Resolution analysis in a lens-free on-chip digital holographic microscope

Lens-free on-chip digital holographic microscopy (LFOCDHM) is a modern imaging technique whereby the sample is placed directly onto or very close to the digital sensor, and illuminated by a partially coherent source located far above it. The scattered object wave interferes with the reference (unscattered) wave at the plane where a digital sensor is situated, producing a digital hologram that can be processed in several ways to extract and numerically reconstruct an in-focus image using the back propagation algorithm. Without requiring any lenses and other intermediate optical components, the LFOCDHM has unique advantages of offering a large effective numerical aperture (NA) close to unity across the native wide field-of-view (FOV) of the imaging sensor in a cost-effective and compact design. However, unlike conventional coherent diffraction limited imaging systems, where the limiting aperture is used to define the system performance, typical lens-free microscopes only produce compromised imaging resolution that far below the ideal coherent diffraction limit. At least five major factors may contribute to this limitation, namely, the sample-to-sensor distance, spatial and temporal coherence of the illumination, finite size of the equally spaced sensor pixels, and finite extent of the image sub-FOV used for the reconstruction, which have not been systematically and rigorously explored until now. In this work, we derive five transfer function models that account for all these physical effects and interactions of these models on the imaging resolution of LFOCDHM. We also examine how our theoretical models can be utilized to optimize the optical design or predict the theoretical resolution limit of a given LFOCDHM system. We present a series of simulations and experiments to confirm the validity of our theoretical models.