Accurate efficient carrier estimation for single-shot digital holographic imaging.

Off-axis digital holograms are commonly processed using the Fourier transform method. This method requires estimation of the carrier frequency peak in the two-dimensional Fourier domain. The accuracy of peak location information using the standard fast Fourier transform (FFT) routines is limited by the pixel size, thus giving rise to a residual carrier component in the reconstructed image. In this Letter, we use an efficient two-step process for cross-term peak location to sub-pixel accuracy where the standard FFT-based peak finding procedure is followed by a high-resolution discrete Fourier transform (DFT) calculation at the nominal peak location. It is shown that the residual tilt artifacts due to a small change in the magnitude of the carrier frequency or due to the rotation of the fringe pattern are uniformly removed with this method. For a digital hologram of size M×N pixels, the high-resolution DFT calculation with an up-sampling factor of α requires an additional computational effort of O(MNα) which is marginal when α≪M,N and, thus, provides a practical single-shot method for accurate demodulation of digital holograms.