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Shearography for non-destructive testing of specular reflecting objects using scattered light illumination
Optics and Laser Technology 112 (2019) 452–457
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Shearography for non-destructive testing of specular reflecting objects using scattered light illumination
T
⁎
Peizheng Yana, Yonghong Wanga, , Fangyuan Suna, Yu Lub, Lu Liua, Qihan Zhaoa a b
School of Instrument Science and Opto-Electronics Engineering, Hefei University of Technology, Hefei, Anhui 230009, China School of Mechanical Engineering, Hefei University of Technology, Hefei, Anhui 230009, China
H I GH L IG H T S
surface is illuminated by scattered light to generate speckle patten. • Specular sensitivity factor is influenced by surface normal of the specular surface. • The specular surface is conjugated to the interferogram in the optical setup. • The • Defects below specular surface is detected by the proposed shearography.
A R T I C LE I N FO
A B S T R A C T
Keywords: Shearography Specular surface Non-destructive testing
Shearography has been widely used in non-destructive testing due to its advantages of fast, full-field, and high sensitivity for nondestructive test and strain measurement. Shearography has been applied successfully to various industry applications. However, traditional shearography requires the surface under test to be sufficiently rough. This study presents a modified shearography setup that can be applied to workpieces with specular surface which is illuminated by light scattered from a rough plane to generate speckle patten. In the optical setup, the specular surface is conjugated to the phase map to simplify the positional correspondence between the interferogram and the internal defects. The sensitivity factor is analyzed through ray tracing method based on geometric optics which is influenced by the surface normal. The experimental results are described and presented as well.
1. Introduction Internal defects, such as air bubbles, impurities, and cracks, are inevitably generated during workpiece production [1]. The internal defects are hidden and affect the performance of the workpiece, which are the primary causes of accidents [2]. Therefore, non-destructive testing (NDT) of internal defects is necessary [3]. Currently, penetrating radiation (e.g., X-ray) and ultrasonic radiation [4] are used to inspect internal defects. However, the detection cost of penetrating radiation is high, and penetrating radiation and ultrasonic radiation have low detection rate [5,6]. Leendertz and Butters applied shearography to measure the first derivative of object deformation [7]. Shearography can reveal the internal defects of an object by identifying its defect-induced deformation anomalies under stress [8,9]. Shearography has been widely used in NDT due to its advantages, such as full-field, non-contact measurement, high precision, real-time measurement, and seismic performance ⁎
[10–13]. Shearography is an invaluable inspection tool for many applications, including rubber tire inspection, adhesive bonding integrity inspection in composite structures, space frame structure inspection in automotive, and flaw detection in aluminum alloy materials in aerospace [14–16]. Shearography technique has been endorsed by USFederal Aviation Administration (FAA) as a compulsory testing and evaluation method for aircraft tires [17]. When conducting traditional shearography, the surface of the object under investigation should be rough [10,18]. If the object surface is a mirror-like surface, most of the light will be mirror reflected and a small amount of speckle will be generated [19]. In this case, shearography cannot be applied. In order to solve this problem, a traditional solution is to treat the object surface by spraying. However, the sample surface is forbidden to or cannot be treated under certain circumstances. Therefore, the demand for shearographic inspection on smooth surface without surface treatment is increasing. A modified shearography setup is introduced by Nan Xu [19], in
Corresponding author. E-mail address: [email protected] (Y. Wang).
https://doi.org/10.1016/j.optlastec.2018.11.029 Received 18 August 2018; Received in revised form 3 October 2018; Accepted 15 November 2018 0030-3992/ © 2018 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 112 (2019) 452–457
P. Yan et al.
Fig. 3. The imaging light path of a point on the measured surface.
but displaced images. The two images are combined coherently to produce an interferometric speckle pattern at the sensor of the camera. The specular surface is conjugated to the CCD camera to easily determine the positional correspondence between the image and the specular surface. In this setup, the specular surface is not parallel to the imaging plane because the specular surface receives oblique illumination, which can be improved by a beam splitter. The imaging light path of point Q on the measured surface is described in Fig. 3, in which the shearing device is ignored. The light scattered from different positions of the rough plane hits point Q and is reflected. The light beam reflected from point Q converges on the image plane at point D through the imaging system, and the aperture angle of the imaging beam depends on the aperture stop of the imaging system. Therefore, the light intensity at point D originates from the interference of light emitted from different positions of the rough plane. The light intensity can be expressed by Eq. (1).
Fig. 1. Disordered locations of points on a curved specular surface tested by the shearography system in Ref. [19]
which a flat and rough plane is embedded into the light path to change the direction of the light path. The laser reflected from the smooth surface hits the embedded rough plane and generates the speckle pattern required in the shearographic detection. The optical path from the surface under test to the imaging device is interrupted by the scattering surface. This condition brings difficulty in obtaining the positional correspondence between the interferogram and the internal defects, especially when the surface being measured is a curved surface. For example, as shown in Fig. 1, the three points S1, S2 and S3 on the specular surface respectively reflect the incident laser light to S1′, S2′ and S3′ on the rough surface, but their locations are disordered. To get Eq. (14) in Ref. [19], the authors assume that the specular surface is parallel to the rough surface, which is not always valid. This study introduces a modified methodology of shearography for NDT of specular objects without treating the surface. NDT theory is expressed in detail, and the experimental results show the feasibility of shearography for NDT of specular objects.
N
E=
∑ Ai e ϕi i=1
(1)
where Ai and ϕi donate the amplitude and phase of light emitted from different positions of the rough plane respectively. The phase of the light from different positions of the rough plane is random. Thus, a laser speckle pattern on the image plane is obtained. For the speckle pattern of shearography, the light contributing to each speckle is reflected by different points on the specular plane separated by the shear distance. Any subsequent deformation of the surface will result in variation of the phase difference between the light reflected from these points, thereby causing a change of intensity of each speckle. For traditional shearography, referring to Fig. 4(a), point P1 (x, y, z) on an object surface is displaced to P1*(x + u, y + v, z + w) after deformation, where (u,v,w) are the Cartesian components of the displacement of the point [20]. The change of the optical path of the ray traveling from the light source S(xS, yS, zS) to the camera at C (xC, yC, zC) via the point P1* is
2. Optical setup and theoretical analysis The schematic of the modified shearography setup for testing objects with specular surface is shown in Fig. 2. The laser is expanded to illuminate a rough plane. The light scattered from the rough plane illuminates the surface under test and is reflected by it. The specular surface is imaged on a CCD camera by using a Michelson shearing interferometer. The shearing device divides the image into two identical
¯ 1 + SP ¯ 1C) δL1 = (SP¯1∗ + SP¯1∗ C ) − (SP
(2)
The optical path of the modified shearography for testing objects with specular surface is analyzed through the improvement of the light path in Fig. 4(a). Fig. 4(b) shows a point on the object surface located at point Q (x, y, z). Before loading, the light scattered by the rough plane is converged to point Q, reflected by the specular surface, and converged by the imaging system to point D (xD, yD, zD) on the CCD, where QD is the chief ray of the imaging light path and BQ is the chief ray of the illumination light path. Obviously, the directions of QD and BQ follow the law of reflection. After the object is deformed, the smooth surface undergoes slight translation and tilt. The out-of-plane displacement of point Q is half of QQ*, which is denoted as w . The tilt angle is θ , which follows the equation tan(θ) = dw / dx . Then the light scattered from the rough plane is reflected by the deformed surface and converges to point Q* (x + δx, y + δy, z + δz). The geometric imaging law of the reflective surface posits that the optical distances from the rough plane to
Fig. 2. A shearography system based on a Michelson shearing interferometer for testing objects with specular surface. 453
Optics and Laser Technology 112 (2019) 452–457
P. Yan et al.
ΔLQ =
y − yD z − zD x − xD δy + δz δx + RD RD RD
where RD =
(4)
(x − xD )2 + (y − yD )2 + (z − zD )2 .
From the geometric relationship shown in Fig. 4(b), Eq. (4) can be rewritten as
ΔLQ = QQ ∗ cos(αQ + θQ ) = 2wQ [cos(θQ ) cos(αQ) − sin(θQ ) sin(αQ )] (5) When deformation is small, dw / dx is also small. Considering tan(θ) = dw / dx , cos(θQ ) and sin(θQ ) approximate to be 1 and 0. Eq. (5) is further simplified into Eq. (6). (a) traditional shearography for testing objects with rough surface[20]
ΔLQ = 2wQ cos(αQ )
(6)
The light arriving at point D (xD, yD, zD) is reflected by points Q1 and Q2 on the object surface. This light reflected from Q2 travels along the other path through the shearing device and is separated from Q1 by the shear distance dx. The out-of-plane displacements of point Q1 and Q2 are denoted as w and w + δw . The change in optical path for Q2 due to deformation is obtained in the same way as Eq. (6) . If the shear dx is small, the difference between αQ1 and αQ2 is small, which indicates αQ1 = αQ2 = α . The optical path difference between the two points is obtained by subtracting ΔLQ1 and ΔLQ2 :
ΔLQ1 − ΔLQ2 = 2 cos(α )(wQ1 − wQ2) = 2 cos(α ) δw
(7)
If the shear dx is small, the displacement difference approximates to the displacement gradient. The optical phase difference can be written as
(b) the modifed shearography for testing objects with specular surface
Δϕ =
Fig. 4. Diagram showing the optical paths before and after deformation.
2π 4π ∂w (ΔLQ1 − ΔLQ2) = cos(α ) dx λ λ ∂x
(8)
4π λ
cos(α ) is the sensitivity factor that depends on the angle between the surface normal and the imaging chief ray, which is also half the angle between the imaging and illumination chief rays. The sensitivity factor is not related to the location of the laser and the rough plane, which is essentially different from that of the traditional shearography [20,21]. The sensitivity factor is influenced by the surface normal under test, regardless of its size. However, when the surface size is small enough compared to the distance of laser and image plane in traditional shearography, the sensitivity factor of different point could approximate to be equal. As shown in the Eq. (8), only the deformation of the surface along the normal direction will cause phase difference of the interferogram, which is determined by the nature of the specular surface. Phase maps, which represent the deformation derivative of the specular surface, can be calculated automatically using phase-shift technique [22–25]. For a curved surface, the measurement involves the influence of the defocus due to the variation of the object distance throughout the curved surface. Defocus does not affect the generation of speckle interference, but it causes a decrease in spatial resolution. In the test, it is necessary to focus on the center of the surface to reduce the amount of defocus, and select a smaller stop aperture to increase the depth of field.
Fig. 5. The polished square metal plate that is edge clamped on a rigid steel frame.
Q and Q* are equal. The optical path from Q and Q* to the image plane is the same with that in Fig. 4(a). Thus the change of optical path due to deformation is given by [20]
ΔLQ = Q ∗ D − QD
3. Experiments, results, and analysis The specular object under test is a piece of 100 mm × 100 mm polished square metal plate that is edge clamped on a rigid steel frame, as shown in Fig. 5. To generate a cone-shape deformation, a micro-head is installed backward to apply a central concentrated loading to the metal plate from behind. An industrial lens produced by Computar is used as the imaging lens, which has a focal length of 50 mm. The relative aperture used in the experiment is 1/8, thus the entrance pupil diameter is 6.25 mm. In the experiment, 4 + 4 temporal phase-shift method is used, that is to say, the number of phase shift steps before loading and after loading are both 4. A 90 degree optical phase shift is introduced into the reference beam between each of the sequentially
(3)
where
QD = Q∗D=
(x − xD )2 + (y − yD )2 + (z − zD )2
(x + δx − xD )2 + (y + δy − yD )2 + (z + δz − zD )2
Using a binomial expansion and taking only the first-order terms, we obtain 454
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Fig. 6. Phase map of the metal plate having a cone-shape deformation.
Fig. 7. Phase map of the metal plate having an irregular deformation.
Fig. 8. Testing result of the mirror-like plastic plate with an internal defect which has a cone-shape deformation.
displacement gradient can be detected. The method is further used for NDT of internal defects below smooth surfaces. The sample to be measured is an acrylic plastic plate with a specular reflection film on its surface and an internal bubble near the mirror reflection film. The diameter of the defect is 5 mm. The plastic plate is edge clamped on a rigid steel frame. A central concentrated loading is applied to the plastic plate to generate a cone-shape deformation. The phase map is shown in Fig. 8, in which a small fringe pattern is marked by a red1 circle to indicate that the displacement
recorded interferograms. The original phase map obtained by phaseshift technique is lowpass filtered five times continuously by an averaging filter which has a window size of 5 * 5 pixels. The testing results are shown in Fig. 6. Fig. 6(a) shows the untreated phase map obtained by phase-shift technique. The fringe pattern is as clear as that of traditional shearography. After smoothing, the phase map can be evaluated quantitatively as shown in Fig. 6(b). A complex loading is applied using the micro-head, which is not perpendicular to the metal plate but slightly inclined, to generate an irregular deformation and further verify the feasibility of measuring displacement gradient. Fig. 7 shows the phase map obtained by phaseshift technique before and after smoothing. As shown in Fig. 7, complex
1 For interpretation of color in Figs. 8 and 9, the reader is referred to the web version of this article.
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Fig. 9. Testing result of the mirror-like plastic plate with an internal defect which has a thermal deformation.
measurement area. If the rough surface is too far from the object surface, it will also cause the measurement area to become smaller. If the rough surface is too close to the object surface, the reflected light by the object surface may be blocked by the rough surface. It is difficult to quantitatively calculate the deformation gradient accurately due to defocus, which is the variation of the object distance caused by the curvature and tilt of the surface and results in a decrease in spatial resolution. However, in a practical NDT application, the clarity of the fringe pattern is more important, where this setup work properly. Fig. 10. The influence of surface titlt on shearography.
5. Conclusion gradient at this location is anomalous. Thermal loading is also applied to the device to detect the strain caused by thermal deformation. The measurement results are shown in Fig. 9, in which an anomalous fringe pattern marked by a red circle is detected. In the position of the internal defect, the mechanical properties of the workpiece will change, thereby resulting in abnormal strain. In both cases, the displacement gradient, which is detected by shearography, jumps at the defect area. The fringe pattern inside the red circle clearly indicates the anomalous deformation induced by the internal bubble. Therefore, the internal defect in the object is successfully detected. The position of the defect is easily determined because the specular surface under test is conjugated to the phase map.
In this study, a new shearography to test specular objects without treating the surface is proposed. The experimental results demonstrate the possibility of applying the shearography system to smooth surfaces without surface treatment, such as spraying. The specular surface under test is conjugated to the phase map. Thus, the positional correspondence between the interferogram and the internal defects is easily confirmed, which eases the use of the method. This new methodology improves the usefulness of shearography especially in practical industrial application which requires metal objects with specular surface. Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 51805137); the open project of Key Laboratory of Micro Opto-electro Mechanical System Technology, Tianjin University, Ministry of Education of China (No. MOMST20156); Natural Science Foundation of Anhui Province (No. 1808085QE129); National Key Research and Development Program of China (No. 2016YFF0101803); and the Natural Science Research Project for the Anhui Universities (No. KJ2018A0600).
4. Discussions In the shearography setup introduced by Xu [19], the laser reflected from the smooth surface hits the embedded rough plane, then the points on the rough plane are imaged on the camera. When the defect area have high local slop, surface tilt will cause the mirror reflection light hit different points on the rough plane, and the defect location on the phase map will be shifted. In the measurement method proposed in this paper, the specular surface is directly imaged on a CCD camera. That is to say, the light reflected by the same point on the surface will be imaged to a constant point on the image plane, regardless of the incident direction. The surface tilt will only cause the light received by the imaging lens to change, however the location on the phase map will not be shifted. An breif schematic is shown in Fig. 10. Before deformation, the light emitted from A1 to B1 is reflected by point Q and enters into the entrance pupil. After deformation, the light emitted from A2 to B2 is reflected by the point Q and enters into the entrance pupil. The light entering the entrance pupil is changed, but the position of point Q on the phase map remains unshifted. In the experiment setup, the location of the rough plate is not strictly required. The location of the rough plate does not affect on speckle size and measurement result, but indeed there are some requirements. If the rough surface is too close to the expand lens, the spot that strikes the rough surface is too small, which results in a smaller
References [1] S.K.U. Rehman, Z. Ibrahim, S.A. Memon, M. Jameel, Nondestructive test methods for concrete bridges: a review, Constr. Build. Mater. 107 (2016) 58–86. [2] A. Kylili, P.A. Fokaides, P. Christou, S.A. Kalogirou, Infrared thermography (IRT) applications for building diagnostics: a review, Appl. Energy 134 (2014) 531–549. [3] H. Heuer, M. Schulze, M. Pooch, S. Gäbler, A. Nocke, G. Bardl, C. Cherif, M. Klein, R. Kupke, R. Vetter, Review on quality assurance along the CFRP value chain–nondestructive testing of fabrics, preforms and CFRP by HF radio wave techniques, Compos. B Eng. 77 (2015) 494–501. [4] A.A. Hassen, H. Taheri, U.K. Vaidya, Non-destructive investigation of thermoplastic reinforced composites, Compos. B Eng. 97 (2016) 244–254. [5] M. Ibrahim, Nondestructive evaluation of thick-section composites and sandwich structures: a review, Compos. A Appl. Sci. Manuf. 64 (2014) 36–48. [6] Y. Ohara, K. Takahashi, S. Murai, K. Yamanaka, High-selectivity imaging of closed cracks using elastic waves with thermal stress induced by global preheating and local cooling, Appl. Phys. Lett. 103 (2013) 031917. [7] J. Leendertz, J. Butters, An image-shearing speckle-pattern interferometer for measuring bending moments, J. Phys. E: Sci. Instrum. 6 (1973) 1107.
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177–185. [18] R.S. Hansen, A compact ESPI system for displacement measurements of specular reflecting or optical rough surfaces, Opt. Lasers Eng. 41 (2004) 73–80. [19] N. Xu, X. Xie, X. Chen, L. Yang, Shearography for specular object inspection, Opt. Lasers Eng. 61 (2014) 14–18. [20] W. Steinchen, L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry, SPIE press, Washington, 2003. [21] X. Wang, Z. Gao, S. Yang, C. Gao, X. Sun, X. Wen, Z. Feng, S. Wang, Y. Fan, Application of digital shearing speckle pattern interferometry for thermal stress, Measurement 125 (2018) 11–18. [22] T.E. Carlsson, A. Wei, Phase evaluation of speckle patterns during continuous deformation by use of phase-shifting speckle interferometry, Appl. Opt. 39 (2000) 2628–2637. [23] B. Bhaduri, N.K. Mohan, M. Kothiyal, R. Sirohi, Use of spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS), Opt. Exp. 14 (2006) 11598–11607. [24] G.H. Kaufmann, G.E. Galizzi, Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods, Appl. Opt. 41 (2002) 7254–7263. [25] M. Moothanchery, V. Bavigadda, M. Pramanik, V. Toal, I. Naydenova, Application of phase shifting electronic speckle pattern interferometry in studies of photoinduced shrinkage of photopolymer layers, Opt. Exp. 25 (2017) 9647–9653.
[8] Y.Y. Hung, Y.S. Chen, S.P. Ng, L. Liu, Y.H. Huang, B.L. Luk, R.W.L. Ip, C.M.L. Wu, P.S. Chung, Review and comparison of shearography and active thermography for nondestructive evaluation, Mater. Sci. Eng. R-Rep. 64 (2009) 73–112. [9] X. Xin, Y. Lianxiang, X. Nan, C. Xu, Michelson interferometer based spatial phase shift shearography, Appl. Opt. 52 (2013) 4063–4071. [10] D. Francis, R.P. Tatam, R.M. Groves, Shearography technology and applications: a review, Meas. Sci. Technol. 21 (2010). [11] Y.H. Peng, G.X. Liu, Y.M. Quan, Q.L. Zeng, The depth measurement of internal defect based on laser speckle shearing interference, Opt. Laser Technol. 92 (2017) 69–73. [12] L. Yang, X. Xie, Digital Shearography: New Developments and Applications, SPIE Press, Bellingham, 2016. [13] L. Yang, F. Chen, W. Steinchen, M.Y. Hung, Digital shearography for nondestructive testing: potentials, limitations, and applications, J. Hologr. Speckle 1 (2004) 69–79. [14] S. Wu, L. Zhu, Q. Feng, L. Yang, Digital shearography with in situ phase shift calibration, Opt. Lasers Eng. 50 (2012) 1260–1266. [15] N. Xu, X. Xie, G. Harmon, R. Gu, L. Yang, Quality inspection of spot welds using digital shearography, SAE Int. J. Mater. Manuf. 5 (2012) 96–101. [16] S. Gholizadeh, A review of non-destructive testing methods of composite materials, Procedia Struct. Integrity 1 (2016) 50–57. [17] K. Ogawa, D. Minkov, T. Shoji, M. Sato, H. Hashimoto, NDE of degradation of thermal barrier coating by means of impedance spectroscopy, NDT E Int. 32 (1999)
457
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Shearography for non-destructive testing of specular reflecting objects using scattered light illumination
T
⁎
Peizheng Yana, Yonghong Wanga, , Fangyuan Suna, Yu Lub, Lu Liua, Qihan Zhaoa a b
School of Instrument Science and Opto-Electronics Engineering, Hefei University of Technology, Hefei, Anhui 230009, China School of Mechanical Engineering, Hefei University of Technology, Hefei, Anhui 230009, China
H I GH L IG H T S
surface is illuminated by scattered light to generate speckle patten. • Specular sensitivity factor is influenced by surface normal of the specular surface. • The specular surface is conjugated to the interferogram in the optical setup. • The • Defects below specular surface is detected by the proposed shearography.
A R T I C LE I N FO
A B S T R A C T
Keywords: Shearography Specular surface Non-destructive testing
Shearography has been widely used in non-destructive testing due to its advantages of fast, full-field, and high sensitivity for nondestructive test and strain measurement. Shearography has been applied successfully to various industry applications. However, traditional shearography requires the surface under test to be sufficiently rough. This study presents a modified shearography setup that can be applied to workpieces with specular surface which is illuminated by light scattered from a rough plane to generate speckle patten. In the optical setup, the specular surface is conjugated to the phase map to simplify the positional correspondence between the interferogram and the internal defects. The sensitivity factor is analyzed through ray tracing method based on geometric optics which is influenced by the surface normal. The experimental results are described and presented as well.
1. Introduction Internal defects, such as air bubbles, impurities, and cracks, are inevitably generated during workpiece production [1]. The internal defects are hidden and affect the performance of the workpiece, which are the primary causes of accidents [2]. Therefore, non-destructive testing (NDT) of internal defects is necessary [3]. Currently, penetrating radiation (e.g., X-ray) and ultrasonic radiation [4] are used to inspect internal defects. However, the detection cost of penetrating radiation is high, and penetrating radiation and ultrasonic radiation have low detection rate [5,6]. Leendertz and Butters applied shearography to measure the first derivative of object deformation [7]. Shearography can reveal the internal defects of an object by identifying its defect-induced deformation anomalies under stress [8,9]. Shearography has been widely used in NDT due to its advantages, such as full-field, non-contact measurement, high precision, real-time measurement, and seismic performance ⁎
[10–13]. Shearography is an invaluable inspection tool for many applications, including rubber tire inspection, adhesive bonding integrity inspection in composite structures, space frame structure inspection in automotive, and flaw detection in aluminum alloy materials in aerospace [14–16]. Shearography technique has been endorsed by USFederal Aviation Administration (FAA) as a compulsory testing and evaluation method for aircraft tires [17]. When conducting traditional shearography, the surface of the object under investigation should be rough [10,18]. If the object surface is a mirror-like surface, most of the light will be mirror reflected and a small amount of speckle will be generated [19]. In this case, shearography cannot be applied. In order to solve this problem, a traditional solution is to treat the object surface by spraying. However, the sample surface is forbidden to or cannot be treated under certain circumstances. Therefore, the demand for shearographic inspection on smooth surface without surface treatment is increasing. A modified shearography setup is introduced by Nan Xu [19], in
Corresponding author. E-mail address: [email protected] (Y. Wang).
https://doi.org/10.1016/j.optlastec.2018.11.029 Received 18 August 2018; Received in revised form 3 October 2018; Accepted 15 November 2018 0030-3992/ © 2018 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 112 (2019) 452–457
P. Yan et al.
Fig. 3. The imaging light path of a point on the measured surface.
but displaced images. The two images are combined coherently to produce an interferometric speckle pattern at the sensor of the camera. The specular surface is conjugated to the CCD camera to easily determine the positional correspondence between the image and the specular surface. In this setup, the specular surface is not parallel to the imaging plane because the specular surface receives oblique illumination, which can be improved by a beam splitter. The imaging light path of point Q on the measured surface is described in Fig. 3, in which the shearing device is ignored. The light scattered from different positions of the rough plane hits point Q and is reflected. The light beam reflected from point Q converges on the image plane at point D through the imaging system, and the aperture angle of the imaging beam depends on the aperture stop of the imaging system. Therefore, the light intensity at point D originates from the interference of light emitted from different positions of the rough plane. The light intensity can be expressed by Eq. (1).
Fig. 1. Disordered locations of points on a curved specular surface tested by the shearography system in Ref. [19]
which a flat and rough plane is embedded into the light path to change the direction of the light path. The laser reflected from the smooth surface hits the embedded rough plane and generates the speckle pattern required in the shearographic detection. The optical path from the surface under test to the imaging device is interrupted by the scattering surface. This condition brings difficulty in obtaining the positional correspondence between the interferogram and the internal defects, especially when the surface being measured is a curved surface. For example, as shown in Fig. 1, the three points S1, S2 and S3 on the specular surface respectively reflect the incident laser light to S1′, S2′ and S3′ on the rough surface, but their locations are disordered. To get Eq. (14) in Ref. [19], the authors assume that the specular surface is parallel to the rough surface, which is not always valid. This study introduces a modified methodology of shearography for NDT of specular objects without treating the surface. NDT theory is expressed in detail, and the experimental results show the feasibility of shearography for NDT of specular objects.
N
E=
∑ Ai e ϕi i=1
(1)
where Ai and ϕi donate the amplitude and phase of light emitted from different positions of the rough plane respectively. The phase of the light from different positions of the rough plane is random. Thus, a laser speckle pattern on the image plane is obtained. For the speckle pattern of shearography, the light contributing to each speckle is reflected by different points on the specular plane separated by the shear distance. Any subsequent deformation of the surface will result in variation of the phase difference between the light reflected from these points, thereby causing a change of intensity of each speckle. For traditional shearography, referring to Fig. 4(a), point P1 (x, y, z) on an object surface is displaced to P1*(x + u, y + v, z + w) after deformation, where (u,v,w) are the Cartesian components of the displacement of the point [20]. The change of the optical path of the ray traveling from the light source S(xS, yS, zS) to the camera at C (xC, yC, zC) via the point P1* is
2. Optical setup and theoretical analysis The schematic of the modified shearography setup for testing objects with specular surface is shown in Fig. 2. The laser is expanded to illuminate a rough plane. The light scattered from the rough plane illuminates the surface under test and is reflected by it. The specular surface is imaged on a CCD camera by using a Michelson shearing interferometer. The shearing device divides the image into two identical
¯ 1 + SP ¯ 1C) δL1 = (SP¯1∗ + SP¯1∗ C ) − (SP
(2)
The optical path of the modified shearography for testing objects with specular surface is analyzed through the improvement of the light path in Fig. 4(a). Fig. 4(b) shows a point on the object surface located at point Q (x, y, z). Before loading, the light scattered by the rough plane is converged to point Q, reflected by the specular surface, and converged by the imaging system to point D (xD, yD, zD) on the CCD, where QD is the chief ray of the imaging light path and BQ is the chief ray of the illumination light path. Obviously, the directions of QD and BQ follow the law of reflection. After the object is deformed, the smooth surface undergoes slight translation and tilt. The out-of-plane displacement of point Q is half of QQ*, which is denoted as w . The tilt angle is θ , which follows the equation tan(θ) = dw / dx . Then the light scattered from the rough plane is reflected by the deformed surface and converges to point Q* (x + δx, y + δy, z + δz). The geometric imaging law of the reflective surface posits that the optical distances from the rough plane to
Fig. 2. A shearography system based on a Michelson shearing interferometer for testing objects with specular surface. 453
Optics and Laser Technology 112 (2019) 452–457
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ΔLQ =
y − yD z − zD x − xD δy + δz δx + RD RD RD
where RD =
(4)
(x − xD )2 + (y − yD )2 + (z − zD )2 .
From the geometric relationship shown in Fig. 4(b), Eq. (4) can be rewritten as
ΔLQ = QQ ∗ cos(αQ + θQ ) = 2wQ [cos(θQ ) cos(αQ) − sin(θQ ) sin(αQ )] (5) When deformation is small, dw / dx is also small. Considering tan(θ) = dw / dx , cos(θQ ) and sin(θQ ) approximate to be 1 and 0. Eq. (5) is further simplified into Eq. (6). (a) traditional shearography for testing objects with rough surface[20]
ΔLQ = 2wQ cos(αQ )
(6)
The light arriving at point D (xD, yD, zD) is reflected by points Q1 and Q2 on the object surface. This light reflected from Q2 travels along the other path through the shearing device and is separated from Q1 by the shear distance dx. The out-of-plane displacements of point Q1 and Q2 are denoted as w and w + δw . The change in optical path for Q2 due to deformation is obtained in the same way as Eq. (6) . If the shear dx is small, the difference between αQ1 and αQ2 is small, which indicates αQ1 = αQ2 = α . The optical path difference between the two points is obtained by subtracting ΔLQ1 and ΔLQ2 :
ΔLQ1 − ΔLQ2 = 2 cos(α )(wQ1 − wQ2) = 2 cos(α ) δw
(7)
If the shear dx is small, the displacement difference approximates to the displacement gradient. The optical phase difference can be written as
(b) the modifed shearography for testing objects with specular surface
Δϕ =
Fig. 4. Diagram showing the optical paths before and after deformation.
2π 4π ∂w (ΔLQ1 − ΔLQ2) = cos(α ) dx λ λ ∂x
(8)
4π λ
cos(α ) is the sensitivity factor that depends on the angle between the surface normal and the imaging chief ray, which is also half the angle between the imaging and illumination chief rays. The sensitivity factor is not related to the location of the laser and the rough plane, which is essentially different from that of the traditional shearography [20,21]. The sensitivity factor is influenced by the surface normal under test, regardless of its size. However, when the surface size is small enough compared to the distance of laser and image plane in traditional shearography, the sensitivity factor of different point could approximate to be equal. As shown in the Eq. (8), only the deformation of the surface along the normal direction will cause phase difference of the interferogram, which is determined by the nature of the specular surface. Phase maps, which represent the deformation derivative of the specular surface, can be calculated automatically using phase-shift technique [22–25]. For a curved surface, the measurement involves the influence of the defocus due to the variation of the object distance throughout the curved surface. Defocus does not affect the generation of speckle interference, but it causes a decrease in spatial resolution. In the test, it is necessary to focus on the center of the surface to reduce the amount of defocus, and select a smaller stop aperture to increase the depth of field.
Fig. 5. The polished square metal plate that is edge clamped on a rigid steel frame.
Q and Q* are equal. The optical path from Q and Q* to the image plane is the same with that in Fig. 4(a). Thus the change of optical path due to deformation is given by [20]
ΔLQ = Q ∗ D − QD
3. Experiments, results, and analysis The specular object under test is a piece of 100 mm × 100 mm polished square metal plate that is edge clamped on a rigid steel frame, as shown in Fig. 5. To generate a cone-shape deformation, a micro-head is installed backward to apply a central concentrated loading to the metal plate from behind. An industrial lens produced by Computar is used as the imaging lens, which has a focal length of 50 mm. The relative aperture used in the experiment is 1/8, thus the entrance pupil diameter is 6.25 mm. In the experiment, 4 + 4 temporal phase-shift method is used, that is to say, the number of phase shift steps before loading and after loading are both 4. A 90 degree optical phase shift is introduced into the reference beam between each of the sequentially
(3)
where
QD = Q∗D=
(x − xD )2 + (y − yD )2 + (z − zD )2
(x + δx − xD )2 + (y + δy − yD )2 + (z + δz − zD )2
Using a binomial expansion and taking only the first-order terms, we obtain 454
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Fig. 6. Phase map of the metal plate having a cone-shape deformation.
Fig. 7. Phase map of the metal plate having an irregular deformation.
Fig. 8. Testing result of the mirror-like plastic plate with an internal defect which has a cone-shape deformation.
displacement gradient can be detected. The method is further used for NDT of internal defects below smooth surfaces. The sample to be measured is an acrylic plastic plate with a specular reflection film on its surface and an internal bubble near the mirror reflection film. The diameter of the defect is 5 mm. The plastic plate is edge clamped on a rigid steel frame. A central concentrated loading is applied to the plastic plate to generate a cone-shape deformation. The phase map is shown in Fig. 8, in which a small fringe pattern is marked by a red1 circle to indicate that the displacement
recorded interferograms. The original phase map obtained by phaseshift technique is lowpass filtered five times continuously by an averaging filter which has a window size of 5 * 5 pixels. The testing results are shown in Fig. 6. Fig. 6(a) shows the untreated phase map obtained by phase-shift technique. The fringe pattern is as clear as that of traditional shearography. After smoothing, the phase map can be evaluated quantitatively as shown in Fig. 6(b). A complex loading is applied using the micro-head, which is not perpendicular to the metal plate but slightly inclined, to generate an irregular deformation and further verify the feasibility of measuring displacement gradient. Fig. 7 shows the phase map obtained by phaseshift technique before and after smoothing. As shown in Fig. 7, complex
1 For interpretation of color in Figs. 8 and 9, the reader is referred to the web version of this article.
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Fig. 9. Testing result of the mirror-like plastic plate with an internal defect which has a thermal deformation.
measurement area. If the rough surface is too far from the object surface, it will also cause the measurement area to become smaller. If the rough surface is too close to the object surface, the reflected light by the object surface may be blocked by the rough surface. It is difficult to quantitatively calculate the deformation gradient accurately due to defocus, which is the variation of the object distance caused by the curvature and tilt of the surface and results in a decrease in spatial resolution. However, in a practical NDT application, the clarity of the fringe pattern is more important, where this setup work properly. Fig. 10. The influence of surface titlt on shearography.
5. Conclusion gradient at this location is anomalous. Thermal loading is also applied to the device to detect the strain caused by thermal deformation. The measurement results are shown in Fig. 9, in which an anomalous fringe pattern marked by a red circle is detected. In the position of the internal defect, the mechanical properties of the workpiece will change, thereby resulting in abnormal strain. In both cases, the displacement gradient, which is detected by shearography, jumps at the defect area. The fringe pattern inside the red circle clearly indicates the anomalous deformation induced by the internal bubble. Therefore, the internal defect in the object is successfully detected. The position of the defect is easily determined because the specular surface under test is conjugated to the phase map.
In this study, a new shearography to test specular objects without treating the surface is proposed. The experimental results demonstrate the possibility of applying the shearography system to smooth surfaces without surface treatment, such as spraying. The specular surface under test is conjugated to the phase map. Thus, the positional correspondence between the interferogram and the internal defects is easily confirmed, which eases the use of the method. This new methodology improves the usefulness of shearography especially in practical industrial application which requires metal objects with specular surface. Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 51805137); the open project of Key Laboratory of Micro Opto-electro Mechanical System Technology, Tianjin University, Ministry of Education of China (No. MOMST20156); Natural Science Foundation of Anhui Province (No. 1808085QE129); National Key Research and Development Program of China (No. 2016YFF0101803); and the Natural Science Research Project for the Anhui Universities (No. KJ2018A0600).
4. Discussions In the shearography setup introduced by Xu [19], the laser reflected from the smooth surface hits the embedded rough plane, then the points on the rough plane are imaged on the camera. When the defect area have high local slop, surface tilt will cause the mirror reflection light hit different points on the rough plane, and the defect location on the phase map will be shifted. In the measurement method proposed in this paper, the specular surface is directly imaged on a CCD camera. That is to say, the light reflected by the same point on the surface will be imaged to a constant point on the image plane, regardless of the incident direction. The surface tilt will only cause the light received by the imaging lens to change, however the location on the phase map will not be shifted. An breif schematic is shown in Fig. 10. Before deformation, the light emitted from A1 to B1 is reflected by point Q and enters into the entrance pupil. After deformation, the light emitted from A2 to B2 is reflected by the point Q and enters into the entrance pupil. The light entering the entrance pupil is changed, but the position of point Q on the phase map remains unshifted. In the experiment setup, the location of the rough plate is not strictly required. The location of the rough plate does not affect on speckle size and measurement result, but indeed there are some requirements. If the rough surface is too close to the expand lens, the spot that strikes the rough surface is too small, which results in a smaller
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