Carrier-frequency estimation for digital holograms of phase objects

Abstract

Accurate estimation of carrier fringe frequency is essential for the demodulation of off-axis digital holograms. The fringe frequency is often associated with the amplitude peak of the cross-term in the two-dimensional Fourier transform of a digital hologram. We point out that this definition of carrier frequency is not valid in general for holograms associated with phase objects. We examine the carrier-envelope representation for digital holograms from the viewpoint of Mandel’s criterion [J. Opt. Soc. Am. 57, 613 (1967)10.1364/JOSA.57.000613]. An appropriate definition of carrier frequency is observed to be the centroid of the power spectrum associated with the cross term. This definition is shown to apply uniformly to holograms associated with phase objects, is robust to noise, and leads to the smoothest (or least fluctuating) envelope representation for the demodulated object wave. The proposed definition is illustrated with simulated as well as experimentally recorded off-axis holograms.