Abstract

Phase-shifting digital holography is applied to the measurement of the surface profile of the inner surface of a pipe for the detection of a hole in its wall. For surface contouring of the inner wall, a two-wavelength method involving an injection-current-induced wavelength change of a laser diode is used. To illuminate and obtain information on the inner surface, a cone-shaped mirror is set inside the pipe and moved along in a longitudinal direction. The distribution of a calculated optical path length in an experimental alignment is used to compensate for the distortion due to the misalignment of the mirror in the pipe. Using the proposed method, two pieces of metal sheet pasted on the inner wall of the pipe and a hole in the wall are detected. This shows that the three-dimensional profile of a metal plate on the inner wall of a pipe can be measured using simple image processing.

© 2011 Optical Society of America

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References

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  1. M. Mizunuma, S. Ogawa, and H. Kuwano, “Deformation detection on the pipe inner wall using a laser-beam scanning displacement sensor,” Proc. SPIE 2066, 98–105 (1993).
    [CrossRef]
  2. W. W. Zhang and B. H. Zhuang, “Non-contact laser inspection for the inner wall surface of a pipe,” Meas. Sci. Technol. 9, 1380–1387 (1998).
    [CrossRef]
  3. E. Wu, Y. Ke, and B. Du, “Noncontact laser inspection based on a PSD for the inner surface of minidiameter pipes,” IEEE Trans. Instrum. Meas. 58, 2169–2173 (2009).
    [CrossRef]
  4. T. Inari, K. Takashima, M. Watanabe, and J. Fujimoto, “Optical inspection system for the inner surface of a pipe using detection of circular images projected by a laser source,” Measurement 13, 99–106 (1994).
    [CrossRef]
  5. O. Duran, K. Althoefer, and L. Seneviratne, “Pipe inspection using a laser-based transducer and automated analysis techniques,” IEEE/ASME Trans. Mech. 8, 401–409 (2003).
    [CrossRef]
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    [CrossRef]
  7. I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
    [CrossRef]
  8. I. Yamaguchi, T. Ida, and M. Yokota, “Measurements of surface shape and position by phase-shifting digital holography,” Strain 44, 349–356 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. Y. Awatsuji, T. Koyama, T. Tahara, K. Ito, Y. Shimozato, A. Kaneko, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel optical-path-length-shifting digital holography,” Appl. Opt. 48, H160–H167 (2009).
    [CrossRef] [PubMed]
  15. T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. 35, 2281–2283 (2010).
    [CrossRef] [PubMed]

2010 (2)

M. Yokota and N. Ishitobi, “Estimation of inner surface profile of a tube by two-wavelength phase-shifting digital holography,” Opt. Rev. 17, 166–170 (2010).
[CrossRef]

T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. 35, 2281–2283 (2010).
[CrossRef] [PubMed]

2009 (3)

Y. Awatsuji, T. Koyama, T. Tahara, K. Ito, Y. Shimozato, A. Kaneko, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel optical-path-length-shifting digital holography,” Appl. Opt. 48, H160–H167 (2009).
[CrossRef] [PubMed]

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[CrossRef]

E. Wu, Y. Ke, and B. Du, “Noncontact laser inspection based on a PSD for the inner surface of minidiameter pipes,” IEEE Trans. Instrum. Meas. 58, 2169–2173 (2009).
[CrossRef]

2008 (1)

I. Yamaguchi, T. Ida, and M. Yokota, “Measurements of surface shape and position by phase-shifting digital holography,” Strain 44, 349–356 (2008).
[CrossRef]

2007 (1)

T. Wakayama and T. Yoshizawa, “Development of a compact inner profile measuring instrument,” Proc. SPIE 6762, 67620D (2007).
[CrossRef]

2003 (1)

O. Duran, K. Althoefer, and L. Seneviratne, “Pipe inspection using a laser-based transducer and automated analysis techniques,” IEEE/ASME Trans. Mech. 8, 401–409 (2003).
[CrossRef]

2001 (1)

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

1999 (1)

1998 (1)

W. W. Zhang and B. H. Zhuang, “Non-contact laser inspection for the inner wall surface of a pipe,” Meas. Sci. Technol. 9, 1380–1387 (1998).
[CrossRef]

1997 (1)

1994 (2)

U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

T. Inari, K. Takashima, M. Watanabe, and J. Fujimoto, “Optical inspection system for the inner surface of a pipe using detection of circular images projected by a laser source,” Measurement 13, 99–106 (1994).
[CrossRef]

1993 (1)

M. Mizunuma, S. Ogawa, and H. Kuwano, “Deformation detection on the pipe inner wall using a laser-beam scanning displacement sensor,” Proc. SPIE 2066, 98–105 (1993).
[CrossRef]

Althoefer, K.

O. Duran, K. Althoefer, and L. Seneviratne, “Pipe inspection using a laser-based transducer and automated analysis techniques,” IEEE/ASME Trans. Mech. 8, 401–409 (2003).
[CrossRef]

Awatsuji, Y.

Du, B.

E. Wu, Y. Ke, and B. Du, “Noncontact laser inspection based on a PSD for the inner surface of minidiameter pipes,” IEEE Trans. Instrum. Meas. 58, 2169–2173 (2009).
[CrossRef]

Duran, O.

O. Duran, K. Althoefer, and L. Seneviratne, “Pipe inspection using a laser-based transducer and automated analysis techniques,” IEEE/ASME Trans. Mech. 8, 401–409 (2003).
[CrossRef]

Fujimoto, J.

T. Inari, K. Takashima, M. Watanabe, and J. Fujimoto, “Optical inspection system for the inner surface of a pipe using detection of circular images projected by a laser source,” Measurement 13, 99–106 (1994).
[CrossRef]

Ida, T.

I. Yamaguchi, T. Ida, and M. Yokota, “Measurements of surface shape and position by phase-shifting digital holography,” Strain 44, 349–356 (2008).
[CrossRef]

Imbe, M.

Inari, T.

T. Inari, K. Takashima, M. Watanabe, and J. Fujimoto, “Optical inspection system for the inner surface of a pipe using detection of circular images projected by a laser source,” Measurement 13, 99–106 (1994).
[CrossRef]

Ishitobi, N.

M. Yokota and N. Ishitobi, “Estimation of inner surface profile of a tube by two-wavelength phase-shifting digital holography,” Opt. Rev. 17, 166–170 (2010).
[CrossRef]

Ito, K.

Juptner, W.

Kaneko, A.

Kato, J.

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

Ke, Y.

E. Wu, Y. Ke, and B. Du, “Noncontact laser inspection based on a PSD for the inner surface of minidiameter pipes,” IEEE Trans. Instrum. Meas. 58, 2169–2173 (2009).
[CrossRef]

Koyama, T.

Kubota, T.

Kuwano, H.

M. Mizunuma, S. Ogawa, and H. Kuwano, “Deformation detection on the pipe inner wall using a laser-beam scanning displacement sensor,” Proc. SPIE 2066, 98–105 (1993).
[CrossRef]

Matoba, O.

Mizunuma, M.

M. Mizunuma, S. Ogawa, and H. Kuwano, “Deformation detection on the pipe inner wall using a laser-beam scanning displacement sensor,” Proc. SPIE 2066, 98–105 (1993).
[CrossRef]

Nishio, K.

Nomura, T.

Ogawa, S.

M. Mizunuma, S. Ogawa, and H. Kuwano, “Deformation detection on the pipe inner wall using a laser-beam scanning displacement sensor,” Proc. SPIE 2066, 98–105 (1993).
[CrossRef]

Ohta, S.

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

Osten, W.

Schnars, U.

Seebacher, S.

Seneviratne, L.

O. Duran, K. Althoefer, and L. Seneviratne, “Pipe inspection using a laser-based transducer and automated analysis techniques,” IEEE/ASME Trans. Mech. 8, 401–409 (2003).
[CrossRef]

Shimozato, Y.

Tahara, T.

Takashima, K.

T. Inari, K. Takashima, M. Watanabe, and J. Fujimoto, “Optical inspection system for the inner surface of a pipe using detection of circular images projected by a laser source,” Measurement 13, 99–106 (1994).
[CrossRef]

Ura, S.

Wagner, C.

Wakayama, T.

T. Wakayama and T. Yoshizawa, “Development of a compact inner profile measuring instrument,” Proc. SPIE 6762, 67620D (2007).
[CrossRef]

Watanabe, M.

T. Inari, K. Takashima, M. Watanabe, and J. Fujimoto, “Optical inspection system for the inner surface of a pipe using detection of circular images projected by a laser source,” Measurement 13, 99–106 (1994).
[CrossRef]

Wu, E.

E. Wu, Y. Ke, and B. Du, “Noncontact laser inspection based on a PSD for the inner surface of minidiameter pipes,” IEEE Trans. Instrum. Meas. 58, 2169–2173 (2009).
[CrossRef]

Yamaguchi, I.

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[CrossRef]

I. Yamaguchi, T. Ida, and M. Yokota, “Measurements of surface shape and position by phase-shifting digital holography,” Strain 44, 349–356 (2008).
[CrossRef]

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

Yokota, M.

M. Yokota and N. Ishitobi, “Estimation of inner surface profile of a tube by two-wavelength phase-shifting digital holography,” Opt. Rev. 17, 166–170 (2010).
[CrossRef]

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[CrossRef]

I. Yamaguchi, T. Ida, and M. Yokota, “Measurements of surface shape and position by phase-shifting digital holography,” Strain 44, 349–356 (2008).
[CrossRef]

Yoshizawa, T.

T. Wakayama and T. Yoshizawa, “Development of a compact inner profile measuring instrument,” Proc. SPIE 6762, 67620D (2007).
[CrossRef]

Zhang, T.

Zhang, W. W.

W. W. Zhang and B. H. Zhuang, “Non-contact laser inspection for the inner wall surface of a pipe,” Meas. Sci. Technol. 9, 1380–1387 (1998).
[CrossRef]

Zhuang, B. H.

W. W. Zhang and B. H. Zhuang, “Non-contact laser inspection for the inner wall surface of a pipe,” Meas. Sci. Technol. 9, 1380–1387 (1998).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Instrum. Meas. (1)

E. Wu, Y. Ke, and B. Du, “Noncontact laser inspection based on a PSD for the inner surface of minidiameter pipes,” IEEE Trans. Instrum. Meas. 58, 2169–2173 (2009).
[CrossRef]

IEEE/ASME Trans. Mech. (1)

O. Duran, K. Althoefer, and L. Seneviratne, “Pipe inspection using a laser-based transducer and automated analysis techniques,” IEEE/ASME Trans. Mech. 8, 401–409 (2003).
[CrossRef]

Meas. Sci. Technol. (1)

W. W. Zhang and B. H. Zhuang, “Non-contact laser inspection for the inner wall surface of a pipe,” Meas. Sci. Technol. 9, 1380–1387 (1998).
[CrossRef]

Measurement (1)

T. Inari, K. Takashima, M. Watanabe, and J. Fujimoto, “Optical inspection system for the inner surface of a pipe using detection of circular images projected by a laser source,” Measurement 13, 99–106 (1994).
[CrossRef]

Opt. Eng. (1)

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[CrossRef]

Opt. Lasers Eng. (1)

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417–428 (2001).
[CrossRef]

Opt. Lett. (2)

Opt. Rev. (1)

M. Yokota and N. Ishitobi, “Estimation of inner surface profile of a tube by two-wavelength phase-shifting digital holography,” Opt. Rev. 17, 166–170 (2010).
[CrossRef]

Proc. SPIE (2)

T. Wakayama and T. Yoshizawa, “Development of a compact inner profile measuring instrument,” Proc. SPIE 6762, 67620D (2007).
[CrossRef]

M. Mizunuma, S. Ogawa, and H. Kuwano, “Deformation detection on the pipe inner wall using a laser-beam scanning displacement sensor,” Proc. SPIE 2066, 98–105 (1993).
[CrossRef]

Strain (1)

I. Yamaguchi, T. Ida, and M. Yokota, “Measurements of surface shape and position by phase-shifting digital holography,” Strain 44, 349–356 (2008).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Height profile h Δ x of the inner surface after speckle-noise reduction obtained for each mirror position inside the pipe; (a) deviation Δ x = 0.0 mm (the mirror center coincided with the pipe center), (b)  Δ x = 0.1 mm , (c)  Δ x = 0.3 mm , and (d)  Δ x = 0.5 mm . Height profiles in both (c) and (d) were obtained after a phase unwrapping process. Reconstruction distance of Z = 364 mm and the deviation in the y-direction of Δ y = 0.0 mm are the same for all cases.

Fig. 3
Fig. 3

Variation of height along the cross-sectional line drawn as a white dotted line in Fig. 2 at (a)  X = 150 pixels and (b)  Y = 150 pixels for each of the height profiles in Fig. 2.

Fig. 4
Fig. 4

Arrangement for the illumination of the inner surface by the cone-shaped mirror whose center was located at ( Δ x , Δ y ) in the observation plane, and the distribution of the optical path length L ( x , y ) = L 0 ( x , y ) + L 1 ( x , y ) over the observation plane.

Fig. 5
Fig. 5

3D illustration of (a) calculated optical path length L ( x , y ) and (b) experimental height profile h 0.1 of Δ x = 0.1 mm .

Fig. 6
Fig. 6

Variation of both experimental height and optical path length along the cross-sectional line at (a)  X = 150 pixels and (b)  Y = 150 pixels of the 3D profiles in Fig. 5.

Fig. 7
Fig. 7

Difference between the calculated L ( x , y ) and the experimental values h 0.1 of Δ x = 0.1 mm in Fig. 5: (a) 2D distribution and (b) variation along cross-sectional line of both Y = 150 pixels and X = 150 pixels .

Fig. 8
Fig. 8

2D distribution of the difference between the calculated L ( x , y ) and the experimental values h Δ x for the deviation of (a)  Δ x = 0.3 mm and (b)  Δ x = 0.5 mm , respectively, and variation along cross-sectional lines of both X = 150 pixels and Y = 150 pixels for (c)  Δ x = 0.3 mm and (d)  Δ x = 0.5 mm , respectively.

Fig. 9
Fig. 9

Locations of the two metal sheets (Al and Cu) pasted on the inner surface and the hole in the wall of the aluminum pipe. Measurement was conducted by moving the cone-shaped mirror from Δ z = 0 to 9 mm in the pipe.

Fig. 10
Fig. 10

Reconstructed intensity image of I 1 I 2 and height profile h obtained from a phase difference Δ ϕ for the detection of the Al sheet on the inner surface with Δ z = 0 mm in Fig. 9. A circular portion of radius 20 pixels is removed from the center of both images.

Fig. 11
Fig. 11

Transformation of the original circular image to a rectangular image using a simple algorithm. The value of the pixels picked up by the variable radius r n with orientation θ was rearranged to the rectangular image.

Fig. 12
Fig. 12

Intensity image and height distribution transformed from the original circular images in Fig. 11.

Fig. 13
Fig. 13

Variation along the cross-sectional lines of (a)  X = 950 and 1100 pixels and (b)  Y = 80 pixels in Fig. 12.

Fig. 14
Fig. 14

Intensity and height distributions at different areas: (a) and (b) for Δ z = 4.5 mm and (c) and (d) for Δ z = 9.0 mm , in the aluminum pipe.

Fig. 15
Fig. 15

Variation along the cross-sectional lines of (a)  X = 630 pixels and Y = 100 pixels of the height profile for Δ z = 4.5 mm and (b)  X = 200 pixels and Y = 80 pixels of the intensity profile for Δ z = 9.0 mm in Fig. 14.

Tables (2)

Tables Icon

Table 1 Standard Deviation σ (mm) for | h 0 ( x , y ) h Δ x ( x , y ) | before and after Compensation

Tables Icon

Table 2 Comparison between Previously Measured and Experimental Values of the Sizes of Metal Sheets (mm)

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I ( x , y ; δ ) = | U R ( x , y ) exp ( i δ ) + U ( x , y ) | 2 = | U R | 2 + | U | 2 + U U R * exp ( i δ ) + U * U R exp ( i δ ) ,
U ( x , y ) = 1 4 U R * ( x , y ) { I ( x , y ; 0 ) I ( x , y ; π ) + i [ I ( x , y ; π / 2 ) I ( x , y ; 3 π / 2 ) ] } .
U I ( X , Y , Z ) = U ( x , y ) exp [ i k ( X x ) 2 + ( Y y ) 2 2 Z ] d x d y ,
Δ ϕ ( X , Y ) = arg U I 1 ( X , Y ) U I 2 * ( X , Y ) = 2 ( k 1 k 2 ) h ( X , Y ) = 4 π h ( X , Y ) / Λ ,

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