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Theoretical and experimental guideline of optimum design of defect-inspection apparatus for transparent material using phase-shift illumination approach


Machine vision system has great significance for the automatic inspection to enhance unclear defects. For the purpose of the improvement of the recognition accuracy in the automation inspection, in addition to development of image-processing technology, the optical technology is also required to emphasize the contrast of defects difficult to find in a camera. Here, we develop both the optical-engineering and image-processing technology with high throughput to enhance defects in transparent material, using the phase-shift illumination method with striped structured illumination. We succeeded in the enhancement of shape defects difficult to visualize in a bright-field observation with our approach to construct the composite image from a few pictures. Our theoretical model clarified the relationship of the composite image to parameters about optical configuration and edge sharpness of surface structures in a target material, and reproduced dependencies of the index in the experiment. Based on the theoretical model, we proposed the optimum design parameters of the equipment for enhancing the scratches in our transmissive phase-shift-illumination method, so that we can maximize the magnitude of enhancement due to the refraction of light rays in the defect shape.

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  1. Yang, J., Xu, Y., Rong, H.-J., Du, S., Zhang, H.: A method for wafer defect detection using spatial feature points guided affine iterative closest point algorithm. IEEE Access. 8, 79056–79068 (2020).

    Article  Google Scholar 

  2. Li, M., Jia, J., Lu, X., Zhang, Y.: A method of surface defect detection of irregular industrial products based on machine vision. Wirel. Commun. Mob. Comput. 2021, 1–10 (2021).

    Article  Google Scholar 

  3. Nguyen, H.T., Yu, G.-H., Shin, N.-R., Kwon, G.-J., Kwak, W.-Y., Kim, J.-Y.: Defective product classification system for smart factory based on deep learning. Electronics 10, 826 (2021).

    Article  Google Scholar 

  4. Jian, C., Gao, J., Ao, Y.: Imbalanced defect classification for mobile phone screen glass using multifractal features and a new sampling method. Multimed. Tools Appl. 76, 24413–24434 (2017).

    Article  Google Scholar 

  5. Benbarrad, T., Salhaoui, M., Kenitar, S.B., Arioua, M.: Intelligent machine vision model for defective product inspection based on machine learning. J. Sens. Actuat. Netw. 10, 7 (2021).

    Article  Google Scholar 

  6. Zhou, X., Wang, Y., Zhu, Q., Liu, X., Xiao, Z., Xiao, C., Chen, T.: Machine vision based automatic apparatus and method for surface defect detection. In: 2018 13th World Congress on Intelligent Control and Automation (WCICA). pp. 1697–1702 (2018)

  7. Li, C., Zhang, X., Huang, Y., Tang, C., Fatikow, S.: A novel algorithm for defect extraction and classification of mobile phone screen based on machine vision. Comput. Ind. Eng. 146, 106530 (2020).

    Article  Google Scholar 

  8. Jian, C., Gao, J., Ao, Y.: Automatic surface defect detection for mobile phone screen glass based on machine vision. Appl. Soft Comput. 52, 348–358 (2017).

    Article  Google Scholar 

  9. Li, D., Liang, L.-Q., Zhang, W.-J.: Defect inspection and extraction of the mobile phone cover glass based on the principal components analysis. Int. J. Adv. Manuf. Technol. 73, 1605–1614 (2014).

    Article  Google Scholar 

  10. Le Tuyen, N., Wang, J.-W., Shih, M.-H., Wang, C.-C.: Novel framework for optical film defect detection and classification. IEEE Access. 8, 60964–60978 (2020).

    Article  Google Scholar 

  11. Cai, L., Li, J.: Research on phone shell detection based on machine vision. J. Phys. Conf. Ser. 1885, 042006 (2021).

    Article  Google Scholar 

  12. Jiang, J., Cao, P., Lu, Z., Lou, W., Yang, Y.: Surface defect detection for mobile phone back glass based on symmetric convolutional neural network deep learning. Appl. Sci. 10, 3621 (2020).

    Article  Google Scholar 

  13. Molina, L., Carvalho, E.A.N., Freire, E.O., Montalvão-Filho, J.R., Chagas, F. de A.: A robotic vision system using a modified Hough transform to perform weld line detection on storage tanks. In: 2008 IEEE Latin American Robotic Symposium. pp. 45–50 (2008)

  14. Dong, Z., Mai, Z., Yin, S., Wang, J., Yuan, J., Fei, Y.: A weld line detection robot based on structure light for automatic NDT. Int. J. Adv. Manuf. Technol. 111, 1831–1845 (2020).

    Article  Google Scholar 

  15. Zhang, L., Ye, Q., Yang, W., Jiao, J.: Weld line detection and tracking via spatial-temporal cascaded hidden markov models and cross structured light. IEEE Trans. Instrum. Meas. 63, 742–753 (2014).

    Article  Google Scholar 

  16. Nguyen, V.H., Pham, V.H., Cui, X., Ma, M., Kim, H.: Design and evaluation of features and classifiers for OLED panel defect recognition in machine vision. J. Inf. Telecommun. 1, 334–350 (2017).

    Article  Google Scholar 

  17. Yuan, L., Zhang, Z., Tao, X.: The development and prospect of surface defect detection based on vision measurement method. In: 2016 12th World Congress on Intelligent Control and Automation (WCICA). pp. 1382–1387 (2016)

  18. Im, J., Fujii, H., Yamashita, A., Asama, H.: Multi-modal diagnostic method for detection of concrete crack direction using light-section method and hammering test. In: 2017 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI). pp. 922–927 (2017)

  19. Tao, J., Zhu, Y., Liu, W., Jiang, F., Liu, H.: Smooth surface defect detection by deep learning based on wrapped phase map. IEEE Sens. J. 21, 16236–16244 (2021).

    ADS  Article  Google Scholar 

  20. Su, X.-Y., Zarubin, A.M., von Bally, G.: Modulation analysis of phase-shifted holographic interferograms. Opt. Commun. 105, 379–387 (1994).

    ADS  Article  Google Scholar 

  21. Ströbel, B.: Processing of interferometric phase maps as complex-valued phasor images. Appl. Opt. 35, 2192 (1996).

    ADS  Article  Google Scholar 

  22. Xue, L., Su, X.: Phase-unwrapping algorithm based on frequency analysis for measurement of a complex object by the phase-measuring-profilometry method. Appl. Opt. 40, 1207 (2001).

    ADS  Article  Google Scholar 

  23. Han, J., Shao, L., Xu, D., Shotton, J.: Enhanced computer vision with microsoft kinect sensor: a review. IEEE Trans. Cybern. 43, 1318–1334 (2013).

    Article  Google Scholar 

  24. Gorthi, S.S., Rastogi, P.: Fringe projection techniques: whither we are? Opt. Lasers Eng. 48, 133–140 (2010)

    Article  Google Scholar 

  25. Chan, F.W.Y.: Reflective fringe pattern technique for subsurface crack detection. NDT E Int. 41, 602–610 (2008).

    Article  Google Scholar 

  26. Geng, J.: Structured-light 3D surface imaging: a tutorial. Adv. Opt. Photonics. 3, 128 (2011).

    ADS  Article  Google Scholar 

  27. Matsuoka, M., Serikawa, S., 欠陥検査装置及び欠陥検査方法, Japan Patent P2019-105458 (2019)

  28. Born, M., Wolf, E.: Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Elsevier (2013)

    MATH  Google Scholar 

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Correspondence to Yoshito Onishi.

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Derivation of Eq. 6 \({\varvec{\Gamma}}\left({\varvec{x}},{\varvec{y}}\right)\)

In Eqs. 2 and 3, \(S\left(x,y\right)\) and \(C\left(x,y\right)\) are newly defined by the following equations:

$$S\left( {x,y} \right) = \frac{{I_{0} \left( {x,y} \right) - I_{\pi } \left( {x,y} \right)}}{{2I_{{{\text{Off}}.}} \left( {x,y} \right)}},$$


$${ }C\left( {x,y} \right) = \frac{{I_{{\frac{\pi }{2}}} \left( {x,y} \right) - I_{{\frac{3\pi }{2}}} \left( {x,y} \right)}}{{2I_{{{\text{Off}}.}} \left( {x,y} \right)}},$$

respectively. Here, \(\Gamma \left(x,y\right)\) can be represented with \(\Gamma \left(x,y\right)=\sqrt{S{\left(x,y\right)}^{2}+C{\left(x,y\right)}^{2}}=\left|C\left(x,y\right)+iS\left(x,y\right)\right|\) in complex form.

Substituting Eq. 4 for \({I}_{\uppsi }\left(x,y\right)\), and then Eq. 5 for \({B}_{\uppsi }(x, y;\uptheta ,\upphi )\) in \(S\left(x,y\right)\), we obtain \(S\left(x,y\right)\). From

$$\begin{aligned} I_{0} \left( {x,y} \right) - I_{\pi } \left( {x,y} \right) & = T\left( {x,y} \right)\mathop \smallint \limits_{{\Omega_{0} }} d\Omega \left( {B_{0} \left( {x^{\prime},y^{\prime};\theta ,\phi } \right) - B_{\pi } \left( {x^{\prime},y^{\prime};\theta ,\phi } \right)} \right)\cos \theta \\ & = T\left( {x,y} \right)B_{Amp.} \mathop \smallint \limits_{{\Omega_{0} }} d\Omega \sin \left( {\frac{2\pi }{L}y^{\prime } } \right)g_{0} \left( {\theta , \phi } \right)\cos \theta \\ \end{aligned}$$


$$I_{{{\text{Off}}{.}}} \left( {x,y} \right) = T\left( {x,y} \right)\frac{{B_{{{\text{Amp}}{.}}} }}{2}\mathop \smallint \limits_{{\Omega_{0} }} d\Omega g_{0} \left( {\theta , \phi } \right)\cos \theta ,$$

\(S\left(x,y\right)\) is given as

$$S\left( {x,y} \right) = \frac{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega \sin \left( {\frac{2\pi }{L}y^{\prime } } \right)g_{0} \left( {\theta , \phi } \right)\cos \theta }}{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega g_{0} \left( {\theta , \phi } \right)\cos \theta }}.$$

Similarly, \(C\left(x,y\right)\) is obtained as

$$C\left( {x,y} \right) = \frac{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega \cos \left( {\frac{2\pi }{L}y^{\prime } } \right)g_{0} \left( {\theta , \phi } \right)\cos \theta }}{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega g_{0} \left( {\theta , \phi } \right)\cos \theta }}.$$

Hence, \(\Gamma \left(x,y\right)\) is given as

$$\begin{aligned} {\Gamma }\left( {x,y} \right) & = \left| {\frac{{\mathop \smallint \nolimits_{{{\Omega }_{0} }} d{\Omega }\left[ {\cos \left( {\frac{2\pi }{L}y^{\prime}} \right) + i\sin \left( {\frac{2\pi }{L}y^{\prime}} \right)} \right]g_{0} \left( {{\uptheta },{ }\phi } \right)\cos \theta }}{{\mathop \smallint \nolimits_{{{\Omega }_{0} }} d{\Omega }g_{0} \left( {{\uptheta },{ }\phi } \right)\cos \theta }}} \right| \\ & = \left| {\frac{{\mathop \smallint \nolimits_{{{\Omega }_{0} }} d{\Omega }\exp \left( {i\frac{2\pi }{L}y^{\prime}} \right)g_{0} \left( {{\uptheta },{ }\phi } \right)\cos \theta }}{{\mathop \smallint \nolimits_{{{\Omega }_{0} }} d{\Omega }g_{0} \left( {{\uptheta },{ }\phi } \right)\cos \theta }}} \right|. \\ \end{aligned}$$

Substituting \({y}^{^{\prime}}\) for \({y}^{^{\prime}}=y-d\mathrm{tan}\theta \mathrm{sin}\phi\), \(\Gamma \left(x,y\right)\) is given as

$$\begin{aligned} \Gamma \left( {x,y} \right) & = \left| {\frac{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega \exp \left( {i\frac{2\pi }{L}\left( {y - d\tan \theta \sin \phi } \right)} \right)g_{0} \left( {\theta , \phi } \right)\cos \theta }}{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega g_{0} \left( {\theta , \phi } \right)\cos \theta }}} \right| \\ & = \left| {\frac{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega \exp \left( { - i\frac{2\pi d}{L}\tan \theta \sin \phi } \right)g_{0} \left( {\theta , \phi } \right)\cos \theta }}{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega g_{0} \left( {\theta , \phi } \right)\cos \theta }}} \right|. \\ \end{aligned}$$

By the approximation that the numerical aperture of the telecentric optical system is small (\(\left|\theta \right|\ll 1\)) and the angular distribution \({g}_{0}\left(\uptheta ,\upphi \right)\) of rays is sufficiently close to constant within the integration interval, \(\Gamma \left(x,y\right)\) is given as

$$\Gamma \left( {x,y} \right) = \left| {\frac{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega \exp \left( { - i\frac{2\pi d}{L}\tan \theta \sin \phi } \right)\cos \theta }}{{\mathop \smallint \nolimits_{{\Omega_{0} }} d\Omega \cos \theta }}} \right|.$$

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Onishi, Y., Seo, Y., Matsuoka, M. et al. Theoretical and experimental guideline of optimum design of defect-inspection apparatus for transparent material using phase-shift illumination approach. Opt Rev (2022).

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  • Defect inspection
  • Phase-shift-illumination approach
  • Transparent optical material
  • Analytical model with ray-tracing