Amplitude and phase retrieval in simultaneous π/2 phase-shifting heterodyne interferometry using the synchrosqueezing transform

This paper presents a method for amplitude and phase retrieval in simultaneous π/2 phase-shifting heterodyne interferometry. The used optical setup admits the introduction of a temporal carrier and simultaneously verifies the two-beam interferometry equation for each intensity signal, which are π/2  rad out of phase (quadrature). The spatiotemporal recovering process is obtained by isolating the object amplitude and phase using wavelet transform analysis of the temporal series composed by the difference between the measured pixel intensities corresponding to each quadrature signal. This process is subsequently improved by introducing a framework based on the synchrosqueezing transform, which recovers the data of interest with higher accuracy when very low scattering amplitudes and phase excursions must be determined in noisy working conditions. The advantages and limitations of the presented method are analyzed and discussed using numerical simulations and also experimental data obtained from temporal speckle pattern interferometry.