Method For Fringe Pattern Analysis Research Articles

Hilbert–Huang transform based advanced Bessel fringe generation and demodulation for full-field vibration studies of specular reflection micro-objects

The Hilbert-Huang transform working principle is used to develop advanced single-frame and two-frame Bessel fringe pattern generation and demodulation algorithms especially tailored to enhance full-field vibration studies using time-averaged interferometry. The Bessel fringe pattern, named as the Besselogram, is understood as calculated amplitude modulation/contrast variation map of the time-averaged interferogram intensity distribution. Proposed Besselogram processing techniques are computationally fast and robust to fringe pattern imperfections and environmental disturbances encountered in interferometric studies of vibrating micro-objects. The advanced fast adaptive bidimensional empirical mode decomposition scheme is employed to filter interferograms, Bessel fringes and their phase maps. Reported Bessel fringe pattern analysis method possesses unique ability to determine both vibration phase and amplitude distribution maps from a single time-averaged interferogram. Comprehensive numerical simulations corroborate advantageous features of proposed methods. Experimental evaluation performed for two resonant modes of a silicon micro-membrane is enclosed for completeness of the analysis.

Complex amplitude reconstruction for dynamic beam quality M2 factor measurement with self-referencing interferometer wavefront sensor.

A real-time complex amplitude reconstruction method for determining the dynamic beam quality M2 factor based on a Mach-Zehnder self-referencing interferometer wavefront sensor is developed. By using the proposed complex amplitude reconstruction method, full characterization of the laser beam, including amplitude (intensity profile) and phase information, can be reconstructed from a single interference pattern with the Fourier fringe pattern analysis method in a one-shot measurement. With the reconstructed complex amplitude, the beam fields at any position z along its propagation direction can be obtained by first utilizing the diffraction integral theory. Then the beam quality M2 factor of the dynamic beam is calculated according to the specified method of the Standard ISO11146. The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment, including the static and dynamic beam process. The experimental method is simple, fast, and operates without movable parts and is allowed in order to investigate the laser beam in inaccessible conditions using existing methods.

Fringe Evaluation and Phase Unwrapping of Complicated Fringe Patterns by the Data-Dependent Fringe Processing Method

Evaluation of noisy fringe patterns is important for solving problems of nondestructive testing and is widely used in moire, holographic, and speckle interferometry. In this paper, a new method of fringe pattern analysis has been proposed based on iterative estimation of local fringe amplitude, spacing, and orientation. Fringe parameter evaluation at each iteration step allows the formation of a two-dimensional (2-D) data-dependent anisotropic impulse response of a spatial filter that allows suppression of the noise influence without decreasing the fringe visibility. When the local fringe parameters are obtained, it is possible to find the phase difference at each point of the fringe pattern and at any other one within the local 2-D area. These local phase differences are utilized to recover the wrapped fringe phase at the point using a local model of the fringe pattern fitted under the criterion of root-mean-square error minimization. The high noise immunity of the proposed method was verified experimentally when processing complicated fringe patterns with 2-D fringe phase unwrapping

Windowed Fourier transform for fringe pattern analysis: addendum.

Novel approaches based on windowed Fourier transform for demodulation of fringe patterns were previously presented [Appl. Opt. 43, 2695-2702 (2004)], where extraction of phase and phase derivatives from either phase-shifted fringe patterns or a single-carrier fringe pattern was the main focus. I show that the same methods can be applied to process a single closed-fringe pattern in either noise reduction or phase approximation, which adds to the versatility of the windowed Fourier-transform method for fringe pattern analysis.

Software calibration of the multifringe pattern analysis of circular zone plates

The linearized perturbation method for fringe pattern analysis and its extension to multifringe analysis have been recently introduced @Hilaire, Ph.D. dissertation ~Rensselaer Polytechnic Institute, Troy, N.Y., 1993!#. For isolating the error component that is due to information processing—as opposed to imageacquisition errors— experimental calibration experiments were conducted by use of computer-generated fringe patterns. The effects of noise, fringe completeness, image resolution, illumination, quantization, and displacement magnitude are tested and discussed in evaluating the software’s performance and accuracy. © 1997 Optical Society of America

Complex phase tracing method for fringe pattern analysis

We present what we believe to be a novel complex phase tracing method for fringe pattern analysis related to the phase-locked loop idea. The image with deformed complex fringes is analyzed with lexicographic scansion that leads directly to the investigated phase without unwrapping. Robustness of the procedure is ensured by the delay mechanism in the process of calculating the reference value. A numerical model and examples of application of the presented method are given.

A New Fringe Pattern Analysis Method Using Elliptically Polarized White Light with Application to Photoviscoelastic Analysis

A New Fringe Pattern Analysis Method Using Elliptically Polarized White Light with Application to Photoviscoelastic Analysis

Software calibration of the multifringe pattern analysis of circular zone plates

The linearized perturbation method for fringe pattern analysis and its extension to multifringe analysis have been recently introduced [Hilaire, Ph.D. dissertation (Rensselaer Polytechnic Institute, Troy, N.Y., 1993)]. For isolating the error component that is due to information processing-as opposed to image-acquisition errors-experimental calibration experiments were conducted by use of computer-generated fringe patterns. The effects of noise, fringe completeness, image resolution, illumination, quantization, and displacement magnitude are tested and discussed in evaluating the software's performance and accuracy.

Generation of the derivative of out-of-plane displacements in the high-sensitivity grating interferometry configuration

A simple method for determining the surface slope of a specimen under test in the high-sensitivity grating interferometry setup is proposed. The information on the derivative of out-of-plane displacement is obtained by software subtraction of two primary interferograms: a conventional one and one with diffraction orders laterally displaced in the image plane. Very good coincidence between the theoretical and experimental results has been obtained. The method can be used for studying static and transient events depending on the fringe pattern analysis method used.

Fringe-pattern analysis using a spatial phase-stepping method with automatic phase unwrapping

Presents a new method of fringe-pattern analysis by spatial phase stepping (SPS). The SPS method combines the computational simplicity of phase stepping with the single-image analysis capability of the Fourier transform method. The technique works by subdividing a linearized fringe pattern into three component images, from which the phase is calculated by a three-phase step algorithm. A computer simulation has been undertaken to demonstrate the theory and to enable an analysis of systematic errors. In addition, an experimental transonic flow field is solved by SPS and a comparison is made with results derived using the Fourier transform method. The experiment also demonstrates the use of the minimum spanning tree phase-unwrapping strategy to create a continuous map of the whole transonic flow field.

Modified procedure for automatic surface topography

A fast technique for automated shape measurement in fringe projection crossed-optical-axes geometry system is proposed. The technique is based on the carrier-frequency phase-shifting method of fringe pattern analysis and automatic correction for the systematic errors. Theoretical analysis and experimental testing of the system are presented. A few examples of application are described.

High accuracy Fourier transform fringe pattern analysis

The principle of the Fourier transform method of fringe pattern analysis is described with emphasis on the refinements for high accuracy measurements. Characteristics of the main sources of errors of the retrieved phase in respect to the interferogram features and the modified software procedure are given. The quantitative results of the analysis of computer-generated and real interferograms are presented. The possibility of obtaining the overall accuracy of λ/100 is proved.

Investigation of the Fourier-transform method of fringe pattern analysis

The tolerance of the Fourier-transform method of fringe pattern analysis to increasing levels of signal-independent random additive noise and increasingly complicated phase functions is investigated. It is shown that the condition that the phase must be a slowly varying function compared to the variation introduced by the carrier frequency is a fairly flexible one.