Noise removal in three-fringe photoelasticity by adaptive colour difference estimation

Three-fringe photoelasticity (TFP) can give the total fringe order from a single-colour isochromatic fringe field. In TFP, the total fringe order is obtained by comparing the colour of the unknown photoelastic fringe pattern with a calibration specimen. Comparison is conventionally done by minimising the colour difference error. This leads to misidentification of fringe order in some regions. A new colour difference formula is proposed with an additional term, which ensures continuity of fringe order data over the domain. Fringe order data obtained by conventional TFP is used as base data and the new method is termed as refined TFP. To enable applicability of the technique to arbitrary geometries, a new boundary identification technique is developed. The new method is demonstrated with some example problems.     

The influence of ambient illumination on colour adaptation in three fringe photoelasticity

In three fringe photoelasticity, a single colour isochromatic image is used to estimate the total fringe order by comparing the colour at each point with that of a calibration table. The generation of the calibration table is critical, and certain nuances involved therein are brought out in this paper. Ideally, the same specimen material and lighting conditions must be used for both the calibration and application experiments, which are often not possible in an industrial scenario, and colour adaptation is a simple way of suitably modifying the calibration table. Till date, only experimental analyses of the colour adaptation procedures are available in the literature; in this paper, the colour adaptation procedures are investigated from an analytical viewpoint. This study has brought out that a two-point colour adaptation scheme accounts not only for tint variation between the calibration and application specimens, but also for ambient illumination. This finding has also been experimentally verified for a benchmark problem, and thereafter extended for reflection photoelastic analyses.     

Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error

The Fourier transform method, widely applied in photomechanics for the automated analysis of interferometric fringe patterns, has been recently extended to the photoelastic isochromatic fringe patterns analysis. Unfortunately, its use in photoelasticity involves some limitations that have not been completely highlighted in literature. This work deals with the influence of the quarter-wave plate tolerance on the evaluation of the retardation. Both theoretical and experimental analyses have shown that the quarter-wave plate error does not affect the retardation only if the principal stress directions in the model and in the carrier are aligned. In general, instead, the tolerance of the quarter-wave plates leads to an amplification of the retardation error due to the influence of the isoclinics with a subsequent restriction of the field in which the method can be applied. For instance, using common quarter-wave plates and tolerating a maximum retardation error of about 0.03 fringe order, than the Fourier transform method cannot be applied as a full-field technique but only in the model zones in which the misalignment between the principal stresses in the model and in the carrier is less than 15°.     

Scanning schemes in white light photoelasticity – Part II: Novel fringe resolution guided scanning scheme

Varied spatial resolution of isochromatic fringes over the domain influences the accuracy of fringe order estimation using TFP/RGB photoelasticity. This has been brought out in the first part of the work. The existing scanning schemes do not take this into account, which leads to the propagation of noise from the low spatial resolution zones. In this paper, a method is proposed for creating a whole field map which represents the spatial resolution of the isochromatic fringe pattern. A novel scanning scheme is then proposed whose progression is guided by the spatial resolution of the fringes in the isochromatic image. The efficacy of the scanning scheme is demonstrated using three problems – an inclined crack under bi-axial loading, a thick ring subjected to internal pressure and a stress frozen specimen of an aerospace component. The proposed scheme has use in a range of applications. The scanning scheme is effective even if the model has random zones of noise which is demonstrated using a plate subjected to concentrated load. This aspect is well utilised to extract fringe data from thin slices cut from a stereo-lithographic model that has characteristic random noise due to layered manufacturing.     

Using coloured structured light in 3-D surface measurement

The widest used algorithms for 3-D surface measurement using structured fringe patterns are phase stepping and Fourier fringe analysis. The techniques currently employed use mostly monochrome fringe patterns as a tool for phase information measurement and further surface reconstruction. However, the information contained in colour images is much more than that of monochrome, in this case, a new colour technique can be employed to analyse a measured scene with colour fringe patterns.This paper presents a new method for improving the measurement of 3-D shapes by using colour information of the measured scene as an additional parameter. The new method is based on primary colours (red, green and blue) to increase the number of the illuminated fringe patterns, which will remove or significantly reduce the common drawbacks of existing methods. The proposed technique produces a number of coloured structured lighting patterns, which are projected from different angles onto the scene. These patterns are analysed using masking algorithms, a specially adapted multi-colour version of the standard Fourier fringe analysis method and calibration routines. In this way a number of the standard difficulties are overcome.     

Phase shifting photoelasticity in white light

The availability of image acquisition systems has led to the development of digital photoelasticity both in monochromatic and white light. In particular white light has been used mainly with the following methods: Spectral Content Analysis, RGB photoelasticity and phase shifting photoelasticity. Phase shifting photoelasticity in the colour domain has been used effectively for the determination of the isoclinic parameter in order to reduce the influence of the isochromatic fringes. The method has been also proposed for the determination of the isochromatic fringe order. This paper concerns the general characteristics of phase shifting photoelasticity in the colour domain. Special attention is drawn towards the influence of spectral content of the light source, the spectral response of the colour camera filters, the dispersion of the birefringence and the error of quarter wave plates.     

Limitation of carrier fringe methods in digital photoelasticity

The carrier fringes method has been proposed in digital photoelasticity in combination with techniques such as Fourier transform and phase shifting method, without considering the influence of the isoclinics on the isochromatic patterns analysis. Unlike other optical methods as moiré and holographic interferometry, in photoelasticity the light intensity emerging from a circular polariscope is related to both the isochromatic retardation and the isoclinic parameter. As it is shown by the theoretical analysis, owing to the misalignment between the principal stresses in the model and in the carrier, the computed retardation is affected by an error which is the same for all photoelastic methods based on the use of carrier fringes. Consequently, the photoelastic analysis carried out by methods that use carrier fringes cannot be applied as a full-field technique. In detail, numerical simulations show that the retardation error is comparable (less than 0.05 fringe orders) with that of other photoelastic methods provided that the misalignment between the principal stresses in the model and in the carrier is less than 30°. On the contrary, in the model zones where the misalignment is higher than 30°, the retardation measurement can be affected by non negligible errors (up to 0.25 fringe orders).     

Review of RGB photoelasticity

Automatic methods of photoelasticity have had a significant progress with the development of automatic acquisition and image processing methods. This article concerns RGB photoelasticity, which allows the determination of the photoelastic retardation using, usually, a single acquisition of the isochromatic fringes in white light by a colour camera. In particular, the article presents an overview of the main characteristics of RGB photoelasticity that is influence of the quarter-wave plate error, number of acquisitions, type of light source, determination of low and high fringe orders, methods for searching the retardation, scanning procedures, calibration on a material different from that under test, combined use of the RGB and phase shifting methods. A short section on the applications of RGB photoelasticity completes the article.     

Automatic evaluation of photoelastic fringe constant by the nonlinear least-squares method

A nonlinear least-squares method was applied to determine the photoelastic fringe constant from isochromatic phase field obtained by digital phase-shifting photoelasticity. To perform automatic evaluation, not only the photoelastic fringe constant but the center coordinates of a disk under diametral compression are also determined simultaneously using the nonlinear least-squares method. A set of over-determined nonlinear equations is obtained to estimate the unknown parameters by an iterative procedure based on Newton–Raphson method. Simulation and experimental results show that the parameters are evaluated accurately from the isochromatic phase field obtained from the phase-shifting photoelasticity. The photoelastic fringe constant and the disk center coordinates can be evaluated easily, simply and automatically by the technique.     

A simple Abel inversion method of interferometric data for temperature measurement in axisymmetric medium

In this work, we describe a simple method of Abel inversion for temperature measurement in a natural convection axisymmetric flow. The essence of the method is that the measured lateral fringe shift profile is fitted with a polynomial with only even powers and then Abel inverse integral is evaluated analytically. This technique is compared with recent existing methods to test the accuracy and error propagation using a simulated interferogram of natural convection flow below a downward-facing heated horizontal disk in air. For this comparison, lateral fringe profiles are simulated using temperature fields computed by solving Navier Stokes and energy equations. Through random-number generation, noise profile is artificially added to the simulated noise-free lateral fringe shift profile. The results showed that the proposed technique for Abel inversion leads to accurate temperature profiles when the lateral fringe shift profile is fitted with even-power polynomials having degrees ranging from 20 to 30.     

Automation of white light photoelasticity by phase-shifting technique using colour image processing hardware

The early application of the digital image processing (DIP) technique to automate photoelastic analysis is based on black and white image processing systems. The various methodologies reported can be said to rely upon one or more features of a black and white DIP system. With the advancements in computer technology, modern colour image processing systems are available at affordable prices. In such systems, the image is identified as a superposition of image planes of red, green and blue. This paper investigates whether one or all of the image planes can be thought of as behaving like an optical filter: with the hardware used, the green channel is found to behave in this way. This idea is then used to extend the phase-shifting technique to colour domain. For the problem of a disk under diametral compression, total fringe order variation along a few lines is evaluated by this new technique and compared with theoretical predictions: the comparison is found to be good.     

基于正弦和三角波条纹投影的三维测量方法

在现有的针对复杂物体表面形貌的三维测量方法中, 为了完成绝对相位的测量, 通常需要处理至少6幅条纹图像, 限制了测量速度。提出了采用2幅正弦条纹和2幅三角波条纹图来获得物体三维形貌的方法。利用两步相移正弦条纹和两步相移三角条纹得到截断相位, 再利用两步相移三角波条纹得到条纹级次, 减少了投影条纹幅数, 提高测量速度。在得到条纹级次时, 计算三角波条纹强度调制和强度对比度, 与计算相位相比, 可以减少数据处理的时间, 进一步提高测量速度, 同时能减小物体表面反射率的影响, 提高了测量精度。测量最大高度为39 mm的阶梯状标准块, 得到的最大绝对误差和最大的RMS误差分别为0.045 mm和0.041 mm。验证了该方法的有效性和实用性, 在高速实时的复杂形貌三维测量中有广泛的应用前景。     

Fourier fringe processing using a regressive Fourier-transform technique

Since the introduction of a fourier fringe algorithm by Takeda, it has been possible to determine the phase of a particular light source impinging on an object from one sole image. This has led to applications in many whole field optical measurement techniques such as ESPI, holography, profilometry and so on. However, the basic processing technique, in case of the 2D-Fourier transform, is subject to a major drawback. Because this technique supposes periodicity in a fringe image, the so-called leakage effects occur. This gives rise to non-negligible errors, which can be resolved by using a regressive Fourier transformation technique. In the method introduced in this article, the fringe signal is represented by a model using sines and cosines where the frequency is not fixed (which is the case for classical FFT-techniques). The coefficients of those sines and cosines together with the frequency components are then estimated locally by means of a frequency domain system identification technique. This allows the fringe pattern to be unwrapped without any distortion. This method will be applied in particular to Fourier-transform profilometry (determines object geometry using shifts of projected fringes) although it can be used in any of the techniques mentioned above. Moreover, it will be shown that the proposed method can deal with other distortions that occur in practice such as over-modulation and varying fringe visibility. The proposed technique will be validated on both simulations and on a profile measurement of a pipe section.     

Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry

In fast phase-measuring profilometry, phase error caused by gamma distortion is the dominant error source. Previous phase-error compensation or gamma correction methods require the projector to be focused for best performance. However, in practice, as digital projectors are built with large apertures, they cannot project ideal focused fringe images. In this Letter, a thorough theoretical model of the gamma-distorted fringe image is derived from an optical perspective, and a highly accurate and easy to implement gamma correction method is presented to reduce the obstinate phase error. With the proposed method, high measuring accuracy can be achieved with the conventional three-step phase-shifting algorithm. The validity of the technique is verified by experiments.     

A novel 3D measuring method for discontinuous object by non-integral twin-frequency grating

A new 3D shape measurement method based on non-integral twin-frequency grating projection is proposed. In this paper, the projected composite grating is composed of two sinusoidal gratings, and the quotient of whose frequencies is not an integer. By using appropriate phase-shifting algorithms, two wrapped phases can be obtained from sixteen frames of the distorted grating patterns. In aid of appropriate phase unwrapping method, the unwrapped phase of high frequency fringe is obtained only from the relation of the two wrapped phases by a pixel-to-pixel phase unwrapping technique. Therefore the unwrapped phase of high frequency fringe pattern is independent of the low frequency fringe pattern, different from traditional integral twin-frequency grating projection methods in which the phase unwrapping error of low frequency fringe pattern may be propagated onto the unwrapped phase of high frequency fringe pattern. The new theory proves that the proposed method is applicable to measure discontinuous object, and has considerable measurement accuracy.     

抑制高阶谐波误差的随机相移条纹分析算法

高阶谐波和随机相移误差是影响条纹分析精度的主要因素。为了同时解决这两个问题,提出了基于频域滤波的迭代相移算法。该算法采用巴特沃斯低通滤波器,从频域上滤除条纹的高阶谐波分量,再运用最小二乘迭代方法从三帧随机相移条纹图像中提取相位信息。数值模拟和实验结果表明,该算法可有效地抑制由高阶谐波和随机相移引入的波纹误差,误差PV值和RMS值分别为0.368 8 rad和0.025 3 rad,其精度高于传统的三步相移算法和Wang算法。该方法适合于高精度干涉测量和三维物体表面轮廓测量。     

Fourier transform profilometry based on composite structured light pattern

In Fourier transform profilometry (FTP), the zero frequency of the imaged patterns will influence the measurement range and precision. The π phase shifting technique is usually used to eliminate the zero order component, but this method requires the capture of two fringe patterns with a π phase difference between them, which will impede the real time application of the method. In this paper, a novel method is proposed, in which a composite structured light pattern is projected onto the object. The composite structured light pattern is formed by modulating two separate fringe patterns with a π phase difference along the orthogonal direction of the two distinct carrier frequencies. This method can eliminate the zero frequency by using only one fringe pattern. Experiments show that there is no decrease in the precision of this novel method compared with the traditional π phase shifting technique.     

Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing

Recently, a study showed that generating sinusoidal fringe patterns by properly defocusing binary ones can significantly simplify three-dimensional shape measurement system development and drastically improve its speed. However, when the fringe stripes are very wide, it is very difficult for this technique to achieve high-quality measurement. This Letter presents a method to improve this technique by selectively eliminating high-frequency harmonics induced by a squared binary pattern. As a result, better sinusoidal fringe patterns can be generated with a small degree of defocusing even for wide fringe stripes. Simulation and experiments will be presented to verify the performance of this proposed technique.     

Robust geometric,phase and colour structured light projection system calibration

This paper introduces a new comprehensive procedure for both geometric and colour calibration of structured light system. In order to perform both geometric and colour calibration procedure, a new calibration artifact is proposed. The intrinsic and extrinsic parameters of projector and camera are estimated by using an extended pinhole camera model with a tangential and radial distortion. Camera image plane coordinates are obtained by extracting features from images of a calibration artifact. Projector image plane coordinates are calculated on the basis of continuous phase maps obtained from a fringe pattern phase reconstruction procedure. In order to stereo calibrate camera-projector system, pairs of corresponding image plane points are calculated with subpixel accuracy. In addition, one of three pattern views is used in colour calibration. RGB values of a colour field pattern detected by camera and their reference values are compared. This comparison leads to derivation of a colour transformation matrix. The performance of the proposed method is tested by measuring plane, sphere and distance reference. Also 360 degrees complex object 3D model from a set of measurements is obtained. Residual mean errors for all tests performed are calculated.