Phase Gradient Estimation Techniques in Fringe Analysis

The thesis introduces novel techniques in the field of fringe analysis for direct estimation of phase gradients or derivatives. A pseudo Wigner-Ville distribution based method is proposed to reliably estimate the phase derivatives from a single fringe pattern. The method's ability for estimating rapidly varying phase derivatives is enhanced by developing an adaptive windowing technique. Further, the two-dimensional extension of the method is presented to handle fringe patterns with severe noise. In addition, a generalized approach is described to enable direct estimation of arbitrary order phase derivatives. Subsequently, methods based on digital holographic moiré and multi-component polynomial phase formulation are introduced to measure the in-plane and out-of-plane displacements and their derivatives for a deformed object in digital holographic interferometry. These methods permit the simultaneous estimation of multiple phases and their derivatives without the need of multiple fringe patterns and complex experimental configurations, which is hitherto not possible with the current state-of-the-art fringe analysis methods. The major advantages of the developed techniques are the ability to directly estimate phase derivatives without relying on complex unwrapping, filtering and numerical differentiation operations, high computational efficiency and strong robustness against noise. In addition, the requirement of a single fringe pattern makes these techniques less error-prone in the presence of vibrations and external disturbances and enhances their applicability for dynamic measurements. Further, the developed techniques offer a potential solution to the challenging problem of simultaneous multi-dimensional deformation analysis in digital holographic interferometry. The reliable performance of these techniques is validated by numerical simulation and their practical applicability is demonstrated in digital holographic interferometry and fringe projection for slope and curvature measurement, defect detection, surface slope evolution studies and measurement of in-plane and out-of-plane displacements and their derivatives. These techniques offer substantial advancements in fringe analysis and exhibit significant application potential in areas such as non-destructive testing, biomechanics, reliability analysis, material characterization and experimental mechanics

Phase estimation using a state-space approach based method

The paper demonstrates a phase estimation method in fringe analysis. The proposed method relies on local polynomial phase approximation and subsequent state-space formulation. The polynomial approximation of phase transforms phase extraction into a parameter estimation problem, and the state-space modeling allows the application of Kalman filter to estimate these parameters. The performance of the proposed method is demonstrated using simulation and experimental results. (C) 2013 Elsevier Ltd. All rights reserved

Detection of defects from fringe patterns using a pseudo-Wigner-Ville distribution based method

The paper presents a method to identify defects from fringe patterns. In the proposed method, the phase derivatives are computed from a fringe pattern using the two-dimensional Pseudo-Wigner–Ville distribution. Since the phase derivative varies rapidly in the vicinity of the defect, the relative change in the derivatives for the normal and defect-containing fringe patterns is compared with respect to a preset threshold to identify the defect in the fringe pattern. The robustness of the method for detecting defects of various sizes and at different noise levels is shown using simulated fringe patterns

Investigations to realize a computationally efficient implementation of the high-order instantaneous moments based fringe analysis method

Recently, a high-order instantaneous moments (HIM)-operator- based method was proposed for accurate phase estimation in digital holographic interferometry. The method relies on piece-wise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients from the HIM operator using single-tone frequency estimation. The work presents a comparative analysis of the performance of different single-tone frequency estimation techniques, like Fourier transform followed by optimization, estimation of signal parameters by rotational invariance technique (ESPRIT), multiple signal classification (MUSIC), and iterative frequency estimation by interpolation on Fourier coefficients (IFEIF) in HIM-operator-based methods for phase estimation. Simulation and experimental results demonstrate the potential of the IFEIF technique with respect to computational efficiency and estimation accuracy. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3454376

Spatiotemporal characterization of a fibrin clot using quantitative phase imaging.

Studying the dynamics of fibrin clot formation and its morphology is an important problem in biology and has significant impact for several scientific and clinical applications. We present a label-free technique based on quantitative phase imaging to address this problem. Using quantitative phase information, we characterized fibrin polymerization in real-time and present a mathematical model describing the transition from liquid to gel state. By exploiting the inherent optical sectioning capability of our instrument, we measured the three-dimensional structure of the fibrin clot. From this data, we evaluated the fractal nature of the fibrin network and extracted the fractal dimension. Our non-invasive and speckle-free approach analyzes the clotting process without the need for external contrast agents

SLIM system.

<p>(A) Imaging setup. HLF: Halogen Lamp Filament, CO: Collector lens, FD: Field Diaphragm, CA: Condenser Annulus, CL: Condenser Lens, SP: Specimen, OL: Objective Lens, FP: Back Focal Plane of Objective, TL: Tube Lens, M: Mirror, IP: Image Plane, FL: Fourier Lens 1, FL: Fourier Lens 2, BS: Beam Splitter, LCPM: Liquid Crystal Phase Modulator. (B) Coherent superposition of scattered and unscattered waves.</p