Review of RGB photoelasticity

Highlights

• Twenty years of RGB Photoelasticity and applications.

• From the basic formulation to the newest regularization and scanning procedures.

• The state of the art of the RGB Photoelasticity for new horizons.

Abstract

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.

Introduction

The development of automated methods of acquisition and processing of images has allowed the realization of several automated methods of photoelasticity based on the use of monochromatic or white light sources. In particular are cited the:

• Phase Shifting Methods (PSM) on monochromatic light and in white light;

• Fourier transform method;

• method known as Spectral Content Analysis (SCA);

• the method known as Gray Field Polariscope (GFP);

• tricolour Photoelasticity and other methods based on the use of white light;

• RGB photoelasticity.

Reviews on the above methods appear periodically in journals [1], [2], [3], [4], [5].

The Phase Shifting Method (PSM) in monochromatic light, introduced in 1986 by Hecker and Morche [6], generally requires at least four acquisitions. After the pioneering work of Hecker and Morche, a significant contribution was made by Patterson and Wang [7], who proposed a method based on the use of circularly polarized light incident on the model and six positions of the analyzer and its quarter wave plate. In the phase shifting method, the maps of the isocline parameter and of the relative retardation are obtained using the arctangent function applied to combinations of acquired light intensities. Because of the periodicity of the tangent function, the above maps are wrapped, it is therefore necessary to apply procedures of unwrapping. Various methods that minimize the influence of the error of quarter-wave plates on isochromatic and isoclines have been proposed [8], [9]. For a survey on the phase shifting methods, the reader is referred to the literature [10].

The use of white light in the phase shifting methods has been considered for the determination of both the isoclinic parameter and the retardation. Thus the PSM in white light has been used by several researchers [11], [12], [13] in order to determine the isoclinic parameter, minimizing the interaction between isochromatics and isoclines and avoiding the use of light sources of several wavelengths [14]. Some authors [15] have shown that the spectral content of the light source influences the retardation and the isoclinic parameter, determined using a monochrome camera. The phase shifting method in white light was used for the determination of the retardation by Ramesh et al. [16], [17].

An analysis of the phase shifting method in white light can be found in [18] with reference to the following aspects: spectral content of the light source, spectral response of the RGB filters of the camera, dispersion of birefringence and error of the quarter wave plates.

The Fourier transform method is based on the acquisition of isochromatics using carrier fringes obtained, for example, by a specimen subjected to bending or by means of a quartz wedge [19]. The retardation is determined using a single image. The benefit of using a single image is partly limited by the restriction due to the orientation of the principal stresses that need to be aligned (less than about 25°) in the model and in the carrier [20], [21]. The combined effect of the error of quarter-wave plates and the misalignment of principal stresses between model and carrier is considered in [22].

The Spectral Content Analysis (SCA) [23], [24], [25] is based on the use of a spectrophotometer that determines, point by point, the spectral content of the light emerging from a circular polariscope illuminated in white light. The emerging intensity is compared with the theoretical intensity considered in an appropriate range of retardations. The unknown retardation is the one that minimizes the difference between experimental and theoretical values of the emerging light intensity. The SCA has also been proposed as a method in full field [26] by the use of a set of eight narrow band filters and a monochrome camera.

The Gray Field Polariscope (GFP) [27] is based on the use of circularly polarized monochromatic light incident on the model, the analysis is carried out using a rotating analyzer. In this way, the system acquires a large number of images using a camera, for what concerns the acquisition the GFP is therefore traceable to the phase shifting methods. The processing of the acquired images is used to determine the retardation and the parameter of the isoclines.

The so-called “tri-colour technique,” based on the use of three wavelengths in plane polarized light, allows the determination of both isochromatics and isoclines [28], [29]. The method uses a dark field plane polariscope illuminated by a source, which emits three narrowband wavelengths (Red at 619 nm, Green at 546 nm and Blue at 436 nm). Using a single acquisition and combining the light intensity detected at the three wavelengths, the retardation and the isoclinic parameter are determined.

Other methods in monochromatic light – The method using the variation of the load applied to the model (load stepping.) [30], [31], [32], [33] allows to determine the retardation regardless of the isoclinic parameter, eliminating the ambiguities of the PSM. It is also not necessary to know the fringe order at one point.

Photoelasticity can also be used effectively to improve the discretization schemes in the finite element method [34], [35]. Another field of application of digital photoelasticity regards the time average photoelasticity [36], [37].

Other methods in white light – A method that is based on the acquisition of the isochromatic in dark and light field in a circular polariscope in white light by a colour CCD camera can be found in [38], [39]. The subsequent subtraction of the above images allows the users to determine the points of zero intensity, which correspond to apparent fringe orders. Finally, using calibration curves that link the fringe order at a particular wavelength with apparent fringe orders, actual fringe orders are determined. A method based on the acquisition of four images using a plane polariscope, in dark field, and a three colour light source, has been proposed to eliminate the influence of quarter-wave plates errors [40]. Finally, Quiroga et al. in [41] have proposed the use of a regularization algorithm to demodulate the isochromatics acquired with a CCD camera using a fluorescent lamp as in discrete spectrum source.

This article concerns the RGB photoelasticity which is a full-field method for the determination of the photoelastic retardation (isochromatic fringe order) using, usually, a single acquisition of white light isochromatics in a circular polariscope by a colour camera. The method was first introduced at the University of Palermo since 1990 [42] and subsequently published (1995) in an international context [43], [44]. Initial further developments are due to Ramesh and Deshmukh [45] and Yoneyama and Takashi [46] who have proposed the use of elliptically polarized light to determine, in addition to the retardation, even the isoclinic parameter.

After the introduction of RGB photoelasticity, RGB applications in the fields of differential interferometry [47] and moiré-contouring [48], [49], [50] have been developed. The method called Colourimetry-based retardation measurement (CBRM) is similar to RGB photoelasticity. The model, illuminated in white light, is placed between two crossed polarizers. A spectrophotometer, however, is used in place of a colour camera [51].

General references to RGB photoelasticity are reported, in addition to the papers [42], [43], [44], [45], in books [10], [52], [53], [54] and in review papers [1], [2], [3], [4], [5].

In the following, after a brief account of the RGB method, the following aspects of RGB photoelasticity are considered:

• Influence of the quarter-wave plate errors;

• Number of acquisitions;

• Light source type and determination of fringe orders more than three;

• Determination of fringe orders less than 0.5;

• Search methods for the retardation;

• Scanning procedures;

• Calibration on a different material and effect of light intensity;

• Combined use of the RGB and phase shifting methods;

• Applications on birefringent coatings, glass residual stresses and others.