  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.
