An auto-focusing method for the lens-free single-shot digital holography based on the dissimilar state

Lens-free digital holography enables multi-focus quantitative phase microscopy for imaging both reflective surfaces and transparent objects. For high-resolution reconstruction in lens-free holographic microscopy, precisely and quickly determining the defocusing distance is essential. In this work, we propose a new single- shot method that relies on the disparity between the captured image and the reconstructions on ergodic planes corresponding to different defocusing distances. This approach effectively generates a unimodal curve, providing a robust solution for auto-focusing and avoiding the need to select different values for discriminative factors across distinct sample types. Furthermore, the simulations and experiments demonstrate that the entire focal-plane search process is simpler and quicker, potentially at least doubling the speed compared to traditional methods. The experiments, conducted in a traditional lens-free system, utilize amplitude and phase resolution targets to validate this method's applicability. We believe that this method will bean alternative refocusing method for lens-free on-chip microscopes.