ReviewReview of RGB photoelasticity
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.
Section snippets
The RGB method in circularly polarized light
In the basic application of RGB photoelasticity, the model is placed in a circular polariscope, generally in dark field, and the isochromatic fringes are acquired in white light using a colour camera and a frame grabber. The camera decomposes the white light into the three primary colours red, green and blue by means of its three broad band filters and a frame grabber digitizes the three primary colours in three levels of intensity, which are usually denoted by the symbols R, G and B.
Due to the
The RGB method in elliptically polarized light
A variation of the RGB method, which allows the determination of both the retardation and the isoclinic parameter from a single image in white light, has been proposed by Yoneyama and Takashi [46]. Instead of the traditional method, this one employs elliptically polarized light; in this case, the light intensity emerging from the three filters of the RGB camera can be expressed by the following approximate relationship:
Effect of the quarter wave plates error
Generally the circular polariscope uses chromatic quarter wave plates, corrected for the reference wavelength, usually monochromatic yellow (589 nm) or green (546 nm) lights. At different wavelengths, an error is introduced, whose effect on the determination of the retardation is considered in references [44], [68].
For given retardation, if the values of the parameter α in the calibration specimen and in the points of the model (where it is necessary to determine the retardation) are different,
Number of acquisitions
Table 1 summarizes the number of acquisitions used in different versions of the RGB method. In the classic method (row 1), only one acquisition in the dark-field circular polariscope is performed. In addition, the method in elliptically polarized light requires a single acquisition [46]. In the second method (row 2), two acquisitions are made using the circular polariscope in light and dark field; in this case the differences of the R, G and B levels in light and dark field are used for the
Combined use of RGB method and phase shifting technique
Techniques based on the combined use of RGB photoelasticity and PSM have been developed for the following purposes:
- 1.
to evaluate the isoclinic parameter and to eliminate the influence of the quarter wave plate errors in RGB photoelasticity [11], [83];
- 2.
to calibrate the retardation maps obtained by the PSM [16], [17], [84], [85];
- 3.
to eliminate the need of unwrapping and improve results of PSM [70], [72] applying the procedure of search of the retardation of the RGB method to the wrapped retardations
Birefringent coatings
The application of the RGB photoelasticity to the birefringent coating technique is reported in [83], [86], [87].
Barone and Petrucci [86] have considered the irregularity of the reflected light field as the most important problem in the application of the classical RGB method to the birefringent coatings.
The fluctuation of the light field can happen due to irregular reflectivity of the bonding surface, variations of the light incidence and reflection angles, non-uniformity of the light source.
Conclusions
In this article, a review of the RGB photoelasticity is presented. The peculiarities of this technique consist in the fact that the images are acquired in white light by a colour digital image processing system and the retardation is determined by a data base search approach. RGB photoelasticity allows the users to determine the photoelastic relative retardation by means of a single image, without the need of external information, although a calibration procedure has usually to be performed.
The
References (109)
- et al.
Data acquisition techniques in digital photoelasticity: a review
Opt Lasers Eng
(1998) - et al.
Whole-field determination of isoclinic parameter by five-step colour phase shifting and its error analysis
Opt Lasers Eng
(2003) - et al.
Digitally whole-field analysis of isoclinic parameter in photoelasticity by four-step colour phase-shifting technique
Opt Lasers Eng
(2007) - et al.
Automation of white light photoelasticity by phase-shifting technique using colour image processing hardware
Opt Lasers Eng
(1997) - et al.
Phase shifting photoelasticity in white light
Opt Lasers Eng
(2007) - et al.
Photoelasticity stress analysis using carrier fringe and FFT techniques
Opt Lasers Eng
(1993) - et al.
Limitation on carrier fringe methods in digital photoelasticity
Opt Lasers Eng
(2007) - et al.
Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error
Opt Lasers Eng
(2002) - et al.
Photoelastic analysis with a single tricolour image
Opt Lasers Eng
(1998) - et al.
Improve determination of retardation in digital photoelasticity by load stepping
Opt Lasers Eng
(2000)
Load-stepping photoelasticity: new developments using temporal phase unwrapping
Opt Lasers Eng
A new method for photoelastic fringe analysis form a single image using elliptically polarized white light
Opt Lasers Eng
Measurement of surface topography by RGB shadow-moirè with direct phase demodulation
Opt Lasers Eng
A modified regularize scheme for isochromatic demodulation in RGB photoelasticity
Opt Lasers Eng
Numerical simulations and experimental measurements of the stress intensity factor in perforated plates
Eng Fract Mech
Elliptical polarized white light photo viscoelastic technique and its application to viscoelastic fracture
Opt Lasers Eng
The influence of the quarter wave plates in automated photoelasticity
Opt Lasers Eng
Noise removal in three fringe photoelasticity by adaptive colour difference estimation
Opt Lasers Eng
Advancing front scanning approach for three-fringe photoelasticity
Opt Lasers Eng
The influence of ambient illumination on colour adaptation in three fringe photoelasticity
Opt Lasers Eng
Completely automated photoelastic fringe analysis
Opt Lasers Eng
Determination of reflection photoelasticity fringes analysis with digital image-discrete processing
Measurement
Whole field evaluation of stress components in digital photoelasticity-issues, implementation and application
Opt Lasers Eng
A simple approach to photoelastic calibration of glass using digital photoelasticity
J Non-Cryst Solids
A review of automated methods for the collection and analysis of photoelastic data
J Strain Anal
Digital photoelasticity: principles, practice and potential
Strain
Digital photoelasticity–A comprehensive review
J Strain Anal
Data acquisition techniques in photoelasticity
Exp Tech
Computer-aided measurement of relative retardations in plane photoelasticity
Towards full field automated photoelastic analysis of complex components
Strain
A method for reducing the influence of quarter-wave plate errors in phase stepping photoelasticity
J Strain Anal
Computer aided photoelasticity by an optimum phase stepping method
Exp Mech
Photoelasticity
Full field evaluation of an isoclinic parameter in white light
Exp Mech
Automatic whole-field measurement of principal stress directions using three wavelengths
Proceedings of the tenth international conference on experimental mechanics
Simulation of errors in automated photoelasticity
Exp Mech
Automation of data acquisition in reflection photoelasticity by phase shifting methodology
Strain
Limitation of Fourier transform photoelasticity: influence of isoclinics
Exp Mech
On the range of accuracy of spectrally scanned white light photoelasticity
Proceeding of the SEM conference on experimental mechanics
The measurement of the complete photoelastic fringe order using a spectral scanner
Proceeding of the SEM conference on experimental mechanics
Automated measurement of birefringence: development and experimental evaluation of the techniques
Exp Mech
Photoelastic analysis using a full field spectral contents analyser
Proceeding of the SEM conference on experimental mechanics
An innovative polariscope for photoelastic stress analysis
Proc. Soc. For Exp. Mech., Spring Conference
Tricolour photoviscoleastic technique and its application to moving contact
Exp Mech
Absolute determination of the isochromatic parameter by load-stepping photoelasticity
Exp Mech
Full field automated photoelasticity using two-load-step method
Opt. Eng.
Role of photoelasticity in evolving discretization schemes for FE analysis
Exp Tech
On interpretation of fringe patterns produced by time average photoelasticity
Exp Tech
Time-averaged photoelastic stress analysis of the ultrasonic wave in a strip
Exp Mech
Cited by (75)
Experimental evaluation of corneal stress-optic coefficients using a pair of force test
2024, Journal of the Mechanical Behavior of Biomedical MaterialsQuantification of full-field stress in continuously loaded fractured rocks using 3D printing and digital photoelasticity
2024, Optics and Lasers in EngineeringAdvancing instantaneous photoelastic method with color polarization camera
2024, Optics and Lasers in EngineeringQuantification of the stress field in extremely complex pores by digital photoelasticity
2023, Measurement: Journal of the International Measurement ConfederationMethod to quantify the dynamic near-fault full-field stress evolution associated with rough fault shear deformation based on 3D printed models and photoelastic measurements
2023, Measurement: Journal of the International Measurement Confederation