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.     

Whole field evaluation of stress components in digital photoelasticity—Issues, implementation and application

In photoelasticity, the method of obtaining the individual values of principal stresses/normal stresses separately is referred to as stress separation. Shear difference is one of the widely used techniques for stress separation in photoelasticity and one needs the value of fringe order and the isoclinic angle free of noise at every pixel over the domain. For accurate parameter determination, a ten-step phase shifting approach which uses a plane polariscope for isoclinic determination and a circular polariscope for isochromatic determination is proposed. A new quality guided approach for isoclinic unwrapping is developed. Isochromatic phasemap free of ambiguous zones is obtained by a new methodology and is unwrapped by a quality-guided approach. Whole field evaluation of stress components and its representation is then presented. The models used in this study are intentionally subjected to moderate loads showing a high level of isochromatic–isoclinic interaction. In view of this, the isoclinic data has several kinks which is found to cause streak formation in the whole field representation of separated stress components. An outlier smoothing algorithm is proposed for getting a smooth variation of the digital photoelastic parameters over the domain. Use of such smoothed data for stress separation has removed the streaks and has also greatly improved the accuracy of the separated stress components.     

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten‐step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.     

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).     

Noise removal in three-fringe photoelasticity by median filtering

In three-fringe photoelasticity, 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 using the least square method. This can give the total fringe order from a single-colour isochromatic field. This technique, however, leads to misidentification of fringe order in some regions. Some researches have proposed boundary identification technique to remove this error. Whilst this ensures continuity of fringe order data over the domain, this does not provide accurate results for every region. A simpler method has been proposed in this paper using median filtering which can be easily undertaken using any standard image processing software. The method is demonstrated with the help of a simple example of disc under diametral compression.     

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.     

Real-time phase-shift ing techniques for determining the photoelastic parameters: a theoretical comparison

Among data acquisition techniques in digital photoelasticity, the integrated phase shifting technique (IPST) can real-time analyze the photoelastic parameters at a video rate of the high speed CCD camera. In this paper, fourteen algorithms are described by different configurations of the rotating an analyzer at a constant rate and an output quarter-wave plate at another constant rate. The theoretical comparisons of the algorithms are given by the simulated phase distributions of the isochromatic and isoclinic parameters of the disk under two cases that the load keeps unchangeable or linearly increasing in exposure time of the camera. Then a guideline is given to alleviate the influence of the load changing with time on the IPST.     

相移法获取三维光弹特征相位差的方法

对于三维光弹模型,次主应力及其方向沿入射光连续变化,根据光学等效的原理,可以将三维光弹模型等效为一个包含线性相位延迟器和旋光器的光学模型。在集成光弹法中,对于每一个测量点,研究者必需通过实验获取三个特征参数。提出了一种用于确定集成光弹中全场特征相位差的五步相移法,给出了偏振光场中元器件的设置方法,并运用Jones算子推导出相移法得出的光强公式。最后使用斜射法对径向受压圆盘进行实验,验证了方法的有效性。     

A numerical comparison of real-time phase-shifting algorithms

Among data acquisition techniques in digital photoelasticity, the integrated phase shifting technique (IPST) can real-time analyze the photoelastic parameters at a video rate of the high speed CCD camera. In this paper, fourteen algorithms are described by different configurations of the rotating an analyzer at a constant rate and an output quarter-wave plate at another constant rate. The theoretical comparisons of the algorithms are given by the simulated phase distributions of the isochromatic and isoclinic parameters of the disk under two cases that the load keeps unchangeable or linear increasing in exposure time of the camera. Then a guideline is given to alleviate the influence of the load changing with time on the IPST.     

光弹性法中时间边缘效应数学模型和应用研究

在光弹性实验中,模型边缘会产生随时间增长的条纹,它干扰正常的由外载荷引起的应力条纹,给实验带来误差。根据时间边缘效应产生的原因建立了时效数学模型,通过对比根据建立的数学模型模拟的等差线和实验得到的等差线,可以验证所建立的数学模型能够准确地反映出时效的特征,并尝试运用数字光弹性相移法去除时效的影响。     

Scanning schemes in white light Photoelasticity – Part I: Critical assessment of existing schemes

The use of white light based Three Fringe Photoelasticity (TFP)/RGB Photoelasticity has gained importance in the recent years. With recent advances in TFP, it is possible to resolve fringe orders upto twelve. The main advantage of this technique is that it requires only a single image for isochromatic demodulation, which makes it suitable especially for problems where recording multiple images is difficult. The accuracy of isochromatic data obtained using TFP/RGB Photoelasticity is dependent on the scanning scheme used to refine the data, which is necessary to incorporate fringe order continuity. In this paper, the existing scanning schemes are critically evaluated for their ability to scan the entire model domain, influence of seed point selection and noise propagation. The scanning schemes are assessed using four problems of increasing level of geometric complexity – Circular disc under compression (simply connected), bi-axially loaded cruciform specimen with an inclined crack, a thick ring subjected to internal pressure and a finite plate with a hole (multiply connected).     

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.     

Load-stepping photoelasticity: new developments using temporal phase unwrapping

A new approach to load-stepping photoelasticity is presented in which the isochromatic phase is unwrapped between load steps rather than spatially. This is based on the technique known as ‘temporal phase unwrapping’ that has mainly been applied in shape measurement. The potential advantages of temporal phase unwrapping are based on the notion that each pixel is unwrapped independently of its neighbours. The benefits for load-stepping photoelasticity for reducing the effects of measurement error are discussed in this paper. New developments using temporal phase unwrapping are applied to experimental data obtained from a bimaterial interface specimen loaded in three-point bend. The results show that a modified approach to unwrapping significantly reduces the effects of systematic noise present in the data.     

光强和方位角误差对光弹性五步彩色相移法的影响

为了了解相移法中的各种参数所产生的误差对最终结果的影响 ,对一些主要参数做深入的误差分析是十分必要的。针对五步彩色相移法所用的白光入射平面偏振场的特点 ,只考虑光强、起偏镜和分析镜方位角所引起的误差影响就可以了。提出一个分析和评估这些误差源对五步彩色相移法确定等倾角参数所产生影响的方法 ,这对合理设计实验装置和执行正确的实验条件将起到积极的作用     

Evaluation of spectral phase in spectrally resolved white-light interferometry: Comparative study of single-frame techniques

Spectral phase in a white-light interferogram contains information about the absolute optical path difference (OPD) in the interferometer. Evaluation of spectral phase is therefore important in applications such as profilometry with white light. In spectrally resolved white-light interferometry (SRWLI) the white-light interferogram is spectrally decomposed by a spectrometer in order to determine this phase. Several single-frame techniques in SRWLI have been proposed for the evaluation of the phase including Fourier transform, Hilbert transform, spatial phase shifting, windowed Fourier transform and wavelet transform. In this paper we present a comparative study of these techniques in this application in relation to the temporal phase-shifting technique which is a multi- frame method. Further, we also propose a modified method to remove the influence of source spectrum modulation in Hilbert transform procedure.     

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.     

Full field automated evaluation of the quarter wave plate retardation by phase stepping technique

Quarter wave plates are optical elements commonly used in photoelasticity to obtain circularly polarized light. They divide the incident light field into two linearly polarized orthogonal components with a phase difference of a quarter of the light wavelength. Due to the tolerance in manufacturing, however, the actual phase shifting produced by the plates is affected by an error, which noticeably influences the photoelastic measurements performed by means of various automated methods. This paper presents a technique, based on the phase stepping method, for the full field automatic evaluation of the quarter wave plate error.     

Cubic polynomial curve-guided method for isochromatic determination in three-fringe photoelasticity

A method for isochromatic determination in three-fringe photoelasticity is presented. It combines the phaseshifting method with cubic polynomial curve-fitting technology to eliminate the errors caused by color repetition.We perform a demonstration of the method on a circular disc subjected to compressive loading and an injectionmolded cover with residual stresses. The test results compare well with the theoretical results.     

Digitally whole-field analysis of isoclinic parameter in photoelasticity by four-step color phase-shifting technique

This paper presents a whole-field method for automatic determination of the isoclinic parameter φ in photoelasticity. The method determines φ in the true phase interval (-π/2<φ+π/2) based on the four-step color phase-shifting approach and a new unwrapping method based on simple logic operations, a binary image and a gray-scale mask. A plane polariscope with a white light source is used for capturing raw photoelastic fringe images. The theoretical validation of the method is done with the problem of a circular disk under compression. Comparisons between theoretical and experimental results are also demonstrated. The experimental confirmation for the proposed method is tested with the photoelastic model having an isotropic point(s) and/or a singular point(s). The results show the method permits the reliable isoclinic parameter to be determined in the true phase interval with almost no defects of the isochromatic parameter.