Method for fringe enhancement in holographic interferometry for measurement of in-plane displacements

Theoretical background along with experimental results are given for a simple method for in-plane fringe enhancement in dual-beam illumination holographic interferometry. In this method, the fringes representing in-plane displacements arise as a moirépattern between two interferograms. To distinguish the in-plane displacement, a sequence of images is recorded while the reference mirror is continuously tilted at random. The in-plane fringes arethen found as the maximum contrast of the out-of-plane fringes in the image sequence. The resulting fringe quality is close to the quality of the out-of-plane fringes.     

Use of the fast Fourier transform method for analyzing linear and equispaced Fizeau fringes

The Fourier transform method is applied to analyze the initial phase of linear and equispaced Fizeau fringes. We develop an algorithm for high-precision phase measurement by using the Fourier coefficient that corresponds to the spatial frequency of the Fizeau fringes, and we describe methods for determining the fringe carrier frequency. Errors caused by carrier frequency fluctuation and data truncation are studied theoretically and by computer simulation. To demonstrate the method we apply it to the real-time calibration of a piezoelectric transducer mirror in a Twyman-Green interferometer.     

Generation of carrier fringes in holography and shearography

Double-exposure holography and double-exposure shearography are often used together with the carrier fringe technique, which requires additional shifting of the light source in a prescribed manner between exposures. In the holographic carrier fringe technique, difficulty in prescribing a suitable movement of the light source may be alleviated through visualization of the moiré fringes that are reconstructed by slight displacement of two overlaid families of ellipsoids in a holodiagram. Because shearography is the first differential of holography, it is often impractical to perform two successive optical differentiations on the ellipsoids to visualize the shearographic carrier fringes. A simple method of discerning holographic and shearographic carrier fringes is described. The method is based on the hyperboloids in a holodiagram that represent Young's (interference) fringes produced by the interference of two point sources. The hyperboloids are analogous to holographic carrier fringes, whereas the moiré patterns reconstructed from two overlaid hyperboloids are analogous to shearographic carrier fringes. Use of this method for explaining the formation of deformation fringes in plate bending, as well as the effect of light-source movement on the deformation fringes, is also illustrated.     

Analysis of low-coherence interference fringes by the Kalman filtering method

Interferometers with low-coherence illumination allow noncontact measurement of rough-surface relief with a wide range of measurement definition by locating the visibility maxima of interference fringes. The problem is light scattering by the surface to be measured, which can cause distortion of low-coherence interferometric signals. We propose to use a stochastic fringe model and a Kalman filtering method for processing noisy low-coherence fringes dynamically. Prediction of the fringe's signal value at each discretization step is based on all the information available before this step; the prediction error is used for dynamic correction of the estimates of the fringe envelope and phase. The advantages of the Kalman filtering method consist in its immunity to noise, optimal fringe evaluation, and data-processing speed.     

Phase retrieval errors in standard Fourier fringe analysis of digitally sampled model interferograms

We investigate the reliability of phase retrieval by use of the fringe Fourier analysis method for measuring the displacements of facets during the growth of equilibriumlike-shaped crystals. The mean phase change between two successive interferometric images contains an inherent error that emerges from the noninteger number of fringes in the image field. The magnitude of the retrieved phase error of the ideal fringe pattern is investigated as a function of spatial carrier frequency, of the initial phase setting, and of the deviation of the number of fringes from the nearest integer value. The suggested modified algorithm suppresses the error more than threefold.     

Robust phase demodulation of interferograms with open or closed fringes

We present two robust algorithms for fringe pattern analysis with partial-field and closed fringes. The algorithm for partial-field fringe patterns is presented as a refinement method for precomputed coarse phases. Such an algorithm consists of the minimization of a regularized cost function that incorporates an outlier rejection strategy, which causes the algorithm to become robust. On the basis of the phase refinement method, we propose a propagative scheme for phase retrieval from closed-fringe interferograms. The algorithm performance is demonstrated by demodulating closed-fringe interferograms with complex spatial distribution of stationary points and gradients in the illumination components.     

Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry

We describe an electronic speckle-pattern interferometry system for analyzing addition fringes generated by the transient deformation of a test object. The system is based on a frequency-doubled twin Nd:YAG laser emitting dual pulses at a TV camera field rate (50 Hz). The main advance has been the automatic, quantitative analysis of dual-pulse addition electronic speckle-pattern interferometry data by the introduction of carrier fringes and the application of Fourier methods. The carrier fringes are introduced between dual pulses by a rotating mirror that tilts the reference beam. The resulting deformation-modulated addition fringes are enhanced with a deviation filter, giving fringe visibility close to that of subtraction fringes. The phase distribution is evaluated with a Fourier-transform method with bandpass filtering. From the wrapped phase distribution, a continuous phase map is reconstructed with an iterative weighted least-squares unwrapper. Preliminary results for a thin plate excited by an acoustic shock show the suitability of the system for the quantitative evaluation of transient deformation fields.     

Transient Deformation Measurement by Double-Pulsed-Subtraction TV Holography and the Fourier Transform Method

We report the measurement of transient bending waves with double-pulsed-subtraction TV holography. The correlation fringe patterns are automatically quantitatively analyzed by the application of Fourier methods. A novel optical setup with two different object-beam optical paths is demonstrated for the generation of carrier fringes. The proposed system is highly immune to environmental disturbances because the optical setup imposes no lower limit on the time separation between laser pulses. One removes the linear phase distribution due to the spatial carrier in the spatial domain by subtracting the phase of the undeformed carrier fringes from the phase of the modulated fringes. Experimental results obtained with an aluminum plate excited by the impact of a piezoelectric translator are presented.     

Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method

Electronic speckle pattern interferometry fringe patterns usually have poor contrast so it is important to enhance fringe contrast for the extraction of phase from a single fringe pattern. We present new enhancement methods based on differential equations (called DE enhancement methods) to electronic speckle pattern interferometry fringes. The DE enhancement methods transform the image processing to solve differential equations. With the proposed methods, the visibility of the correlation speckle fringe patterns can be improved significantly. We tested the proposed methods on computer-simulated speckle correlation fringes and experimentally obtained fringes, and we compared the new method with other contrast enhancement techniques. The experimental results illustrate the performance of this approach.     

Enhanced dual-frequency pattern scheme based on spatial-temporal fringes method

One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et al proposed a dual-frequency method based on the Fourier transform profilometry, yet the low-frequency lobes are close to each other for accurate band-pass filtering. In the light of this problem, a novel dual-frequency pattern based on the spatial-temporal fringes (STF) method is developed in this paper. Three fringe patterns with two different frequencies are required. The low-frequency phase is obtained from two low-frequency fringe patterns by the STF method, so the signal lobes can be extracted accurately as they are far away from each other. The high-frequency phase is retrieved from another fringe pattern without the impact of the DC component. Simulations and experiments are conducted to demonstrate the excellent precision of the proposed method.     

气流场ESPI载频条纹图的消噪处理与相位提取方法

为拓展ESPI方法在流动可视化测量技术中的应用,对气流场ESPI载频条纹图进行了傅立叶变换、数字全低通滤波,和傅立叶逆变换的处理以消除散斑噪声,并直接将其替换为原散斑相关条纹图,进而成为保留了流场信息的高对比度、低噪声的灰度条纹图,便于提取原散斑图中流动相位信息。根据模拟数据确定了由这两种条纹图互换所引起的空间相移量和相应流场测量中的修正量。提出了用灰度扫描法对互换后的条纹图进行一维灰度扫描,由灰度计算得出气流扰动的一维相位差分布和流场一维温度分布;同时也用FTP法对该图进行了二维相位展开和温度分布计算,亦可对多帧条纹图进行时间轴上的逐点相位提取以计算其他流场参数。结果表明,计算数据与实测符合,方法简单易行,为在气流场参数测量中应用动态ESPI方法提供了一种实用有效的方法。     

Lau Effect in Reflection

Abstract

The interference phenomenon known as the Lau effect is usually produced when two transmission gratings are located in tandem and are illuminated incoherently. This paper extends the study on this effect by analysing the optical arrangement in which the second transmission grating is replaced by a reflection grating. The interference fringes produced under incoherent illumination in this new reflection Lau geometry are, in certain respect, similar to those in the usual transmission geometry. The new set of fringes, however, become changeable in their profile when one of the gratings is subjected to an in-plane translatory motion in the direction perpendicular to the grating lines. The characteristics of the fringe formation phenomenon are examined quantitatively from the viewpoint of the incoherent superposition of multi-diffraction patterns of the gratings. We present a theoretical analysis and a supporting experimental verification of this phenomenon.     

Uneven fringe projection for efficient calibration in high-resolution 3D shape metrology

A novel uneven fringe projection technique is presented whereby nonuniformly spaced fringes are generated at a digital video projector to give evenly spaced fringes in the measurement volume. The proposed technique simplifies the relation between the measured phase and the object's depth independent of pixel position. This method needs just one coefficient set for calibration and depth calculation. With uneven fringe projection the shape data are referenced to a virtual plane instead of a physical reference plane, so an improved measurement with lower uncertainty is achieved. Further, the method can be combined with a radial lens distortion model. The theoretical foundation of the method is presented and experimentally validated to demonstrate the advantages of the uneven fringe projection approach compared with existing methods. Measurement results on a National Physical Laboratory (UK) "step standard" confirm the measurement uncertainty using the proposed method.     

A fast 3D shape measurement method based on sinusoidal and triangular fringe projection

Existing methods to measure 3D shape of complex object involve processing more than six captured images to obtain the absolute phase, which limit the measurement speed. This paper presents two sinusoidal fringes and two triangular wave fringes which is used to measure 3D shape of complex object. The two-step phase-shifting sinusoidal fringes and two-step phase-shifting triangular wave fringes are calculated to obtain the wrapped phase, and then the two-step phase-shifting triangular wave fringes are used to determine the fringe order. Due to decrease the number of projection fringes, the speed of measurement increases. The triangular wave fringe carries more information of the object than linear increasing/decreasing ramp fringe in the actual measurement, more noise in the base phase to be overcome, thus improving the measurement accuracy. The benefits can be widely applied in high-speed, real-time 3D measurement of complex shape. Experimental results have demonstrated that the proposed method is simple, but effective.     

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an object's surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique. Usually a minimum of three phase-shifted fringe patterns is necessary for extraction of the object shape. In this method, a new algorithm based on a two-step phase-shifting technique produces the 3-D object shape. Unlike in the conventional method, phase unwrapping is performed directly by use of an arccosine function without the need for a wrapped phase map. Hence, shape measurement can be speeded up greatly with this approach. A small coin is evaluated to demonstrate the validity of the proposed measurement method, and the experimental results are compared with those of the four-step phase-shifting method and the conventional mechanical stylus method.     

Contouring of diffused objects using lensless Fourier transform digital moiré holography

A method is proposed for contouring of diffused objects using digital holographic moiré interferometry in lensless Fourier transform configuration. Fringe projection moiré technique combined with digital double-exposure holography produces the contours in this method. Two digital holograms of a 10?mm aluminum alloy cube are recorded by tilting the illumination angle slightly between exposures, and a third one is recorded by translating the detector a little laterally with the final illumination angle unchanged. Upon numerical processing of the first two holograms, a plane parallel fringe system seems to be projected onto the object. This fringe system can be referred to as the modified grid. Processing of the second and the third hologram results in another grid, the reference grid. In effect, processing of the first and the third hologram combines the modified and the reference grids to produce the moiré contour fringes. The range of contour intervals obtained remains between 2.73 and 0.38?mm with seven different contours in between. The present method can measure details of a great variety of sizes on objects of large dimensional range. Deviations in the measured contour intervals from the theoretically calculated values are found to be within 12%-18%. This seems to be because of the deviation in the present experimental geometry from the ideal theoretical configuration, the hologram digitization, and the particular reconstruction algorithm used in the present experimental arrangement.     

Recovery of absolute phases for the fringe patterns of three selected wavelengths with improved anti-error capability

Abstract

In a recent published work, we proposed a technique to recover the absolute phase maps of fringe patterns with two selected fringe wavelengths. To achieve higher anti-error capability, the proposed method requires employing the fringe patterns with longer wavelengths; however, longer wavelength may lead to the degradation of the signal-to-noise ratio (SNR) in the surface measurement. In this paper, we propose a new approach to unwrap the phase maps from their wrapped versions based on the use of fringes with three different wavelengths which is characterized by improved anti-error capability and SNR. Therefore, while the previous method works on the two-phase maps obtained from six-step phase-shifting profilometry (PSP) (thus 12 fringe patterns are needed), the proposed technique performs very well on three-phase maps from three steps PSP, requiring only nine fringe patterns and hence more efficient. Moreover, the advantages of the two-wavelength method in simple implementation and flexibility in the use of fringe patterns are also reserved. Theoretical analysis and experiment results are presented to confirm the effectiveness of the proposed method.     

Isochromatics demodulation from a single image using the regularized phase tracking technique

Abstract

In this work we propose a robust fringe demodulation technique applied to the analysis of a single isochromatics fringe pattern produced in photoelasticity. The method used is a regularized phase tracking algorithm with a new sequential scanning technique specifically adapted for the characteristics of the isochromatic fringe patterns: possible apparition of closed fringes, large dynamic range in its spatial frequency content and low noise. The performance of the method is discussed and experimental results are presented.     

Enhanced two-frequency phase-shifting method based on generalized phase-shifting algorithm

In this paper, we develop a novel dual-frequency pattern which not only releases the restriction of conventional two-frequency phase-shifting algorithm that at least six fringe patterns are needed, but reduces the noise impact by decreasing the frequency ratio between the high- and low-components. To decrease the number of necessary patterns to five, a novel composite dual-frequency pattern scheme combining together a high- with a low-frequency pattern is employed. To make the algorithm less sensitivity to noise, the low-frequency component is with more than one period fringes, which is relatively prone to recover the continuous result by simple spatial phase unwrapping approach. Besides, the restriction of special phase shifts between two-frequency components in conventional methods is released by the generalized phase-shifting algorithm. Simulations and experiments are conducted to demonstrate that in addition to maintaining the minimum number of patterns, the proposed method reveals higher accuracy of phase retrieval.