Multiscale windowed Fourier transform for phase extraction of fringe patterns

A multiscale windowed Fourier transform for phase extraction of fringe patterns is presented. A local stationary length of signal is used to control the window width of a windowed Fourier transform automatically, which is measured by an instantaneous frequency gradient. The instantaneous frequency of the fringe pattern is obtained by detecting the ridge of the wavelet transform. The numerical simulation and experiment have proved the validity of this method. The combination of the windowed Fourier transform and the wavelet transform makes the extracted phase more precise than other methods.     

Phase measuring algorithm for extraction of isochromatics of photoelastic fringe patterns

In recent years phase-measuring techniques have been applied to the problem of extracting information of photoelastic data. We present a new phase-measuring algorithm for extraction of the isochromatics of photoelastic fringe patterns. The algorithm permits the extraction of the isochromatic phase with almost no influence from the isoclinics, thus avoiding the usual problems of low-modulation areas associated with isoclinics. The isochromatic phase map obtained with this algorithm is well suited for a full separation of the stress components in a sample. The algorithm can be used with any commercial diffuse-light circular polariscope.     

Direct extraction of phase gradients from Fourier-transform and phase-step fringe patterns

An approach to computing pixel-by-pixel gradients of optical phase directly from digitally encoded Fourier-transform or phase-stepped fringe patterns is described. This approach can be classified as a phase unwrapping but is really a sine-cosine demodulation technique that finds its roots in the differential cross-multiplier phase-demodulation technique commonly used by the optical fiber sensor community. This technique is algorithmically simple, does not rely on a computation of the arctangent, and therefore is not subject to some of the limitations of the standard phase-unwrapping methodologies. The proposed phase-gradient technique is demonstrated by the calculation of strain fields from moir6 interferometric fringe patterns.     

New spin filters for interferometric fringe patterns and grating patterns

The basic spin filter for interferometric fringe patterns is improved and developed into several new versions for different applications. These spin filters can filter off random noise efficiently and have almost no blurring effect and phase distortion for the fringe patterns. First, they find the local fringe tangent direction, and then they apply a one-dimensional low-pass filter on this direction. In this way the spin filters can separate easily and clearly high-frequency noise from a real fringe signal with nearly zero frequency. The new spin filters are suitable not only for various fringe patterns but also for wrapped-phase, line-grating, and cross-grating patterns, which are impossible by common filters.     

Design of adaptive digital filters for phase extraction in complex fringe patterns obtained using the Ronchi test

A powerful technique is presented for processing complex fringe patterns with high noise levels and arbitrary distributions of spatial frequencies, which can successfully extract the phase information. Artifacts that arise from phase extraction in local filtering approaches are avoided by using a simple design and implementation strategy for the adaptive filter, based on the theory of digital filter design used in electronics, and applied to pixel rows (or columns) in the fringe-pattern. The filter designed in this manner is then applied to phase extraction in an experimental fringe pattern measured in a digital Ronchi test setup using a Carré phase-shifting procedure. The filtering strategy has a very low computational cost and allows phase extraction in noisy ronchigrams regardless their spatial frequency distribution, provided the fringes are still visible.     

Assessment of local residual strain by electron backscatter patterns and nanoindentation

Abstract

Nickel base superalloy and aluminium single crystal and polycrystalline specimens have been examined using mechanical property microprobe (MPM) measurements and electron backscatter patterns (EBSPs) as a function of applied strain. Grids of lines deposited on to the specimens before three point bending were used to determine the macroscopic strain. The MPM, or nanoindenter, has been used to produce arrays of five by three indents across the edge of the specimens, both before and after bending. Electron microscope film EBSPs have been produced from regions within the nanoindenter arrays. The effects of strain can be seen in the change in Kikuchi band profile and thus EBSP ‘image quality’ and in changes in the hardness of the sample. Software is being developed to quantify these differences. It has been found that when the nickel base superalloy calibration specimens were bent, stress relief occurred by the formation of slip bands. This caused problems with strain calibration, and alternative methods are being investigated.

MST/3677     

Fast half-quadratic regularized phase tracking for nonnormalized fringe patterns

Although one of the simplest and powerful approaches for the demodulation of a single fringe pattern with closed fringes is the regularized phase-tracking (RPT) technique, this technique has two important drawbacks: its sensibility at the fringe-pattern modulation and the time employed in the estimation. We present modifications to the RPT technique that consist of the inclusion of a rough estimate of the fringe-pattern modulation and the linearization of the fringe-pattern model that allows the minimization of the cost function through stable numerical linear techniques. With these changes, the demodulation of nonnormalized fringe patterns is made with a significant reduction in the processing time, preserving the demodulation accuracy of the original RPT method.     

Spin filtering with curve windows for interferometric fringe patterns

Filtering off noise from fringe patterns is important for the processing and analysis of interferometric fringe patterns. Spin filters proposed by the author have been proven to be effective in filtering off noise without blurring and distortion to fringe patterns with small fringe curvature. But spin filters still have problems processing fringe patterns with large fringe curvature. We develop a new spin filtering with curve windows that is suitable for all kinds of fringe pattern regardless of fringe curvature. The experimental results show that the new spin filtering provides optimal results in filtering off noise without distortion of the fringe features, regardless of fringe curvature.     

基于特征端元提取的像元分解方法

通过对端元概念的引申,提出了更具一般性的特征端元的概念,从而将端元方法的适用范围从高光谱数据拓展到了多光谱数据和全色遥感数据.同时改进了端元提取算法,并提出了基于特征端元提取的像元分解方法.实验结果表明,基于特征端元提取的混合像元分解方法可以得到较好的像元分解结果,并且该方法与传统的端元概念及混合像元分解结果具有良好的可比性.     

Characterization of isochromatic fringe patterns for a dynamically propagating interface crack

The isochromatic fringes surrounding a crack propagating along a bimaterial interface have been developed and characterized. A parametric investigation has also been conducted to study the influence of various fracture parameters on this isochromatic fringe pattern. The relevant fracture parameters of interest were the crack-tip velocity, the mode mixity of loading and the non-singular stress field component. In all the cases the fringe pattern was compared with the more familiar patterns that are generated for the case of crack propagation in homogeneous media. It was found that both the crack tip velocity and the mode mixity of loading have a significant effect on the size and shape of the isochromatic fringe pattern surrounding a crack tip propagating along a bimaterial interface. However, the non-singular stress field component was found not to have a substantial effect on the fringe pattern. This is in contrast with the case of crack propagation in homogeneous media, where the non-singular stress field component determines the tilt of the fringe contours. The paper also presents an appropriate scheme to analyze experimental fringe contours to extract the various fracture parameters of interest. Finally, this scheme is employed to analyze actual experimental data from a typical bimaterial interface fracture experiment.     

Tangent least-squares fitting filtering method for electrical speckle pattern interferometry phase fringe patterns

An efficient method is proposed to reduce the noise from electrical speckle pattern interferometry (ESPI) phase fringe patterns obtained by any technique. We establish the filtering windows along the tangent direction of phase fringe patterns. The x and y coordinates of each point in the established filtering windows are defined as the sine and cosine of the half-wrapped phase multiplied by a random quantity, then phase value is calculated using these points' coordinates based on a least-squares fitting algorithm. We tested the proposed methods on the computer-simulated speckle phase fringe patterns and the experimentally obtained phase fringe pattern, respectively, and compared them with the improved sine/cosine average filtering method [Opt. Commun. 162, 205 (1999)] and the least-squares phase-fitting method [Opt. Lett. 20, 931 (1995)], which may be the most efficient methods. In all cases, our results are even better than the ones obtained with the two methods. Our method can overcome the main disadvantages encountered by the two methods.     

A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns

A general method is presented for determining mixed-mode stress intensity factors K_I and K_II from isochromatic fringes near the crack tip. The method accounts for the effects of the far-field, non-singular stress, σ_ox. A non-linear equation is developed which relates the stress field in terms of K_I, K_II, and σ_ox to the co-ordinates, r and θ, defining the location of a point on an isochromatic fringe of order N.

Four different approaches for the solution of the non-linear equation are given. These include: a selected line approach in which data analysis is limited to the line θ = π and the K---N relation can be linearized and simplified, the classical approach in which two data points at (r_m, θ_m) are selected where r_m/θ = 0; a deterministic method where three arbitrarily located data points are used; and an over-deterministic approach where m (>3) arbitrarily located points are selected from the fringe field.

Except for the selected line approach, the method of solution involves an iteractive numerical procedure based on the Newton-Raphson technique. For the over-deterministic approach, the method of least squares was employed to fit the K-N relation to the field data.

All four methods provide solutions to 0.1% providing that the input parameters r, θ, and N describing the isochromatic field are exact. Convergence of the iterative methods is rapid (3–5 iterations) and computer costs are nominal. When experimental errors in the measurements of r and θ are taken into consideration, the over-deterministic approach which utilizes the method of least squares has a significant advantage. The method is global in nature and the use of multiple-point data available from the full-field fringe patterns permits a significant improvement in accuracy of K_I, K_II, and σ_ox determinations.     

Fringe-orientation maps and fringe skeleton extraction by the two-dimensional derivative-sign binary-fringe method

The fringe-orientation information of an interferometric fringe pattern is provided in the form of a fringe-orientation map by spin filtering. The fringe-orientation information is an important feature of fringe patterns and is helpful in many fringe-pattern processing algorithms. With the help of a fringe-orientation map the two-dimensional derivative-sign binary-fringe method is developed to extract fringe skeletons from a fringe pattern with an arbitrary fringe distribution. This fringe skeleton extraction method does not require thresholds and a thinning process. It is relatively robust and highly accurate.     

Constant cross section calibration beam for setting resistance strain gauges to normalized biaxial deformations

The distribution of longitudinal and transverse deformations was studied on the surface of a bent calibration beam of rectangular cross section to find the axial and transverse sensitivity of resistance strain gauges mounted on the beam surface along and across its axis. Translated from Izmeritel'naya Tekhnika, No. 5, pp. 35–39, May, 1998.     

Error analysis for determination of stress intensity factors from isochromatic crack tip fringe patterns

A statistical error analysis for the stress intensity factor as determined by the classical apogee point method is represented. Random errors in the measurements of apogee distance, tilt angle and crack tip position are considered the most typical sources for inaccuracies in the determination of the stress intensity factor.     

Hypothesis of local determinability for five-dimensional strain trajectories

Summary Hypothesis of local determinabilily predicting the behavior of the angles between a stress vector and a Frenet's frame established on a strain trajectory in a five-dimensional vector space of strain deviator is discussed to formulate a plastic constitutive equation of metals under complex loadings. Namely, a set of equations giving the rates of angles at the relevant instant for arbitrary five-dimensional curved strain trajectories is derived first on the basis of the previously reported experiments for the deformation along three-dimensional orthogonal trilinear strain trajectories. Then, a simple constitutive equation is formulated by employing the above equations together with the relation between the magnitude of stress vector and the arc-length of strain trajectory for pure torsion. It is found that the resulting equation reproduced well the above experimental results.With 4 Figures     

Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry

We present a ray-tracing-based method for simulation of interference fringe patterns (IFPs) for measuring gear tooth flanks with a two-path interferometer. This simulation method involves two steps. In the first step, the profile of an IFP is achieved by means of ray tracing within the object path of the interferometer. In the second step, the profile of an IFP is filled with interference fringes, according to a set of functions from an optical path length to a fringe gray level. To examine the correctness of this simulation method, simulations are performed for two spur involute gears, and the simulated IFPs are verified by experiments using the actual two-path interferometer built on an optical platform.     

Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns

One of the powerful approaches to demodulate a single fringe pattern is the regularized phase tracking (RPT) technique. Here, a new improvement in the RPT technique is presented. This new improvement consists in the addition of one term that models the fringe-pattern modulation. With this new term, the RPT technique can be used for the demodulation of nonnormalized fringe patterns. The performance of the improved RPT technique is shown on examples of various fringe patterns.     

Generalized spin filtering and an improved derivative-sign binary image method for the extraction of fringe skeletons

Generalized spin filters, including several directional filters such as the directional median filter and the directional binary filter, are proposed for removal of the noise of fringe patterns and the extraction of fringe skeletons with the help of fringe-orientation maps (FOM's). The generalized spin filters can filter off noise on fringe patterns and binary fringe patterns efficiently, without distortion of fringe features. A quadrantal angle filter is developed to filter off the FOM. With these new filters, the derivative-sign binary image (DSBI) method for extraction of fringe skeletons is improved considerably. The improved DSBI method can extract high-density skeletons as well as common density skeletons.