High resolution lensless microscopy based on Fresnel propagation

Digital holography allows for the recording and reconstruction of three-dimensional
images using interference and diffraction principles. The propagation of light from
the hologram plane to the reconstruction plane is a crucial step, often achieved
through Fresnel propagation, a method that inherently transforms the reconstructed
pixel pitch to provide diffraction-limited imaging. However, the accuracy of this
method is limited by the Fresnel approximation, especially in applications such
as digital holographic microscopy. We present a simple method that significantly
improves the accuracy of the Fresnel approximation by incorporating higher orders
of the binomial approximation. We validate the effectiveness of our approach
through high numerical aperture simulations and experimental results, demonstrating superior sub-micron resolution and reduced distortions compared with standard
Fresnel propagation.