- Email: [email protected]
Shearography for specular object inspection
Optics and Lasers in Engineering 61 (2014) 14–18
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Shearography for specular object inspection Nan Xu, Xin Xie, Xu Chen, Lianxiang Yang n Optical Laboratory, Department of Mechanical Engineering, Oakland University, Rochester, MI 48309, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 12 February 2014 Received in revised form 17 April 2014 Accepted 26 April 2014 Available online 15 May 2014
Digital shearography is a laser speckle pattern interferometry based, non-destructive testing (NDT) method, which has a great potential in revealing the defects inside the objects e.g. composite materials. It has been applied successfully in various industry applications. However, due to its essence of laser speckle utilization, the object surface needs to be rough enough, otherwise, the object surface has to be specially treated. Considering the situations that the surface treatment under some cases is not allowed, an improved optical setup has been introduced and described in this paper. A modified shearography setup which can be applied on samples with specular surface is introduced. The theory and experiment results are described and presented. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Shearography Specular surface Non-destructive testing
1. Introduction Shearography, also called speckle pattern shearing interferometry, is a laser based, whole field, non-contact and nondestructive optical method that is capable of directly measuring strain information [1–3], and thus suited well for non-destructive testing of composite materials, such as glass/carbon fiber reinforced materials, honeycomb structures etc [4–7]. As a laser interferometry technology, shearography utilizes speckle interferometry which is generated by a coherent light reflected from a rough object surface. When the object under test is deformed, the speckle pattern captured by the sensor will be slightly altered. When two speckle patterns corresponding to deformed and undeformed states are obtained and subtracted, a fringe pattern, i.e. a shearogram, is generated [8,9]. In order to utilize the shearography system, the first essential requirement is the speckle pattern generated on the object surface, which demands the surface to be a rough surface. If the object surface is a mirror-like surface, most of the light will be mirror reflected and there will be little speckle generated, so that the shearography cannot be applied. For solving this problem, a traditional solution is to treat the object surface, such as spraying. However, under some circumstances, it may be impossible or forbidden to treat the sample surface. Therefore, demand for shearographic inspection on smooth surface without surface treatment is increasing. This paper introduces a methodology of shearography for nondestructive testing of specular or quasi-specular objects without
n
Corresponding author. Tel.: þ 1 248 370 2283. E-mail address: [email protected] (L. Yang).
http://dx.doi.org/10.1016/j.optlaseng.2014.04.015 0143-8166/& 2014 Elsevier Ltd. All rights reserved.
treating the surface. The theory is expressed in detail, and experiment results shown the feasibility of shearography for nondestructive testing on specular objects are demonstrated.
2. The optical setup and theoretical analysis The modified shearography setup schematic for testing the object with specular surface is shown in Fig. 1. Comparing to the traditional shearography setup, a flat and white (rough) plane M is embedded into the light path, which changes the direction of the light path. The laser reflected from the smooth surface hits the embedded rough plane M and generates the speckle pattern required in the shearographic testing. A coherent laser is expanded to illuminate the object. The light reflected from the object surface normally consists of two parts, the specular reflected light and diffusive reflected light. Both of the two parts carry the deformation information. Typically, the diffusive part which can generate speckle pattern is useful in shearography but the other part is not. However, when the object surface is specular or quasi-specular, most of the laser energy is mirror reflected, the speckle generated by the diffusive light is not sufficient for the measurement. To solve this problem, a rough and white image plane is embedded into the light path. When the specular reflected light reaches the rough plane, the beam will be diffusively reflected and the speckle pattern is generated. Digital shearography can make use of the speckle pattern and measure the deformation. Same as the standard shearographic testing procedure, the speckle pattern is separated into two beams by the shearing device. The two beams merge into the CCD camera and generate the interference. The difference between the two interferograms
N. Xu et al. / Optics and Lasers in Engineering 61 (2014) 14–18
15
path change analysis will be only from the laser source S to the image plane M. Based on Fig. 2, the light path before deformation can be expressed by Eq. (1). Lb ¼
Fig. 1. Schematic of the modified shearography system; L is a laser; E is the expander; M is the embedded white and rough plane; M1 and M2 are the two mirrors in the Michelson Interferometer; α is the incident angle; γ is the image plane incident angle; Z1 and Z2 are a pair of orthogonal polarizers.
θ1
β
P
α ω
θ1
P’
ð1Þ
where D1 is the distance from the light source to the object, D2 is the distance from the object to the image plane and α is the incident angle; α is the incidental angle. After deformation, due to the rotation of the point P in deformation, the reflected light on the image plane M will shift a small distance Δm. Considering rotation angle θ1, the light path after deformation Lf can be expressed as Eq. (2). Lf ¼
D1 ω ðD2 ωþ D2 tan α tan θ2 Þ sin θ2 þ cos ðα þ βÞ sin ð2θ1 þθ2 α βÞ
ð2Þ
where ω is the out-of-plane component of the deformation at point P; θ1 is the rotation angle of point P; θ2 is the tilting angle of the image plane; β is the angle change of the incidental light. Making subtraction of Eqs. (1) and (2) on both sides, the light path difference due to the deformation is calculated by Eq. (3).
S
D1
D1 D2 þ cos α cos α
N’
ΔL ¼
N θ2
M’ Δm
D1 þD2 ðD1 ωÞ D2 ð1 þ tan α tan θ2 Þ ω sin θ2 cos ðα þ βÞ cos ðα þ β 2θ1 θ2 Þ cos α
The incidental angle change β is related to the out-of-plane deformation and the original incident angle. This angle can be expressed by Eq. (4).
M D2
Fig. 2. The light path difference analysis. S is the laser source; P is the testing point; M is the corresponding point of P on the image plane; α is the incident angle; PN is the normal line at point P; D1 is the distance from the object surface to the laser source and image plane; D2 is the distance from the object to the image plane; ω is the out of deformation on point P; P0 is the same point after deformation; θ1 is the turning angle at point P due to the deformation; θ2 is the tilting angle of the image plane; β is the incident light turning angle; P0 N0 is the normal line at P0 ; Δm is the light shift on the image plane.
before and after deformation illustrates the first derivative of the deformation. Z1 and Z2 in Fig. 1 are a pair of orthogonal polarizers. In the practical measurement, If the object is purely specular, the polarizes are not necessary, however, if the object surface is quasi-specular, the diffusive light reflected from the object is much stronger. The diffusive reflected laser will also interfere with the mirror reflected laser and generate unexpected speckle pattern mixed with the demanding signals. It will greatly influence the measurement. The orthogonal polarizers Z1 and Z2 in the system are to eliminate the disturbance and improve the measuring results. Z1 is located between the laser source and the object, so that the incident laser will be linearly polarized. After the laser is reflected from the object, the mirror reflected portion keeps linearly polarization but its polarization orientation is turned 90 degree, while the diffuse reflected portion will have random polarization orientations. In this case, the polarizer Z2 between the object to the CCD sensor, which is orthogonal to Z1, will allow only the mirror reflected laser to transmit and be received by the CCD sensor. Fig. 2 shows the light path vectors and its change due to the object deformation. Because the specular reflected light does not carry the in-plane deformation, only the out-of-plane deformation ω will be discussed. Because the distance from the image plane to the shearography sensor doesn't change during the object deformation, the light
ð3Þ
β ¼ arctan
ω sin α cos α D1 ω cos 2 α
ð4Þ
Considering the distance between the laser source to the object, D1 is far bigger than the object size, so the incidental angle α is very small, and the term cos 2 α is close to 1. In this case, Eq. (4) can be simplified as Eq. (5). β ¼ arctan
ω sin 2α 2ðD1 ωÞ
ð5Þ
With Eq. (5), the relationship between ΔL and ω shown in Eq. (3) is clear with all the other parameters measurable. In the practical experiment, the optical setup can be more carefully built, so that the embedded image plane is parallel to the object plane and the laser source S is on the image plane as well. The light path vector chart is changed to Fig. 3. Comparing Figs. 2 and 3, the differences include D1 ¼ D2 ¼ D, θ ¼ θ1 and
Fig. 3. The light path vector chart when the image plane is parallel to the object. D is the distance from the laser source to the object plane and the distance from the object to the embedded image plane; θ is the rotation angle of point P.
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N. Xu et al. / Optics and Lasers in Engineering 61 (2014) 14–18
θ2 ¼ 0, so Eq. (3) is simplified as Eq. (6). 1 1 2D þ ΔL ¼ ðD ωÞ cos ðα þ βÞ cos ðα þ β 2θÞ cos α
¼ ð6Þ
where D is the distance from the laser source to the object. Put φ ¼ α þ β θ, which is the incident angle after deformation, then Eq. (6) becomes, 1 1 2D ΔL ¼ ðD ωÞ þ ð7Þ cos ðφ þ θÞ cos ðφ θÞ cos α The light spot shift distance on the image plane due to deformation can be calculated by Eq. (8). Δm ¼ D tan α ðD ωÞ tan ðφ θÞ
ð8Þ
In the real experiments, the distance from the laser source to the object is much larger than the object size, so the incidental angle α is close to 0 and β is close to 0 accordingly. The light path difference ΔL in Eq. (7) can be further simplified to Eq. (9) ΔL ¼ 2ðD ωÞ
cos 2 θ 2D cos ð2θÞ
Δϕ ¼
cos 2 θ
Δϕ ¼
ð10Þ
sin θ
According to the classical digital shearography equations [10], the relative phase change ΔΦ originates from the difference between phase changes ΔΦ1 and ΔΦ2 created by the loading, which correspond to the light beams on the object's surface scattered from points P1 and P2. The phase difference ΔΦ1 or ΔΦ2 is scattered by the laser beam from one point of the object's surface due to loading. ΔΦ can be calculated by Eq. (11). Δϕ ¼ Δϕ1 Δϕ2 2
¼
2
2π D sin θ ω1 cos θ D sin θ ω2 cos θ 2 2 λ cos 2 θ sin 2 θ cos 2 θ sin 2 θ 2
2
!
ð12Þ
4π 1 δω δx λ 1 tan 2 θ δx
ð13Þ
Considering tan θ ¼ δω=δx, tan 2 θ ¼ ðδω=δxÞ2 is very small so that it is close to 0. Eq. (13) is further simplified into Eq. (14). Δϕ ¼
2
2π 2 cos 2 θ δω δx λ cos 2θ δx
Eq. (12) can be transferred to Eq. (13)
ð9Þ
D sin 2 θ ω cos 2 θ
ð11Þ
where ΔΦ1 and ΔΦ2 are the phase difference at P1 and P2 respectively; ω1 and ω2 represent the out-of-plane deformations at P1 and P2 respectively; Δω is the difference between ω1 and ω2. Assuming the laser and the camera lie in XoZ plane, and the shearing direction is in x-direction with the shearing amount of Δx, divide both sides of Eq. (11) by Δx, it becomes:
Eq. (9) can also be expressed as ΔL ¼ 2
2π δω cos 2 θ 2 λ cos 2θ
4π δω δx λ δx
ð14Þ
For very small shearing amounts δx, Eq. (14) can be rewritten as Δϕ ¼
4π ∂ω δx λ ∂x
ð15Þ
In the same sense, if the shearing direction is in y-direction, the equation is Eq. (16). Δϕ ¼
4π ∂ω δy λ ∂y
ð16Þ
Eqs. (15) and (16) are the same as the typical digital shearography equations [10], which show that the first derivative out-ofplane component ∂w/∂x or ∂w/∂y can be measured by a single illumination beam shown in Fig. 1.
Fig. 4. Fringe pattern comparison by using the conventional and improved shearography system; (a) traditional shearography result before smooth; (b) traditional shearography result after smooth; (c) modified shearography result before smooth; (d) modified shearography result after smooth.
N. Xu et al. / Optics and Lasers in Engineering 61 (2014) 14–18
17
Fig. 5. Honeycomb sample testing results; (a) raw results; (b) smooth results.
3. Experiments, results and analysis In the experiments, there are two kinds of situations for the object surface, specular and quasi-specular. The main difference is on the portion of the diffusive reflection. The experiments on both situations will be discussed in this section. The specular object tested is a piece of 100 mm 100 mm square metal-coated plastic plate, edge clamped on a rigid steel frame. A micro-head is installed backward which can apply a central concentrated loading on the plastic plate from behind in order to generate a cone-shape deformation. The testing results are shown in Fig. 4. The phase maps in Fig. 4(a) and (b) are the results from the traditional shearography system, before and after smoothing respectively. Because of the specular surface, there is little diffusive light available for generating speckles or carry information; and furthermore when the surface is deformed, the incident angle for surface has been changed, more reflected light is received by the CCD sensor and overwhelmed the phase information. As a result, only a small area in the phase map has fringes, and the major area is meaningless. On the contrary, by embedding a rough image plane as a media, the mirror reflected light generates speckle on the plane so that the shearography system can make use of this part of light and obtains phase maps shown in Fig. 4(c) and (d). The fringe pattern is as clear as usual. After smoothing, the phase map can be evaluated quantitatively. If the object surface is quasi-specular, the diffusive light reflected from the object will significantly influence the measurement. The pair of orthogonal polarizers will eliminate the influence. The object tested is a piece of aluminum skinned honeycomb structural composite material with a small delaminating area. The honeycomb sample is simply supported on the optical table. Because the object surface is aluminum which is quasispecular, the testing will make use of the pair of orthogonal polarizers. In the testing, the sample was slightly warmed by a heat gun. Theoretically, the delaminating area will deform more than the other good area under heat expansion. In this case, the first derivative of the deformation, which the shearography detects, jumps at the defect area. The testing result is shown below (Fig. 5). The fringe pattern inside the red circle clearly indicates the delaminating area. The defect in the object is successfully detected.
4. Conclusion The experiment results demonstrate the possibility of applying the shearography system on the smooth surface, either specular or quasi-specular, with no need of surface treatment e.g. spraying which is time consuming and economical waste, or even
prohibitive under some circumstances. This modification improves the usefulness of shearography especially in practical industrial application, where a lot of metal objects possess specular surface. The embedded image plane can be rigidly fixed with the object so that it does not increase the instability of the system. Because of the light shift on the image plane, it will be difficult to quantitatively calculate the deformation gradient accurately. However, in a practical NDT application, the clarity of the fringe pattern is more important, which the modified shearography is well promising. Acknowledgments The authors would like to express our sincere thanks to Mr. Bernard Sia of the Optical Lab of Oakland University who carefully and thoroughly read the manuscript and provide valuable criticisms. References [1] Yang L, et al. Digital shearography for nondestructive testing: potentials, limitations, and applications. J Holography Speckle 2004;1.2:69–79. [2] Hung M, Yang L, Huang Y. Nondestructive evaluation (NDE) of composites: digital shearography. In: Vistasp M, Karbhari Non-Destructive, editors. Evaluation of polymer matrix composites: methods and applications, Chapter 5. Woodhead Publishing Ltd; 2013 (ISBN 0–85709-344-4). [3] Yang L. Recent developments in digital shearography for nondestructive testing. Mater Eval 2006;64(7):704–9. [4] Wu S, Zhu L, Feng Q, Yang L. Digital shearography with in situ phase shift calibration. Opt Laser Eng 2012;50(9):1260–6. [5] Xu N, Xie X, Harmon G, Gu R, Yang L. Quality inspection of spot welds using digital shearography. SAE Int J Mater Manuf 2012;5(1):96–101. [6] Xu N, Yang L, Lev L, et al. NDT of weld joints using shearographic interferometry and dynamic excitation. SAE Tech Paper 2011:01–996. [7] Wu S, Xu N, Feng Q, Yang L. Precision measurement of deformation using a self-calibrated digital speckle pattern interferometry (DSPI). SAE Tech Paper 2010:01–958. [8] Hung YY, Taylor CE. Measurement of slopes of structural deflections by speckle-shearing interferometry. Exp Mech 1974;14.7:281–5. [9] Hung YY, Liang CY. Image-shearing camera for direct measurement of surface strains. Appl Opt 1979;18.7:1046–51. [10] Wolfgang S. Digital shearography: theory and application of digital speckle pattern shearing interferometry. . SPIE Press; 2003.
NAN XU graduated as PhD studies in mechanical engineering from Oakland University in 2013. Nan joined the Optical Laboratory in 2009. He received his bachelor's degree in Computer Science from Northeastern University, Shenyang, China, in 2004 and his master's degree in Optical Engineering from Beijing Jiaotong University, China, in 2008. He worked in the Institute of Electronics, Chinese Academy of Sciences as a software developer from 2004 to 2005. His research interests now include optical metrology, nondestructive testing with digital shearography, experimental strain/stress analysis, nondestructive testing, 3D computer vision, and software programming and development. He is now working on his PhD thesis with the title of “Development of Digital Shearography for Quality Inspection of Resistance Spot Weld” and he also participated
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N. Xu et al. / Optics and Lasers in Engineering 61 (2014) 14–18
in a number of projects with DOE and GM related to this topic. So far, he has published three journal papers and seven international conference papers in this field. He also holds a US patent in non-destructive weld testing.
XIN XIE is a PhD candidate working in the Optical Laboratory of Mechanical Engineering at Oakland University (OU) supersized by Professor Lianxiang Yang. He received his bachelor's degree in Precision Mechanical Engineering from Hefei University of Technology, Hefei, China, in 2010. After that, he went to Oakland University to continue his graduate studies in mechanical engineering. He joined the Optical Measurement and Quality Inspection Laboratory and began his research in optical methods for mechanical measurement. In fall 2012, he received his master's degree in mechanical engineering from OU. During his two years in the optical lab, he participated in four research projects from USAMP, Auto/Steel Partnership, and US Air Force and so on. Based on his research experience, he has published three journals and three conference papers. In 2013, he started his PhD program study in the optical laboratory. His research field includes optical metrology, phase-shift technology, digital image correlation and nondestructive testing.
XU CHEN is a PhD candidate of the Department of Mechanical Engineering, Oakland University. He is currently working in the Optical Measurement and Quality Inspection Laboratory leaded by Prof. Lianxiang Yang. He obtained his bachelor's degree in Tianjin University, China. After that, he continued his studies at OU and got his master's degree in 2010. During his studies in OU, he focused on Digital Image Correlation (DIC), a modern technique for full-field 3D shape, displacement and strain measurement. In the past several years, he devoted himself in developing the system and expanding the application of DIC. His main work includes: high temperature (over 1200 1C) strain measurement supported by the US Air Force and full-field strain behavior analysis on steels supported by DoE. As an enthusiastic researcher, he has already published seven research papers (3 journal and 4 conference papers) and received the ‘Best Poster Award’ from the North American Deep Drawing Research Group in 2012.
LIANXIANG YANG received his PhD in mechanical engineering from the University of Kassel, Germany in 1997. He is the director of optical laboratory and a professor in the department of mechanical engineering at Oakland University in USA. Prior to joining Oakland University in 2001, he was a R&D scientist at JDSUniphase, Canada, from 2000 to 2001, a senior engineer at Dantec-Ettemeyer AG (currently called DantecDynamics GmbH), Germany, from 1998 to 2000, a research and senior research fellow at the University of Kassel, Germany from 1991 to 1998, and a lecture at Hefei University of Technology, China, from 1986 to 1991. Professor Yang has multi-disciplinary research experiences including: optical metrology, experimental strain/stress analysis, nondestructive testing, and 3D computer vision. He is a fellow of SPIE, a Changjiang Scholar of Hefei University of Technology, and an adjunct professor of Beijing Information Science &Technology University.
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Shearography for specular object inspection Nan Xu, Xin Xie, Xu Chen, Lianxiang Yang n Optical Laboratory, Department of Mechanical Engineering, Oakland University, Rochester, MI 48309, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 12 February 2014 Received in revised form 17 April 2014 Accepted 26 April 2014 Available online 15 May 2014
Digital shearography is a laser speckle pattern interferometry based, non-destructive testing (NDT) method, which has a great potential in revealing the defects inside the objects e.g. composite materials. It has been applied successfully in various industry applications. However, due to its essence of laser speckle utilization, the object surface needs to be rough enough, otherwise, the object surface has to be specially treated. Considering the situations that the surface treatment under some cases is not allowed, an improved optical setup has been introduced and described in this paper. A modified shearography setup which can be applied on samples with specular surface is introduced. The theory and experiment results are described and presented. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Shearography Specular surface Non-destructive testing
1. Introduction Shearography, also called speckle pattern shearing interferometry, is a laser based, whole field, non-contact and nondestructive optical method that is capable of directly measuring strain information [1–3], and thus suited well for non-destructive testing of composite materials, such as glass/carbon fiber reinforced materials, honeycomb structures etc [4–7]. As a laser interferometry technology, shearography utilizes speckle interferometry which is generated by a coherent light reflected from a rough object surface. When the object under test is deformed, the speckle pattern captured by the sensor will be slightly altered. When two speckle patterns corresponding to deformed and undeformed states are obtained and subtracted, a fringe pattern, i.e. a shearogram, is generated [8,9]. In order to utilize the shearography system, the first essential requirement is the speckle pattern generated on the object surface, which demands the surface to be a rough surface. If the object surface is a mirror-like surface, most of the light will be mirror reflected and there will be little speckle generated, so that the shearography cannot be applied. For solving this problem, a traditional solution is to treat the object surface, such as spraying. However, under some circumstances, it may be impossible or forbidden to treat the sample surface. Therefore, demand for shearographic inspection on smooth surface without surface treatment is increasing. This paper introduces a methodology of shearography for nondestructive testing of specular or quasi-specular objects without
n
Corresponding author. Tel.: þ 1 248 370 2283. E-mail address: [email protected] (L. Yang).
http://dx.doi.org/10.1016/j.optlaseng.2014.04.015 0143-8166/& 2014 Elsevier Ltd. All rights reserved.
treating the surface. The theory is expressed in detail, and experiment results shown the feasibility of shearography for nondestructive testing on specular objects are demonstrated.
2. The optical setup and theoretical analysis The modified shearography setup schematic for testing the object with specular surface is shown in Fig. 1. Comparing to the traditional shearography setup, a flat and white (rough) plane M is embedded into the light path, which changes the direction of the light path. The laser reflected from the smooth surface hits the embedded rough plane M and generates the speckle pattern required in the shearographic testing. A coherent laser is expanded to illuminate the object. The light reflected from the object surface normally consists of two parts, the specular reflected light and diffusive reflected light. Both of the two parts carry the deformation information. Typically, the diffusive part which can generate speckle pattern is useful in shearography but the other part is not. However, when the object surface is specular or quasi-specular, most of the laser energy is mirror reflected, the speckle generated by the diffusive light is not sufficient for the measurement. To solve this problem, a rough and white image plane is embedded into the light path. When the specular reflected light reaches the rough plane, the beam will be diffusively reflected and the speckle pattern is generated. Digital shearography can make use of the speckle pattern and measure the deformation. Same as the standard shearographic testing procedure, the speckle pattern is separated into two beams by the shearing device. The two beams merge into the CCD camera and generate the interference. The difference between the two interferograms
N. Xu et al. / Optics and Lasers in Engineering 61 (2014) 14–18
15
path change analysis will be only from the laser source S to the image plane M. Based on Fig. 2, the light path before deformation can be expressed by Eq. (1). Lb ¼
Fig. 1. Schematic of the modified shearography system; L is a laser; E is the expander; M is the embedded white and rough plane; M1 and M2 are the two mirrors in the Michelson Interferometer; α is the incident angle; γ is the image plane incident angle; Z1 and Z2 are a pair of orthogonal polarizers.
θ1
β
P
α ω
θ1
P’
ð1Þ
where D1 is the distance from the light source to the object, D2 is the distance from the object to the image plane and α is the incident angle; α is the incidental angle. After deformation, due to the rotation of the point P in deformation, the reflected light on the image plane M will shift a small distance Δm. Considering rotation angle θ1, the light path after deformation Lf can be expressed as Eq. (2). Lf ¼
D1 ω ðD2 ωþ D2 tan α tan θ2 Þ sin θ2 þ cos ðα þ βÞ sin ð2θ1 þθ2 α βÞ
ð2Þ
where ω is the out-of-plane component of the deformation at point P; θ1 is the rotation angle of point P; θ2 is the tilting angle of the image plane; β is the angle change of the incidental light. Making subtraction of Eqs. (1) and (2) on both sides, the light path difference due to the deformation is calculated by Eq. (3).
S
D1
D1 D2 þ cos α cos α
N’
ΔL ¼
N θ2
M’ Δm
D1 þD2 ðD1 ωÞ D2 ð1 þ tan α tan θ2 Þ ω sin θ2 cos ðα þ βÞ cos ðα þ β 2θ1 θ2 Þ cos α
The incidental angle change β is related to the out-of-plane deformation and the original incident angle. This angle can be expressed by Eq. (4).
M D2
Fig. 2. The light path difference analysis. S is the laser source; P is the testing point; M is the corresponding point of P on the image plane; α is the incident angle; PN is the normal line at point P; D1 is the distance from the object surface to the laser source and image plane; D2 is the distance from the object to the image plane; ω is the out of deformation on point P; P0 is the same point after deformation; θ1 is the turning angle at point P due to the deformation; θ2 is the tilting angle of the image plane; β is the incident light turning angle; P0 N0 is the normal line at P0 ; Δm is the light shift on the image plane.
before and after deformation illustrates the first derivative of the deformation. Z1 and Z2 in Fig. 1 are a pair of orthogonal polarizers. In the practical measurement, If the object is purely specular, the polarizes are not necessary, however, if the object surface is quasi-specular, the diffusive light reflected from the object is much stronger. The diffusive reflected laser will also interfere with the mirror reflected laser and generate unexpected speckle pattern mixed with the demanding signals. It will greatly influence the measurement. The orthogonal polarizers Z1 and Z2 in the system are to eliminate the disturbance and improve the measuring results. Z1 is located between the laser source and the object, so that the incident laser will be linearly polarized. After the laser is reflected from the object, the mirror reflected portion keeps linearly polarization but its polarization orientation is turned 90 degree, while the diffuse reflected portion will have random polarization orientations. In this case, the polarizer Z2 between the object to the CCD sensor, which is orthogonal to Z1, will allow only the mirror reflected laser to transmit and be received by the CCD sensor. Fig. 2 shows the light path vectors and its change due to the object deformation. Because the specular reflected light does not carry the in-plane deformation, only the out-of-plane deformation ω will be discussed. Because the distance from the image plane to the shearography sensor doesn't change during the object deformation, the light
ð3Þ
β ¼ arctan
ω sin α cos α D1 ω cos 2 α
ð4Þ
Considering the distance between the laser source to the object, D1 is far bigger than the object size, so the incidental angle α is very small, and the term cos 2 α is close to 1. In this case, Eq. (4) can be simplified as Eq. (5). β ¼ arctan
ω sin 2α 2ðD1 ωÞ
ð5Þ
With Eq. (5), the relationship between ΔL and ω shown in Eq. (3) is clear with all the other parameters measurable. In the practical experiment, the optical setup can be more carefully built, so that the embedded image plane is parallel to the object plane and the laser source S is on the image plane as well. The light path vector chart is changed to Fig. 3. Comparing Figs. 2 and 3, the differences include D1 ¼ D2 ¼ D, θ ¼ θ1 and
Fig. 3. The light path vector chart when the image plane is parallel to the object. D is the distance from the laser source to the object plane and the distance from the object to the embedded image plane; θ is the rotation angle of point P.
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N. Xu et al. / Optics and Lasers in Engineering 61 (2014) 14–18
θ2 ¼ 0, so Eq. (3) is simplified as Eq. (6). 1 1 2D þ ΔL ¼ ðD ωÞ cos ðα þ βÞ cos ðα þ β 2θÞ cos α
¼ ð6Þ
where D is the distance from the laser source to the object. Put φ ¼ α þ β θ, which is the incident angle after deformation, then Eq. (6) becomes, 1 1 2D ΔL ¼ ðD ωÞ þ ð7Þ cos ðφ þ θÞ cos ðφ θÞ cos α The light spot shift distance on the image plane due to deformation can be calculated by Eq. (8). Δm ¼ D tan α ðD ωÞ tan ðφ θÞ
ð8Þ
In the real experiments, the distance from the laser source to the object is much larger than the object size, so the incidental angle α is close to 0 and β is close to 0 accordingly. The light path difference ΔL in Eq. (7) can be further simplified to Eq. (9) ΔL ¼ 2ðD ωÞ
cos 2 θ 2D cos ð2θÞ
Δϕ ¼
cos 2 θ
Δϕ ¼
ð10Þ
sin θ
According to the classical digital shearography equations [10], the relative phase change ΔΦ originates from the difference between phase changes ΔΦ1 and ΔΦ2 created by the loading, which correspond to the light beams on the object's surface scattered from points P1 and P2. The phase difference ΔΦ1 or ΔΦ2 is scattered by the laser beam from one point of the object's surface due to loading. ΔΦ can be calculated by Eq. (11). Δϕ ¼ Δϕ1 Δϕ2 2
¼
2
2π D sin θ ω1 cos θ D sin θ ω2 cos θ 2 2 λ cos 2 θ sin 2 θ cos 2 θ sin 2 θ 2
2
!
ð12Þ
4π 1 δω δx λ 1 tan 2 θ δx
ð13Þ
Considering tan θ ¼ δω=δx, tan 2 θ ¼ ðδω=δxÞ2 is very small so that it is close to 0. Eq. (13) is further simplified into Eq. (14). Δϕ ¼
2
2π 2 cos 2 θ δω δx λ cos 2θ δx
Eq. (12) can be transferred to Eq. (13)
ð9Þ
D sin 2 θ ω cos 2 θ
ð11Þ
where ΔΦ1 and ΔΦ2 are the phase difference at P1 and P2 respectively; ω1 and ω2 represent the out-of-plane deformations at P1 and P2 respectively; Δω is the difference between ω1 and ω2. Assuming the laser and the camera lie in XoZ plane, and the shearing direction is in x-direction with the shearing amount of Δx, divide both sides of Eq. (11) by Δx, it becomes:
Eq. (9) can also be expressed as ΔL ¼ 2
2π δω cos 2 θ 2 λ cos 2θ
4π δω δx λ δx
ð14Þ
For very small shearing amounts δx, Eq. (14) can be rewritten as Δϕ ¼
4π ∂ω δx λ ∂x
ð15Þ
In the same sense, if the shearing direction is in y-direction, the equation is Eq. (16). Δϕ ¼
4π ∂ω δy λ ∂y
ð16Þ
Eqs. (15) and (16) are the same as the typical digital shearography equations [10], which show that the first derivative out-ofplane component ∂w/∂x or ∂w/∂y can be measured by a single illumination beam shown in Fig. 1.
Fig. 4. Fringe pattern comparison by using the conventional and improved shearography system; (a) traditional shearography result before smooth; (b) traditional shearography result after smooth; (c) modified shearography result before smooth; (d) modified shearography result after smooth.
N. Xu et al. / Optics and Lasers in Engineering 61 (2014) 14–18
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Fig. 5. Honeycomb sample testing results; (a) raw results; (b) smooth results.
3. Experiments, results and analysis In the experiments, there are two kinds of situations for the object surface, specular and quasi-specular. The main difference is on the portion of the diffusive reflection. The experiments on both situations will be discussed in this section. The specular object tested is a piece of 100 mm 100 mm square metal-coated plastic plate, edge clamped on a rigid steel frame. A micro-head is installed backward which can apply a central concentrated loading on the plastic plate from behind in order to generate a cone-shape deformation. The testing results are shown in Fig. 4. The phase maps in Fig. 4(a) and (b) are the results from the traditional shearography system, before and after smoothing respectively. Because of the specular surface, there is little diffusive light available for generating speckles or carry information; and furthermore when the surface is deformed, the incident angle for surface has been changed, more reflected light is received by the CCD sensor and overwhelmed the phase information. As a result, only a small area in the phase map has fringes, and the major area is meaningless. On the contrary, by embedding a rough image plane as a media, the mirror reflected light generates speckle on the plane so that the shearography system can make use of this part of light and obtains phase maps shown in Fig. 4(c) and (d). The fringe pattern is as clear as usual. After smoothing, the phase map can be evaluated quantitatively. If the object surface is quasi-specular, the diffusive light reflected from the object will significantly influence the measurement. The pair of orthogonal polarizers will eliminate the influence. The object tested is a piece of aluminum skinned honeycomb structural composite material with a small delaminating area. The honeycomb sample is simply supported on the optical table. Because the object surface is aluminum which is quasispecular, the testing will make use of the pair of orthogonal polarizers. In the testing, the sample was slightly warmed by a heat gun. Theoretically, the delaminating area will deform more than the other good area under heat expansion. In this case, the first derivative of the deformation, which the shearography detects, jumps at the defect area. The testing result is shown below (Fig. 5). The fringe pattern inside the red circle clearly indicates the delaminating area. The defect in the object is successfully detected.
4. Conclusion The experiment results demonstrate the possibility of applying the shearography system on the smooth surface, either specular or quasi-specular, with no need of surface treatment e.g. spraying which is time consuming and economical waste, or even
prohibitive under some circumstances. This modification improves the usefulness of shearography especially in practical industrial application, where a lot of metal objects possess specular surface. The embedded image plane can be rigidly fixed with the object so that it does not increase the instability of the system. Because of the light shift on the image plane, it will be difficult to quantitatively calculate the deformation gradient accurately. However, in a practical NDT application, the clarity of the fringe pattern is more important, which the modified shearography is well promising. Acknowledgments The authors would like to express our sincere thanks to Mr. Bernard Sia of the Optical Lab of Oakland University who carefully and thoroughly read the manuscript and provide valuable criticisms. References [1] Yang L, et al. Digital shearography for nondestructive testing: potentials, limitations, and applications. J Holography Speckle 2004;1.2:69–79. [2] Hung M, Yang L, Huang Y. Nondestructive evaluation (NDE) of composites: digital shearography. In: Vistasp M, Karbhari Non-Destructive, editors. Evaluation of polymer matrix composites: methods and applications, Chapter 5. Woodhead Publishing Ltd; 2013 (ISBN 0–85709-344-4). [3] Yang L. Recent developments in digital shearography for nondestructive testing. Mater Eval 2006;64(7):704–9. [4] Wu S, Zhu L, Feng Q, Yang L. Digital shearography with in situ phase shift calibration. Opt Laser Eng 2012;50(9):1260–6. [5] Xu N, Xie X, Harmon G, Gu R, Yang L. Quality inspection of spot welds using digital shearography. SAE Int J Mater Manuf 2012;5(1):96–101. [6] Xu N, Yang L, Lev L, et al. NDT of weld joints using shearographic interferometry and dynamic excitation. SAE Tech Paper 2011:01–996. [7] Wu S, Xu N, Feng Q, Yang L. Precision measurement of deformation using a self-calibrated digital speckle pattern interferometry (DSPI). SAE Tech Paper 2010:01–958. [8] Hung YY, Taylor CE. Measurement of slopes of structural deflections by speckle-shearing interferometry. Exp Mech 1974;14.7:281–5. [9] Hung YY, Liang CY. Image-shearing camera for direct measurement of surface strains. Appl Opt 1979;18.7:1046–51. [10] Wolfgang S. Digital shearography: theory and application of digital speckle pattern shearing interferometry. . SPIE Press; 2003.
NAN XU graduated as PhD studies in mechanical engineering from Oakland University in 2013. Nan joined the Optical Laboratory in 2009. He received his bachelor's degree in Computer Science from Northeastern University, Shenyang, China, in 2004 and his master's degree in Optical Engineering from Beijing Jiaotong University, China, in 2008. He worked in the Institute of Electronics, Chinese Academy of Sciences as a software developer from 2004 to 2005. His research interests now include optical metrology, nondestructive testing with digital shearography, experimental strain/stress analysis, nondestructive testing, 3D computer vision, and software programming and development. He is now working on his PhD thesis with the title of “Development of Digital Shearography for Quality Inspection of Resistance Spot Weld” and he also participated
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in a number of projects with DOE and GM related to this topic. So far, he has published three journal papers and seven international conference papers in this field. He also holds a US patent in non-destructive weld testing.
XIN XIE is a PhD candidate working in the Optical Laboratory of Mechanical Engineering at Oakland University (OU) supersized by Professor Lianxiang Yang. He received his bachelor's degree in Precision Mechanical Engineering from Hefei University of Technology, Hefei, China, in 2010. After that, he went to Oakland University to continue his graduate studies in mechanical engineering. He joined the Optical Measurement and Quality Inspection Laboratory and began his research in optical methods for mechanical measurement. In fall 2012, he received his master's degree in mechanical engineering from OU. During his two years in the optical lab, he participated in four research projects from USAMP, Auto/Steel Partnership, and US Air Force and so on. Based on his research experience, he has published three journals and three conference papers. In 2013, he started his PhD program study in the optical laboratory. His research field includes optical metrology, phase-shift technology, digital image correlation and nondestructive testing.
XU CHEN is a PhD candidate of the Department of Mechanical Engineering, Oakland University. He is currently working in the Optical Measurement and Quality Inspection Laboratory leaded by Prof. Lianxiang Yang. He obtained his bachelor's degree in Tianjin University, China. After that, he continued his studies at OU and got his master's degree in 2010. During his studies in OU, he focused on Digital Image Correlation (DIC), a modern technique for full-field 3D shape, displacement and strain measurement. In the past several years, he devoted himself in developing the system and expanding the application of DIC. His main work includes: high temperature (over 1200 1C) strain measurement supported by the US Air Force and full-field strain behavior analysis on steels supported by DoE. As an enthusiastic researcher, he has already published seven research papers (3 journal and 4 conference papers) and received the ‘Best Poster Award’ from the North American Deep Drawing Research Group in 2012.
LIANXIANG YANG received his PhD in mechanical engineering from the University of Kassel, Germany in 1997. He is the director of optical laboratory and a professor in the department of mechanical engineering at Oakland University in USA. Prior to joining Oakland University in 2001, he was a R&D scientist at JDSUniphase, Canada, from 2000 to 2001, a senior engineer at Dantec-Ettemeyer AG (currently called DantecDynamics GmbH), Germany, from 1998 to 2000, a research and senior research fellow at the University of Kassel, Germany from 1991 to 1998, and a lecture at Hefei University of Technology, China, from 1986 to 1991. Professor Yang has multi-disciplinary research experiences including: optical metrology, experimental strain/stress analysis, nondestructive testing, and 3D computer vision. He is a fellow of SPIE, a Changjiang Scholar of Hefei University of Technology, and an adjunct professor of Beijing Information Science &Technology University.