Indian Journal of Engineering & Materials Sciences Vol.20, August 2013, pp 237-244
Developing digital image correlation techniques for using water immersion to improve strain field measurement in micro-scale Ming-Hsiang Shiha, Jui-Chao Kuob, Wen-Pei Sungc & Shih-Heng Tungd* a
Department of Civil Engineering, National Chi Nan University, Nantou 545, Taiwan Department of Materials Science and Engineering, National Cheng-Kung University, Tainan 701, Taiwan c Department of Landscape Architecture, Integrated Research Center for Green Living Technologies, National Chin-Yi University of Technology, Taichung 411, Taiwan d Department of Civil and Environmental Engineering, National University of Kaohsiung, Kaohsiung 811, Taiwan b
Received 13 August 2012; accepted 1 April 2013 Light reflection on the surface of test specimen leads to analyse error of strain measurement by using digital image correlation (DIC) technique in micro-scale test. In this study, water immersion is firstly proposed to combine with DIC technique to reduce the influence of light reflection on the surfaces of measured sample in a micro-scale experiment. Then, all test images are transformed into two dimensional K-space to compare the influence degree of light reflection on the various configurations of test specimens. Furthermore, the effects of light projection direction and the angle of light source are investigated into the analysis accuracy of strain measurement for the various configurations of test specimens. The test and analysis results from K-space indicate that the frequency signals of images, measured from test samples, observed in air are higher than the results from this proposed method. Otherwise, no matter how the variation of the light projection direction and the angle of light source are, the standard deviations of strain from this proposed method are diminished, reduced to below 0.001. The analysis accuracies of strain analysis for using water immersion method have been verified. Keywords: Digital image correlation, Water immersion, Light reflection, K-space
Strain distribution analysis for mechanical engineering is an important topic. The traditional strain measurement methods are: (i) using a strain meter that cannot obtain the strain for the whole filed and (ii) making grids on test sample to measure the displacement before and after deformation, this method is tedious and time-consuming. As the resolution of digital image and the calculation capacity of computer have been significantly improved recently, the digital image correlation based on high techniques of cameras and computers, plays an important role in measuring strain field for various scales of test specimens1-6. The digital image correlation (DIC) technique has been developed for measuring strain variation of test materials from microscale to nanoscale by combining with optical microscopy7, laser scanning confocal microscope (LSCM)8, scanning electron microscopy (SEM)9, digital microscopy10, atomic force microscopy (AFM)11 and scanning tunneling microscope (STM)12. Furthermore, a low-cost and non-contact digital image correlation method (DIC) has been developed by our —————— *Corresponding author (E-mil:
[email protected])
research team to apply to measure the macro-scale tests, such as the observation of cracks in the brick wall13 and the monitoring of static and dynamic deformation of bridges and building structure under the excitation of external forces14-17. The test and analysis results reveal that this developed DIC method with rapid advances in digital photography and computer can achieve high analysis precision and accuracy requirement to perform analyses of strain distribution. The principle of this developed DIC technique is based on the image correlation function, which determines the degree of similarity between two digital images of the specimen surface before and after deformation. Therefore, the strain field can be computed from the measured displacement field. The measurement accuracy of DIC is significantly affected by hardware system (the loading system, the imaging system) and software system such as the correlation formulation and optimization algorithm. The errors related to the hardware system are the quality of the speckle pattern on the specimen surface, non-parallel CCD sensor and object surface and out-of-plane displacement, image distortions and
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image noises.18 The image noises come from image acquisition as well as from light illumination. In the case of light illumination, in order to obtain a good quality of images, it takes a long exposure time at lower illumination. Therefore, the noises resulting from light illumination is impossible to reduce at low illumination. In addition, deformation, translation or rotation of a specimen during a static experiment as well as a dynamic experiment leads to the change of the relative position between specimen and illumination source. This causes the variation of the location of noises induced by light illumination and negative influence on the analysis result. Thus, in order to reduce the effect of illumination lighting fluctuation, a new and simple test method is proposed in this study. This method is applied the developed DIC techniques with using water immersion to measure the micro-scale strain filed variation of test specimens. Then, the efficiencies of this proposed test method are investigated on the accuracy of strain field measurement with various illumination light direction. Digital Image Correlation Method DIC is a non-contact high-accuracy measurement method. The principle of digital image correlation method (DIC) is to compare the grayscale relationship between the images before and after deformation. The corresponding point location on the image before deformation will be determined on the image after deformation, as shown in Fig. 1. Assuming the relationship between the coordinates of corresponding points before and after deformation can be expressed as the following equations: X * = X + u( X ,Y )
it means that P* is exactly the sub-image of P after deformation.13 After determining the relationship of Eq. (1), the displacement field and strain field can then be established. The analysis program is developed by our research team. This program has been tested and verified by real test20. Experimental Procedure In order to investigate the effects of this proposed test method for applying the developed DIC technique with water immersion for test specimens, the test and analysis results of different test methods are compared with one another to verify the accuracy of strain field measurement. A canon EOS 400D Digital single-lens reflex camera (DSLR camera) with objective lens and microscope lens are used to capture images of specimen for strain measurement. DSLR camera is combined with the parts of a single-lens reflex camera (SLR) and a digital camera back to replace the photographic film. In the reflex design scheme, light travels through a single lens and a mirror is used to reflect a portion of that light through the view finder19. Objective lens and microscope lens, used in this research, collect the visible light emerging from the test specimens into the DSLR camera. Microscope lens use visible light to magnify images of small samples, they can be used to immerse in water. A light source is used to raise light reflection. Nevertheless, the blaze of light reflection on test samples causes overexposure to result in analysis errors. Therefore, the surfaces of test specimens are sprayed with black color (Fig. 2) to avoid this phenomenon. The microscopic lens and camera are
… (1)
Y * = Y + v( X , Y )
If P and P* are the sub-images before and after deformation separately, the grayscale correlation between these two sub-images can be defined as1: COF =
∑ g g ∑ g ⋅ ∑ g ij
ij
2
ij
2
… (2)
ij
Where g ij and g ij are the grayscale value at
( )
coordinate ( i, j ) on image P and at coordinate i, j
on image P*. The greater the correlation coefficient, the stronger the relationship between these two subimages. When the correlation coefficient is equal to 1,
Fig. 1—Schematic drawing of relative location of sub-images of deformed and un-deformed images on surface
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fixed on a platform. The specimen of dimensions 2×2×2 cm3 (Fig. 2) is observed under the microscopic lens. The schematic diagram of experimental set-up of traditional test method is shown in Fig. 3. Because the absorption spectrum for water molecule is wavelength between 760 nm to 660 nm, water molecule contains weak overtone to absorb red light and appear its complementary color. Therefore, the water immersion method for DIC techniques is proposed in this research to improve the quality of captured images. A glass water tank and a microscope cover glass are proposed to add in this measured system. To investigate the effect of this proposed water immersion method, three specimen configurations, named as A, W and AGW are employed. In configuration A the specimen is directly observed in air under the microscopic lens as shown in Fig. 4 and in configuration W the microscopic lens is submerged in water above the specimen (Fig. 5). In
the case of configuration AGW, the specimen is also directly observed under the microscopic lens. The surface of specimen is covered with a microscope cover glass between the specimen and the cover glass which filled up this gap with a drop of water (Fig. 6). In addition, illumination light was projected from incident directions of 0, 45, 90, 135 and 180 degrees on the specimen from outside of the test platform in order to investigate the influence of illumination light direction. Post treatment of all images captured from the test samples of configuration A, AGM and W are analyzed by our developed program. The analysis accuracy of this program has been tested and verified20. Results and Discussion Effect of water immersion on reducing light reflection
The test results are shown in Fig. 7. These images are captured from the surface of specimens of various test setup for configuration of A, AGW and W respectively. The image of Fig. 7(a) reveals that the light reflection phenomenon is more obvious than the other two images of Figs 7(b) and 7(c). The
Fig. 2—Dimensions of specimen for strain measurement Fig. 4—Experimental setup of configuration A
Fig. 3—Schematic illustration of experimental setup
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Fig. 5—Experimental setup of configuration W
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images quality of Fig. 7(b) compares hardly with that of Fig. 7(c). To compare the influence degree of light reflection, these test images are transformed into Kspace. K-space is the two-dimensional or threedimensional Fourier transform of the image measured. Typically, K-space has the same number of rows and columns as the final image and is filled with raw data during the scan21. In this study, the influence of light reflection from test specimen is only considered as a two-dimensional signal. Therefore, all test images are converted into the two dimensional Fourier transformation, the corresponding two-dimensional (2D) frequency domain is also known as the K-space.21-23 Low-frequency signal lies at the center of a 2D K-space and the outer area is the high frequency signal. As the signals are found mainly in the inner region, that is, in the low-frequency region, the image is considered having high image quality with few noises. Contrarily, the light reflection causes very fine shining spots in the image. It leads to an abrupt grayscale variation around a light spot and results in high frequency signals. Using Fourier transformation to transform all captured images of test specimens into K-space, shown in Fig. 8. The diagrams of K-space, transformed from three various configurations of test specimens, consist of different radius of circles. The radius of the circle in configuration A is much larger than that in configurations AGW and W respectively, shown in Fig. 8(a)~8(c). According to the characteristic of K-space diagram, this means that there are more noises, happened in configuration A. The amplitude profiles of configuration A, AGW and W along the red dashed line are plotted in Fig. 8(d). It obviously shows that the amplitude of configuration A is larger than that of configuration AGW and W respectively when the frequency value researches to 0.08 cyc/pixel. It is consistent with the observation result from Fig. 7. This result reveals that the water immersion of configuration W and AGW respectively can reduce light reflection phenomenon on the surfaces of test sample effectively.
Fig. 6—Experimental setup of configuration AGW
Effect of water immersion on improving DIC accuracy
Fig. 7—Magnification images of specimen configuration (a) A, (b) AGW, and (c) W
surface
for
In the previous section, the illumination light in configuration A, AGW and W was projected from incident direction of 0° on the specimen which is recorded as the reference image having a grid size 128 pixels. To investigate the effect of light projection direction, firstly, the incident direction is fixed at 45°. Figure 9 shows a measured area at the light projection
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Fig. 8—K-space diagrams of (a) A, (b) AGW, and (c) W configurations. (d) Amplitude profiles of frequency along the diagonal for A, W and AGW
Fig. 9—Measured area in white with the lattice grid marked in red
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direction of 45°. Figure 10 reveals that the analysis diagrams of strains for configurations A, AGW and W respectively at 45° of light projection direction. The measured strains should be zero without any deformation, induced by changing the light projection direction. The cause of strain deviation is in virtue of the effect of the light reflection, shown in Fig. 10. Figure 10 shows that the strain deviation in configuration A is larger than that in configuration
AGW and W respectively. The standard deviation values of strains, caused by various light projection direction, are plotted in Fig. 11 for configuration A, AGW and W respectively. Figure 11 displays clearly that the standard deviations of strain for configuration of AGW and W respectively are much smaller than that for configuration of A. The light reflection phenomenon randomly occurs on the surface of specimen in accordance with light projection
Fig. 10—Strain maps of ε x and ε y at 45° light projection direction in configuration (a) A, (b) AGW and (c) W, where Ex and Ey are ε x and ε y , respectively
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Fig. 12—Strain standard deviation in (a) x and (b) y directions in configuration A, AGW and W as the light incident angle changes
Fig. 11—Strain standard deviation as a function of the projection direction in (a) x and (b) y directions in configuration A, AGW and W
direction. But, the blaze of light reflection cannot be absorbed by air. Therefore, the standard deviations of strain in configuration A are larger than those in configuration of AGW and W respectively, while the standard deviations of strain in configuration AGW and W respectively are almost constant, shown in Fig. 11. These test and analysis results demonstrate that the influence of light reflection on the specimen surface of configuration A causes serious errors. Otherwise, the advantage of water immersion method for absorbing the light reflection can improve the quality of captured images and follow-up strains analysis, obtained from DIC techniques in a microscale experiment. Figure 11 shows that the accuracies of strains measurement from DIC achieve about 0.001. There is no significant difference in the
accuracy of strain measurement between configuration AGW and configuration W. In order to confer the influence of the variance of light incident angle, the light source is raised about 50 cm from its initial position. At this initial position the direction of light is defined as 0°, shown in Fig. 3, the captured image at this position is defined as the referenced image. Then, the light is raised up to about 50 cm. The compared image is captured at present position to compare with the reference image. The test and analysis results of the standard deviations of strain, obtained from DIC, are shown in Fig. 12. Figure 12 indicates that the analysis strain standard deviations of the configuration AGW and W are much smaller than those of configuration A. The analysis results of Figs 11 and 12 demonstrate that this proposed test method can reduce the influence of light reflection on the surface of test specimen as well improve the accuracy of DIC-based strain measurement. The main reasons of the effect of this proposed test method is that the refractive index of water is 1.33. The velocity of light in water is only 3/4 of that in air. Therefore, it leads to that the wavelength of light in water is 3/4 of that in air. A short wavelength increases the observation resolution of microscope as well as the scattering intensity on object surface24. In addition, as the light reflected from the water comes back into the air, it increases in refraction angle and the reflected light is limited. As a result, the light reflection problem is able to be solved.
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Conclusions The light reflection problem causes analysis errors for measuring strain of the surface of test specimens. The test and analysis results show that light reflection problem causes the analysis errors for the images, captured from digital image correlation technique. Therefore, in order to improve the strain measurement in micro-scale for applying DIC techniques, water immersion method for test samples is proposed in this research. The following conclusions can be drawn from this study: (i) The frequency signals and amplitude of test specimen of configuration A are larger than test specimens of configuration AGW and W respectively. These phenomena reveal that this proposed water immersion method can reduce light reflection phenomenon on the surfaces of test sample effectively. (ii) The influence of various light projection direction and light incident angle for using water immersion method verify that the analysis accuracy of this proposed method is unaffected by the variation of light projection direction and light incident angle. But, the standard deviations of strain for test specimen in air are affected obviously by the variation of light projection direction and light incident angle. (iii) The test and analysis results reveal that the standard deviations of strain are reduced to below 0.001 employing water immersion configuration no matter what variation of the light direction and the angle of light source are. The light reflection problem on the strain measurement for using DIC technique in a micro-scale experiment is able to be improved by using water immersion configuration. (iv) This proposed method for using water immersion has been tested and verified its analysis accuracy. The test results confirm that this water immersion method for DIC technique can absorb the wave length of light to improve the test and analysis quality of DIC technique.
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