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).     

Determination of isoclinics in photoelasticity with a fast regularized estimator

The determination of isoclinics from photoelastic fringe patterns is a key problem in photoelasticity. Dealing with this problem, however, is not a simple task when isotropic points are present which is common for most experimental situations. Because of this, few researchers have proposed effective and practical solutions. Visualizing this problem as the problem of the determination of the modulo 2π fringe orientation, in this paper it is proposed an efficient regularized algorithm to solve it. Experimental results show that the proposal is effective and can be used with either monochromatic or white light.     

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.     

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°.     

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.     

Classification of holographic fringe patterns inherent in through hole drilling in residual stress field

Comparative analysis of actual fringe patterns, which are induced by combined implementing the hole drilling method and reflection hologram interferometry for residual stresses determination, is presented. Involved considerations are related to plane thin-walled structural elements. A set of interferograms of perfect (ideal) form is selected proceeding from one-side measurements. A base for recognising each specific ideal configuration is a fine coincidence between actual interferograms and analogous reference fringe patterns constructed for the same stress state. Perfect (ideal) both actual and reference fringe patterns are defined as a response of pure membrane 2D stress field on through hole drilling between exposures. Main principles of creating the regular catalogue of reference fringe patterns inherent in through hole drilling in thin-walled components are formulated. Emphasis is made on a careful collecting and classifying actual interferograms with clear indications of bending stress presence in total residual stress field. Evidences needed for a reliable classification of the type of residual stresses field of interest are established and verified. A response of superimposed residual stress field, which consists of both membrane and bending components, is characterised by various deviations of each specific fringe pattern from an ideal form. More deep analysis of fringe patterns related to superimposed residual stress field is based on specially designed technique. The main essence of the approach developed is simultaneous measurements of through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Sophisticated optical set-up that is capable of obtaining high-quality fringe patterns in the course of two-side measurements is developed and implemented. Typical set of fringe patterns obtained for single probe hole on opposite specimen faces is presented.     

基于光弹性贴片法的材料表面应变场测量研究

针对常用电阻应变片法的点测结果不易反映构件表面应变场分布的问题,将光弹性贴片方法应用于材料表面应变场测量。制作了光弹性贴片,并标定光弹性贴片的材料条纹值,通过几种典型形状光弹性贴片试件的加载实验掌握应力场分布的条纹图像判读方法。开展光弹性贴片在简支钢梁的应变场测量应用,在薄弱点位置光弹性贴片法相比电阻应变片法应变值偏差在5%以内。对C30混凝土试块进行4.4 MPa～39.6 MPa的应力加载过程中,有效监测到混凝土表面裂缝产生、稳定扩展及失稳破坏过程中的条纹图像变化过程。实验表明,光弹性贴片方法可以直观可靠地测量金属及混凝土的表面应力场变化。     

New approaches to the full-field analysis of photoelastic stress patterns

This paper presents two new methods that provide a complete solution for the automatic fringe analysis of photoelastic data. Previous solutions have not yet provided a complete full-field analysis of both fringe sets (isochromatic and isoclinic) over a multiple number of fringes with an automatic measurement of absolute magnitude. This paper reviews previous approaches and discusses the options along which this work has been directed. Specifically, two new algorithms are presented. Firstly, the combination of phase maps at three wavelengths in order to remove the isochromatic ambiguity at every π turning point, that would occur in a single phase map. Additionally, this algorithm allows the automatic measurement of absolute magnitude, providing the neutral axis is within the field of view. Secondly, a new method is proposed that removes the areas of 2π ambiguity in an isoclinic phase map by cross-correlating regions of low modulation at two different wavelengths. The algorithms are demonstrated by applying them to the analysis of an engine connecting rod. The rod was manufactured as a full-scale three-dimensional model in araldite (Ciba-Geigy CT200), from which a central slice was taken after having been stress frozen.     

Anisotropic partial differential equation noise-reduction algorithm based on fringe feature for ESPI

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a new anisotropic partial differential equation noise-reduction algorithm based on fringe orientation for interferometric fringe patterns. The proposed equation performs diffusion along the two directions of fringe gradient and isophote line, which are extracted accurately according to fringe feature. By restriction of diffusion in the gradient direction of fringe patterns, this method can provide optimal results in denoising but does not destroy fringe edges. The experimental results show that this technique is more capable of significantly improving the quality of the fringe patterns than the classical anisotropic diffusion equation proposed by Perona and Malik. Based on our filtered fringe patterns, the phase map obtained by phase-shifting technique can be extracted more accurately. It is an effective pre-processing method for electronic speckle pattern interferometry.     

On photoelastic stress measurements in optically absorbing medium

The effects of optical absorption in a photoelastic medium on the formation of the fringe patterns are studied by taking into account the stress-induced anisotropy of both the refractive index and the absorption coefficient. The propagation of optical waves in a dielectric solid under the influence of stress is formulated by incorporating complex elasto-optical tensor elements in the wave equation. The expression for optical transmission from the plane polariscope configuration consisting of an absorbing photoelastic specimen is derived using the Jones calculus formalism including complex optical retardation terms. It is observed that the photoelastic fringe fields are substantially modified due to these effects which must be considered for accurate interpretation of the experimentally obtained fringes.     

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.     

Dynamic photoelasticity using a laser scanner

Over the years, several techniques have been developed to record dynamic fringe patterns in photoelasticity. Due to the whole field recording capability, the photoelastic technique continues to be of interest to the experimental mechanics community. A low-cost dynamic recording system employing an out-dated fax scanner is presented in this article. Details of the optical and electronic functions are discussed. The feasibility of the system is demonstrated by recording dynamic fringe patterns off a simply supported beam subjected to impact loading. Further modifications to the set-up to improve the quality of the fringe patterns are discussed briefly.     

An improved stair phase encoding method for absolute phase retrieval

An improved phase unwrapping method is proposed to reduce the projection fringes in three-dimensional (3D) surface measurement. Color fringe patterns are generated by encoding with sinusoidal fringe and stair phase fringe patterns in red and blue channels. These color fringe patterns are projected onto the tested objects and then captured by a color CCD camera. The recorded fringe patterns are separated into their RGB components. Two groups of four-step phase-shifting fringe patterns are obtained. One group of the stripes are four sinusoidal patterns, which are used to determine the wrapped phase. The other group of stripes are four sinusoidal patterns with the codeword embedded into stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of sinusoidal fringe phase, which are used to determine the fringe order for the phase unwrapping. The experimental results are analyzed and compared with those of the method in Zheng and Da (2012. Opt Express 20(22):24139–24150). The results show that the proposed method needs only four fringe patterns while having less error. It can effectively reduce the number of projection fringes and improve the measuring speed.     

A new method for photoelastic fringe analysis from a single image using elliptically polarized white light

A new two-dimensional photoelastic method for the analysis of fringe order and the principal direction of birefringence from a single image combining an elliptically polarized white light and color image processing is demonstrated. To determine fringe order, a database-search approach based on the primary color analysis is employed. After determining fringe order, the principal direction of birefringence is obtained by solving a non-linear equation. The equation of emerging light intensity is derived and the theory of the proposed method is described. Then, the successful application of the method to photoelastic analysis is shown. It is emphasized that the proposed method can be applicable to time-varying phenomena since multiple exposures are not necessary for sufficient data acquisition for the completion of stress analysis.     

Photoelasticity stress analysis using carrier fringe and FFT techniques

A novel carrier fringe technique for photoelasticity stress analysis is described and verified experimentally. Linear carrier fringes generated by using a quartz wedge are superimposed on fringes formed by the stressed model. The resultant fringe pattern is then captured using a charge coupled device camera and stored in a digital frame buffer. A fast Fourier transform method is then used to process the complete photoelastic fringe image over the whole surface of the model. The experiment also uses a minimum spanning tree phase unwrapping strategy to create a continuous map of the whole stress field. Finally, the whole principal stress difference field has been calculated and plotted from one single exposure showing the methods' potential for use as a reflection analysis system suitable for application to nonstationary objects and complicated stress patterns.     

The leveling of mask and wafer in proximity nanolithography using fringe pattern phase analysis

The fringe pattern phase analysis method is proposed for the leveling of mask and wafer in proximity lithography. The tilt between mask and wafer in the space is reflected in the tilted fringe pattern. The method combining the 2-D Fourier transform and 2-D Hanning window is proposed for processing the tilted fringe pattern. The offset and angle of tilt are extracted through phase analysis. Computer simulation and experiment are both performed to verify this method. The results indicate that the tilt of the mask and wafer in the space can be extracted with high accuracy through this method.     

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.     

Multi-directional lateral shearing interferometer based on rotatable prism pairs

The common camera lens usually includes the spherical glass/plastic lens and aspheric glass/plastic lens. However, spherical/aspheric shape measurement is still a key problem in the process of optical lens fabrication. At present, the in-process measurement of spherical/aspheric shape is conducted mainly by the probe-contacting method. But after a long time, its probe could be scratched severely and cause some big errors. Laser shearing interferometry is a good substitute to some degree. Nevertheless, it is not convenient for general shearing interferometer to carry out the in-process measurement because it is only suitable for certain kind of spherical/aspheric with respect to aperture or asperity. Here a new lateral shearing interferometer is proposed to solve the described problems. It is based on two Jamin plates and rotatable prism pairs which are used not only for shearing displacement and direction, but also for fringe period and tilt degree, in order to meet requirements of various spherical/aspheric shapes or asperities. The new interferometer features a simple optical structure and two symmetric light paths, which makes its system with minimal error. The relation between shearing displacement, fringe period and prism angle of rotation is given in this paper. And the error source is primarily from the manufacture errors of prisms and plates. The final experiments show that one can achieve good-quality fringe patterns according to the requirement of measurement, concerning the shearing direction, shearing displacement, fringe period, tilt degree, etc.     

多光束莫尔偏折术的探讨

本文探讨了莫尔偏折术应用的新方法——多光束莫尔偏折术.该法无需测量莫尔条纹偏折角,而是记录条纹对比度最好时试件的位置.文章阐述了其基本原理,并在光栅栅距和光楔楔角测量上进行了实验验证,取得较好的结果.     

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.