Reconstruction of local frequencies for recovering the unwrapped phase in optical interferometry

Abstract

In optics, when interferograms or digital holograms are recorded and their phase is recovered, it is common to obtain a wrapped phase with some errors, noise and artifacts such as singularities due to the non linearities of the demodulation process. This paper shows how to reconstruct the frequency field of the wrapped phase by using adaptive Gabor filters. Gabor filters are Gaussian quadrature filters tuned in at a certain frequency. We adapt these Gabor filters by tuning them locally and estimating the frequency using wrapped finite differences of the estimated phase. Doing this process iteratively, the frequency estimation is refined and smoothed. The unwrapped phase is easily recovered by integrating the recovered frequency field using, for example, a simple line raster integration. We don’t have problems with phase inconsistencies or residues while integrating the phase, because these are removed. The obtained unwrapped phase is clean, consistent and practically error-free. We show estimation errors with simulated data and the performance of the proposed method using real-world recorded wavefronts.

Smart filtering of phase residues in noisy wrapped holograms

“…In contrast, numerical techniques for phase unwrapping have become more popular with the improvement in computer processing speed and the reduction in computational costs. Numerical techniques are mainly based on either directly unwrapping [21][22][23][24][25][26][27] or filtering [28][29][30][31][32][33][34][35] the wrapped phase. Examples of the first of these types of numerical techniques have been developed using global algorithms 23,24 , path-following algorithms 25 , and region-based algorithms 26,27 .…”

“…Several filters have been designed for reducing the noise in a wrapped phase. These include the fringe smoothing approach 28 , local fringe frequency estimation 29 , regularized phase-tracking method 30 , windowed Fourier filtering (WFF) 31 , windowed Fourier filtering and quality-guiding (WFF-QG) 32 , windowed Fourier ridges method 33 , Gabor filter local frequency 34 , and sine/cosine average filter (SCAF) 35 . These techniques reduce the noise level of highly wrapped and noisy phases.…”

Phase retrieval at all defocus distances

“…The coherence requirements of the equation include the same frequency, the same vibration direction and the same phase difference. The phase retrieval algorithm based on TIE can directly obtain the absolute phase without reference beam, and compared to the phase unwrapping method, it is fast and accurate [10,11] but sensitive to noise. On the other hand, the algorithm needs to use the method of intensity difference to approximate the intensity differential, so it needs to collect the focused image and defocus image in the propagation direction of the light field, and the distance between them is usually called ''defocus distance''.…”