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.     

轮胎激光散斑干涉相位条纹图局域多方向频域滤波方法

为解决激光数字剪切散斑干涉技术应用于轮胎缺陷检测中,轮胎缺陷相位条纹图中噪声对包裹相位图解包和轮胎缺陷尺寸测量产生严重影响的问题,该文通过对散斑干涉相位图的条纹特征分析,研究一种根据条纹密度将相位图划分成不同滤波区域进行多方向频域滤波的方法。实验结果表明:在两组模拟的相位图滤波实验中,局域多方向滤波方法的相位误差均值P_(mean)和相位均方根误差RMS都比正余弦滤波方法、多方向频域滤波方法要小,滤波结果更接近真值;在第3组滤波实验中,局域多方向频域滤波方法的残差点数分别是正余弦滤波方法、多方向频域滤波方法的11.39%、56.25%,体现出较好的滤波特性。     

Two-wavelength laser-diode interferometer with fractional fringe techniques

A two-wavelength interferometer with a fractional fringe technique (the method of coincidence) has been constructed by using dual frequency-ramped laser diodes. The respective wavelengths of two optical phases were measured by the heterodyne technique. The detected two phases are employed with real-time electronic processing to produce two signals that correspond to the integer and the fractional fringe numbers at a single wavelength. These summed signals can yield a synthetic phase having a single-wavelength resolution. The upper limits for the measurement accuracy are theoretically analyzed.     

A digital correlation speckle shift interferometer

The optical circuit of a speckle shift interferometer with two arms of different lengths is presented and its operating principle described. The device includes a semiconductor laser that serves as the radiation source and a digital camera interfaced to a computer.     

Additive-subtractive phase-modulated electronic speckle interferometry: analysis of fringe visibility

Fringe-visibility issues of additive-subtractive phase-modulated (ASPM) electronic speckle pattern interferometry (ESPI) are explored. ASPM ESPI is a three-step method in which additive-speckle images are acquired rapidly in an analog fashion in every frame of a video sequence, a speckle phase modulation is intentionally introduced between frames, and a digital subtraction of consecutive pairs of additive-speckle images is performed. We show that this scheme has the good high-frequency noise immunity associated with additive-ESPI techniques as well as the good fringe visibility associated with subtractive-ESPI techniques. The method has better fringe visibility than can be obtained with purely additive ESPI and also does not suffer from the fringe distortions that can occur with subtractive ESPI in the presence of high-frequency noise. We show that even if full speckle decorrelation were to occur between the two additive speckle images that are to be subtracted, the visibility of ASPM ESPI fringes can be made to approach unity by suitable adjustment of the reference-to-object beam-intensity ratio.     

Special features of Newton-type fringe formation in a diffraction interferometer

An interferometer with a Fresnel zone plate located in the center of curvature of a concave mirror was studied. Attention was paid to the unique features of the interference field, which has a special point at which the path difference is equal to zero, thereby allowing for the observation of Newton-type fringes in white and quasi-monochromatic light. The conditions necessary for reducing the instrumental error to values less than lambda/20 were determined. Methods for suppressing noise and destructive interference patterns were also found. Metrological tests were carried out, and they proved the possibility of using this interferometer for industrial testing of spherical and parabolic mirrors.     

Real-time displacement measurement using a multicamera phase-stepping speckle interferometer

Surface point displacements can be measured by using standard phase-stepping speckle interferometry, but the measured data are vulnerable to disturbances during the interferogram recordings. To overcome this an interferometer with a computational system has been developed to record three phase-stepped interferograms simultaneously and to calculate displacements. This system is evaluated by measurements of the out-of-plane rotation of a flat surface. The surface displacement is calculated at a rate of 25 times/s. If one reduces noise by filtering, hardware limitations decrease the speed to 12.5 displacement calculations/s. With this system displacements can be measured with an accuracy exceeding λ/55 if filtering is applied.     

Real-time speckle interferometry fringe formation with an adaptive phase mask

We describe what we believe is a novel speckle-pattern interferometry method of applying a spatial light modulator (SLM) as an adaptive phase mask to obtain real-time fringes of a deformed object without using conventional correlation methods of electronic subtraction or addition. The method is to use a SLM to cancel initial phase in the speckled image before the object is deformed. The fringes from the deformed object can be visualized directly after the initial phase has been canceled. A commercial liquid-crystal television is used as a SLM. The performance of using this SLM in an out-of-plane speckle interferometer is demonstrated.     

Data compression for speckle correlation interferometry temporal fringe pattern analysis

Temporal fringe pattern analysis is gaining prominence in speckle correlation interferometry, in particular for transient phenomena studies. This form of analysis, nevertheless, necessitates large data storage. Current compression schemes do not facilitate efficient data retrieval and may even result in important data loss. We describe a novel compression scheme that does not result in crucial data loss and allows for the efficient retrieval of data for temporal fringe analysis. In sample tests with digital speckle interferometry on fringe patterns of a plate and of a cantilever beam subjected to temporal phase and load evolution, respectively, we achieved a compression ratio of 1.6 without filtering out any data from discontinuous and low fringe modulation spatial points. By eliminating 38% of the data from discontinuous and low fringe modulation spatial points, we attained a significant compression ratio of 2.4.     

Optimization of fringe pattern calculation with direct correlations in speckle interferometry

A direct correlation technique is used to calculate correlation fringe patterns from consecutive speckle patterns acquired with a dual-beam electronic speckle interferometer. Although more calculations are required than in standard image differencing routines, an advantage of the method is that the illumination over the surface of the object need not be uniform. In the method, Pearson's coefficient of correlation between the intensities within a set of adjacent pixels is calculated. This has the added advantage of being directly related to the theoretical phase-dependent correlation. A mapping of this measure of correlation results in the correlation fringe pattern. Laboratory tests were carried out with in-plane translations ranging from 5 to 45 mum. The correlation calculations were carried out by using cells (square sets of pixels) in the raw speckle images with dimensions ranging from 2 pixels x 2 pixels to 19 pixels x 19 pixels. Both cell dimension and translation magnitude dependent decorrelation effects influence the quality of the correlation fringe patterns.     

Determination of the zero-order fringe position in digital speckle pattern interferometry

A method for determining the position of the zero-order fringe in a metrological experiment with digital speckle pattern interferometry is proposed. It is based on an averaging procedure with shifted images obtained before and after a load is applied. This technique is a complement to the phase-shifting methods. Experimental examples are shown.     

Electronic speckle pattern shearing interferometer with a photopolymer holographic grating

A photopolymer holographic grating is used to produce the two sheared images in an electronic speckle pattern shearing interferometer. A ground glass screen following the grating eliminates unwanted diffraction orders and removes the requirement for the CCD camera to resolve the diffraction grating's pitch. The sheared images on the ground glass are further imaged onto the CCD camera. The fringe pattern contrast was estimated to be above 90%. A validation of the system was done by comparing the theoretical phase difference distribution with the experimental data from the three-point bending test.     

Analysis of crack-tip Moiré fringe patterns

Near crack-tip displacement fields of static brittle cracks in elastic isotropic homogeneous materials are examined. Simple evaluation formulae for determination of stress intensity factorsK ₁ andK ₂ are derived employing characteristic properties of the moiré fringes. Higher order terms of the Westergaard stress function are considered in the analysis, their effect onto the overall moiré fringe pattern is discussed and the associated fringe patterns are classified. It is shown that crack-tip moiré fringe patterns are sensitive to variations of Poisson's ratio.     

Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces

A point diffraction interferometer (PDI) with adjustable fringe contrast is presented for the high-precision testing of spherical surfaces. The polarizing components are employed in the PDI to transform the polarization states of the test and reference beams, and a good fringe contrast can be realized by adjusting the relative intensities of interfering waves. The proposed system is compact and simple in structure, and it provides a feasible way for high-precision testing of spherical surfaces with low reflectivity. The theory of the interferometer is introduced in detail, along with the properties of optical components employed in the system, numerical analysis of systematic error, and the corresponding calibration procedure. Compared with the testing results of the ZYGO interferometer, a high accuracy with RMS value about 0.0025λ is achieved with the proposed interferometer. Finally, the error consideration in the experiment is discussed.     

Method to obtain a clear fringe pattern with a zone-plate interferometer

When a zone-plate interferometer is used, a bright spot appears at the center of the image plane. The spot makes it difficult to analyze the interference fringes. A simple technique that is based on the principle of fringe-intensity reversal is proposed to analyze the fringes efficiently. A zone plate with a phase fraction of π/2 or 3π/2 is used in this technique to diminish the bright spot. Unlike the masking technique, no part of the data on the fringes is lost. The fringes can, therefore, be analyzed completely. The technique is described in detail, and the results of an experiment in which the shape error of a concave mirror was measured with the proposed zone plate is presented. The experimental results agree well with the results obtained with the Fizeau interferometer.     

Analysis of mixed-mode isochromatic crack-tip fringe patterns

Summary Westergaard stress function representations of the stress field around the tip of a stationary crack subjected to mixed-mode loading are employed to develop a general relationship between the isochromatic fringe orderN, its position parametersr and and the general stress field expressed in terms of several parameters, the stress intensitiesK ₁,K ₂, a far field stress parameter , and higher order term parameters ₁ and ₂. These parameters are varied and isochromatic crack tip fringe patterns are constructed for a set of classified combinations. Since the size, shape, orientation, and other particular features of the fringe patterns depend strongly on the combination of parameters chosen they can be used to classify crack tip fringe patterns. The introduction of fringe loop diagrams not only facilitates the classification procedure and enables a classification without plotting fringe patterns, but it also permits qualitative and quantitative evaluation of the isochromatic patterns. Isochromatics which classify fourtyeight different states of stress are investigated and the majority of them have been illustrated.

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Analyse von Isochromatenfeldern um Rißspitzen unter gemischter Beanpruchungsart

Zusammenfassung Isochromatenbilder, welche den Spannungszustand um eine im gemischten Spannungsfeld ruhende Rißspitze repräsentieren, werden untersucht. Eine allgemeine Beziehung wird hergeleitet zwischen der Ordnung der IsochromatenN, deren Lageparameterr und und dem allgemeinen Spannungsfeld um die Rißspitze, welches im Rahmen einer mehrparametrigen Bruchmechanik durch die SpannungsintensitätsfaktorenK ₁ undK ₂, einem Fernspannungsfeldparameter und zweier weiterer Parameter ₁ und ₂ definiert ist. Die beiden letzteren Parameter sind mit den Gliedern höherer Ordnung in der Entwicklung der Westergaardschen Spannungsfunktionen verwandt. Die Parameterm=K ₂/K ₁, , ₁, und ₂ werden variiert und Isochromatenbilder für eine Reihe von Parameterkombinationen dargestellt.Die Tatsache, daß die verschiedenen Parameter Größe, Gestalt, Orientierung und weitere wesentliche Charakteristika des Isochromatenbildes parameterspezifisch verändern, gestattet eine vollständige Klassifizierung der Isochromatenbilder. Die Einführung von Isochromatendiagrammen erleichtert nicht nur das Kalssifizieren der Isochromatenfelder sondern erübrigt aufwendige numerische Zeichenprogramme zu deren Darstellung und dem Studium derer Charakteristika. Darüber hinaus ist eine qualitative wie auch quantitative auswertung in einfacher Form möglich. Zwillingsbildung von Isochromaten sowie lokale Minima von Isochromatenfeldern sind durch diese Diagramme quantitativ erfaßbar. Das Klassifikationsschema umfaßt 48 Grundfälle. Die Mehrheit der damit verbundenen Isochromatenfeldern ist abgebildet.

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With 21 Figures     

Zero fringe visibility in the classical localization plane of a two-beam interferometer

In 1987 we published "Fringe localization depth" [Appl. Opt. 26, 5125 (1987)], where, with first principles, we generalized the van Cittert-Zernike theorem for two-beam amplitude-division interferometers illuminated by extended sources. In this generalization the complex degree of coherence between the interfering beams is equivalent to the Fraunhofer diffraction pattern of an aberrated optical system. In 1989 Hariharan and Steel [Appl. Opt. 28, 29 (1989)] commented on this paper and pointed out that the fringe visibility can be zero in the localization plane determined by the conventional pair-of-rays method. Now, we numerically and experimentally show a situation where the equivalent aberrations are such that this finding is verified and that the localization region splits in two, one ahead of and the other behind the classical localization plane.