefront, which we termed the "sparsity of the gradient" (SoG). We demonstrated the success of SoG by imaging a wide range of objects, including resolution test targets, stained and unstained Papanicolaou smears, stained tissue sections, and blood smears.