Hybrid fractional Fourier transform for filtering and imaging in a single digital holography workflow.

We propose a hybrid fractional Fourier transform (hybrid FrFT) framework for off-axis digital holographic microscopy. This framework combines optical FrFT, implemented via a novel, to the best of our knowledge, three-lens object arm design, with digital FrFT filtering into a unified process. By replacing all FFT operations with FrFT, our approach adaptively minimizes conjugate overlap in spatial frequency distribution and improves the recovery of higher-frequency diffraction components. Both simulations and experimental results reveal significant enhancements in the resolution of amplitude and phase reconstruction while adhering to practical optical design constraints.