Signal tracking approach for phase estimation in digital holographic interferometry

Abstract

In this research work, we introduce a novel approach for phase estimation from noisy reconstructed interference fields in digital holographic interferometry using an unscented Kalman filter. Unlike conventionally used unwrapping algorithms and piecewise polynomial approximation approaches, this paper proposes, for the first time to the best of our knowledge, a signal tracking approach for phase estimation. The state space model derived in this approach is inspired from the Taylor series expansion of the phase function as the process model, and polar to Cartesian conversion as the measurement model. We have characterized our approach by simulations and validated the performance on experimental data (holograms) recorded under various practical conditions. Our study reveals that the proposed approach, when compared with various phase estimation methods available in the literature, outperforms at lower SNR values (i.e., especially in the range 0-20 dB). It is demonstrated with experimental data as well that the proposed approach is a better choice for estimating rapidly varying phase with high dynamic range and noise.

Phase unwrapping with Kalman filter based denoising in digital holographic interferometry

“…The resultant noisy wrapped phase is shown Performance of unwrapping operation by FFT based method is hindered when the data is severely corrupted by noise and rapidly varying. So, to demonstrate the effectiveness of the proposed method on rapidly varying holographic data, we have adapted the same experimental data set used in [15] for validation purpose. Figure 2 shows the simulation results of the proposed algorithm on rapidly varying real holographic data.…”

“…It is an optimal estimator in Minimum Mean Squared Error (MMSE) sense, if the state space model is linear. In this section, we propose a linear state space model based on Taylor series expansion of the phase map [15]. The proposed approach here uses Kalman filter for denoising on top of unwrapping algorithm.…”

“…All the unwrapping methods available in the literature don't consider the effect of noise in the wrapped phase and result in noisy phase maps and frequently employ ad-hoc heuristic techniques such as median filtering to remove noise. The piecewise polynomial approximation approach [12] and signal tracking approach [15], [16] provides unwrapped phase directly, but the non-linear measurement model limits the performance of those methods. In this paper we propose a mathematically sound and more reliable restoration approach for the estimation of accurate phase map by exploiting the properties of Taylor series expansion with Kalman filter framework.…”

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter

“…The spatial evolution of phase and measurements are given by a state space representation. Extended Kalman filter (EKF) [26,27] and unscented Kalman filter (UKF) [28][29][30] have been the main choices for the purpose of state estimation. The proposed algorithm falls under this catergory of phase unwrapping methods.…”

Simultaneous estimation of phase and itspth order derivatives

“…Accordingly, various fringe analysis techniques have appeared in the literature to extract the interference phase and phase derivatives from the noisy phase fringe patterns. In recent times, many techniques have been developed for the estimation of the interference phase [2][3][4][5][6]. The phase derivatives can be computed by numerical differentiation of the interference phase.…”