Fast and accurate carrier frequency estimation for off-axis holography by maximizing projection in the Fourier domain via simplex search

Off-axis digital holography enables single‑exposure acquisition via spatial carrier modulation, where accurate carrier frequency estimation is essential for phase reconstruction. Conventional methods are limited by the subpixel nature of carrier frequencies and high computational complexity, restricting real‑time, high‑resolution applications. We propose a Fourier‑domain simplex carrier estimation (FDSCE) method that reformulates carrier estimation as a continuous two‑dimensional optimization, maximizing the projection of the sampled hologram onto a complex exponential basis. A three‑vertex simplex initialized near the FFT peak iteratively refines the frequency estimate. Unlike grid‑based techniques, FDSCE operates directly in the continuous frequency domain without dense spectral sampling, markedly improving both accuracy and efficiency. Simulation and experimental results demonstrate that FDSCE achieves precise subpixel estimation with reduced computational cost, offering an effective solution for real‑time holographic imaging.