A single-exposure lens-free holography method with auto-focusing capability using non-similar states

In lens-free holographic microscopy, achieving high-resolution reconstructions requires the accurate and rapid determination of the defocus distance. Here, we introduce a novel single-shot technique that leverages the discrepancy between the captured image and the reconstructions obtained on ergodic planes with varying defocus distances. This method successfully produces a unimodal curve, offering a reliable auto-focusing solution and eliminating the need to choose different discriminative factor values for different sample types. To further validate its applicability, we performed simulations and experiments using a traditional lens-free system with amplitude and phase resolution targets. This method thus represents a viable and efficient alternative for refocusing in lens-free on-chip microscopes.