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The Sparsity of the Gradient (SoG) is a robust autofocusing criterion forholography, where the gradient modulus of the complex refocused hologram iscalculated, on which a sparsity metric is applied. Here, we compare twodifferent choices of sparsity metrics used in SoG, specifically, the Gini index(GI) and the Tamura coefficient (TC), for holographic autofocusing ondense/connected or sparse samples. We provide a theoretical analysis predictingthat for uniformly distributed image data, TC and GI exhibit similar behavior,while for naturally sparse images containing few high-valued signal entries andmany low-valued noisy background pixels, TC is more sensitive to distributionchanges in the signal and more resistive to background noise. These predictionsare also confirmed by experimental results using SoG-based holographicautofocusing on dense and connected samples (such as stained breast tissuesections) as well as highly sparse samples (such as isolated Giardia lambliacysts). Through these experiments, we found that ToG and GoG offer almostidentical autofocusing performance on dense and connected samples, whereas fornaturally sparse samples, GoG should be calculated on a relatively small regionof interest (ROI) closely surrounding the object, while ToG offers moreflexibility in choosing a larger ROI containing more background pixels.

Comparison of Gini index and Tamura coefficient for holographic autofocusing based on the edge sparsity of the complex optical wavefront