Generalized phase-shifting digital holography using normalized phase-shifted holograms

We propose a normalization method for the speckle-like holograms observed in digital holography. We show that the norm of phase-shifted holograms can be approximated by the same value, regardless of the phase shift, when the phase distribution of an object wave in a Fresnel diffraction field satisfies the randomness condition. We present an object-wave retrieval algorithm that uses normalized phase-shifted holograms to calculate the amplitude and phase of the object wave directly, without estimating phase-shift values. In addition, we develop a scheme to estimate a direct-current term by averaging several randomly phase-shifted holograms. The proposed method is verified through numerical simulations and optical experiments.