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.