Non-iterative nonlinear cross-correlation imaging for Fresnel incoherent correlation holography

Realizing fast and high signal-to-noise-ratio (SNR) reconstruction of holograms in the Fresnel incoherent correlation holography (FINCH) system remains one of the key research topics of interest to researchers. In this paper, we propose a non-iterative nonlinear cross-correlation reconstruction (NCCR) method for a single-exposure hologram. In the NCCR method, two-step iterative deconvolution is first used to obtain a resolution-enhanced point spread hologram of a large-size point object. Then, the reconstructed image is obtained using a cross-correlation reconstruction method based on a single modulation parameter. Simulation and experimental results demonstrated the effectiveness of the NCCR method in improving the SNR of reconstructed images and restoring object detail compared to multi-step phase-shifting techniques and other reconstruction methods in point spread function engineering. The NCCR method extends the viability of obtaining a reconstructed hologram image in point spread function engineering and provides an effective reference method for the fast and high SNR reconstruction of a hologram in the FINCH system.