Abstract

Profile measurement taken with liquid-crystal gratings and a phase-shifting technique is proposed, and its effectiveness is verified by experiment. The surface profile is obtained by measurement of the phase distributions of the sinusoidal gratings deformed by an object’s surface. The liquid-crystal grating gives an accurate phase shift, an arbitrary projection pitch, and a constant surface brightness compared with conventional gratings such as a laser interference fringe grating and a Ronchi grating. Therefore a flexible measuring system may be developed with it. Two gratings with different pitches are used to measure an object with large steps. A two-color projection system can be used to produce such gratings simultaneously. Locally varying reflectivity on a surface can also be compensated by adjustment of the color component of the projected grating with a liquid-crystal grating. Thus the contrast in the projected grating can be made uniform, and a good profile measurement can be accomplished.

© 1999 Optical Society of America

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References

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  1. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1988), Vol. 26, Chap. 5, pp. 348–393.
  2. S. Kakunaim, K. Iwata, M. Hasegawa, S. Yamaguchi, “Grating projection method for profile measurement using phase-shifting technique,” J. Jpn. Soc. Precis. Eng. 55, 141–145 (1989).
    [CrossRef]
  3. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef]
  4. S. Kakunai, K. Iwata, M. Hasegawa, T. Sakamoto, “Profile measurement by projecting phase-shifted interference fringes,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. SPIE1163, 128–136 (1989).
    [CrossRef]
  5. R. Komatsubara, T. Yoshizawa, “Grating projection system for profiling with the aid of fringe scanning method,” J. Jpn. Soc. Precis. Eng. 55, 1817–1822 (1989).
    [CrossRef]
  6. S. Kakunai, T. Sakamoto, K. Iwata, “Profile measurement by an active light source,” in Proceedings of The Far East Conference on Nondestructive Testing and the Republic of China’s Society for Nondestructive Testing Ninth Annual Conference, W.-H. Chen, T.-T. Wu, K.-C. Wu, eds. (The Republic of China’s Society for Nondestructive Testing, Taipai, Taiwan, 1994), pp. 237–242.
  7. R. A. Andrade, B. S. Gilbert, S. C. Cahall, S. Kozaitis, J. Blatt, “Real-time optically processed target recognition system based on arbitrary moiré contours,” in Imaging and Illumination for Metrology and Inspection, Svetkoff, ed., Proc. SPIE2348, 170–180 (1994).
    [CrossRef]
  8. C.-H. Hu, Y.-W. Qin, “Digital color encoding and its application to the moiré technique,” Appl. Opt. 36, 3682–3685 (1997).
    [CrossRef] [PubMed]
  9. J.-M. Desse, “Three-color differential interferometry,” Appl. Opt. 36, 7150–7156 (1997).
    [CrossRef]
  10. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef] [PubMed]
  11. S. Kakunai, K. Iwata, S. Saitoh, T. Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 877–882 (1992).
    [CrossRef]

1997 (2)

1992 (1)

S. Kakunai, K. Iwata, S. Saitoh, T. Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 877–882 (1992).
[CrossRef]

1989 (2)

R. Komatsubara, T. Yoshizawa, “Grating projection system for profiling with the aid of fringe scanning method,” J. Jpn. Soc. Precis. Eng. 55, 1817–1822 (1989).
[CrossRef]

S. Kakunaim, K. Iwata, M. Hasegawa, S. Yamaguchi, “Grating projection method for profile measurement using phase-shifting technique,” J. Jpn. Soc. Precis. Eng. 55, 141–145 (1989).
[CrossRef]

1987 (1)

1984 (1)

Andrade, R. A.

R. A. Andrade, B. S. Gilbert, S. C. Cahall, S. Kozaitis, J. Blatt, “Real-time optically processed target recognition system based on arbitrary moiré contours,” in Imaging and Illumination for Metrology and Inspection, Svetkoff, ed., Proc. SPIE2348, 170–180 (1994).
[CrossRef]

Blatt, J.

R. A. Andrade, B. S. Gilbert, S. C. Cahall, S. Kozaitis, J. Blatt, “Real-time optically processed target recognition system based on arbitrary moiré contours,” in Imaging and Illumination for Metrology and Inspection, Svetkoff, ed., Proc. SPIE2348, 170–180 (1994).
[CrossRef]

Cahall, S. C.

R. A. Andrade, B. S. Gilbert, S. C. Cahall, S. Kozaitis, J. Blatt, “Real-time optically processed target recognition system based on arbitrary moiré contours,” in Imaging and Illumination for Metrology and Inspection, Svetkoff, ed., Proc. SPIE2348, 170–180 (1994).
[CrossRef]

Creath, K.

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1988), Vol. 26, Chap. 5, pp. 348–393.

Desse, J.-M.

Gilbert, B. S.

R. A. Andrade, B. S. Gilbert, S. C. Cahall, S. Kozaitis, J. Blatt, “Real-time optically processed target recognition system based on arbitrary moiré contours,” in Imaging and Illumination for Metrology and Inspection, Svetkoff, ed., Proc. SPIE2348, 170–180 (1994).
[CrossRef]

Halioua, M.

Hasegawa, M.

S. Kakunaim, K. Iwata, M. Hasegawa, S. Yamaguchi, “Grating projection method for profile measurement using phase-shifting technique,” J. Jpn. Soc. Precis. Eng. 55, 141–145 (1989).
[CrossRef]

S. Kakunai, K. Iwata, M. Hasegawa, T. Sakamoto, “Profile measurement by projecting phase-shifted interference fringes,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. SPIE1163, 128–136 (1989).
[CrossRef]

Hu, C.-H.

Iwata, K.

S. Kakunai, K. Iwata, S. Saitoh, T. Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 877–882 (1992).
[CrossRef]

S. Kakunaim, K. Iwata, M. Hasegawa, S. Yamaguchi, “Grating projection method for profile measurement using phase-shifting technique,” J. Jpn. Soc. Precis. Eng. 55, 141–145 (1989).
[CrossRef]

S. Kakunai, K. Iwata, M. Hasegawa, T. Sakamoto, “Profile measurement by projecting phase-shifted interference fringes,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. SPIE1163, 128–136 (1989).
[CrossRef]

S. Kakunai, T. Sakamoto, K. Iwata, “Profile measurement by an active light source,” in Proceedings of The Far East Conference on Nondestructive Testing and the Republic of China’s Society for Nondestructive Testing Ninth Annual Conference, W.-H. Chen, T.-T. Wu, K.-C. Wu, eds. (The Republic of China’s Society for Nondestructive Testing, Taipai, Taiwan, 1994), pp. 237–242.

Kakunai, S.

S. Kakunai, K. Iwata, S. Saitoh, T. Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 877–882 (1992).
[CrossRef]

S. Kakunai, T. Sakamoto, K. Iwata, “Profile measurement by an active light source,” in Proceedings of The Far East Conference on Nondestructive Testing and the Republic of China’s Society for Nondestructive Testing Ninth Annual Conference, W.-H. Chen, T.-T. Wu, K.-C. Wu, eds. (The Republic of China’s Society for Nondestructive Testing, Taipai, Taiwan, 1994), pp. 237–242.

S. Kakunai, K. Iwata, M. Hasegawa, T. Sakamoto, “Profile measurement by projecting phase-shifted interference fringes,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. SPIE1163, 128–136 (1989).
[CrossRef]

Kakunaim, S.

S. Kakunaim, K. Iwata, M. Hasegawa, S. Yamaguchi, “Grating projection method for profile measurement using phase-shifting technique,” J. Jpn. Soc. Precis. Eng. 55, 141–145 (1989).
[CrossRef]

Komatsubara, R.

R. Komatsubara, T. Yoshizawa, “Grating projection system for profiling with the aid of fringe scanning method,” J. Jpn. Soc. Precis. Eng. 55, 1817–1822 (1989).
[CrossRef]

Kozaitis, S.

R. A. Andrade, B. S. Gilbert, S. C. Cahall, S. Kozaitis, J. Blatt, “Real-time optically processed target recognition system based on arbitrary moiré contours,” in Imaging and Illumination for Metrology and Inspection, Svetkoff, ed., Proc. SPIE2348, 170–180 (1994).
[CrossRef]

Liu, H. C.

Qin, Y.-W.

Saitoh, S.

S. Kakunai, K. Iwata, S. Saitoh, T. Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 877–882 (1992).
[CrossRef]

Sakamoto, T.

S. Kakunai, K. Iwata, S. Saitoh, T. Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 877–882 (1992).
[CrossRef]

S. Kakunai, K. Iwata, M. Hasegawa, T. Sakamoto, “Profile measurement by projecting phase-shifted interference fringes,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. SPIE1163, 128–136 (1989).
[CrossRef]

S. Kakunai, T. Sakamoto, K. Iwata, “Profile measurement by an active light source,” in Proceedings of The Far East Conference on Nondestructive Testing and the Republic of China’s Society for Nondestructive Testing Ninth Annual Conference, W.-H. Chen, T.-T. Wu, K.-C. Wu, eds. (The Republic of China’s Society for Nondestructive Testing, Taipai, Taiwan, 1994), pp. 237–242.

Srinivasan, V.

Yamaguchi, S.

S. Kakunaim, K. Iwata, M. Hasegawa, S. Yamaguchi, “Grating projection method for profile measurement using phase-shifting technique,” J. Jpn. Soc. Precis. Eng. 55, 141–145 (1989).
[CrossRef]

Yoshizawa, T.

R. Komatsubara, T. Yoshizawa, “Grating projection system for profiling with the aid of fringe scanning method,” J. Jpn. Soc. Precis. Eng. 55, 1817–1822 (1989).
[CrossRef]

Appl. Opt. (4)

J. Jpn. Soc. Precis. Eng. (3)

S. Kakunai, K. Iwata, S. Saitoh, T. Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 877–882 (1992).
[CrossRef]

S. Kakunaim, K. Iwata, M. Hasegawa, S. Yamaguchi, “Grating projection method for profile measurement using phase-shifting technique,” J. Jpn. Soc. Precis. Eng. 55, 141–145 (1989).
[CrossRef]

R. Komatsubara, T. Yoshizawa, “Grating projection system for profiling with the aid of fringe scanning method,” J. Jpn. Soc. Precis. Eng. 55, 1817–1822 (1989).
[CrossRef]

Other (4)

S. Kakunai, T. Sakamoto, K. Iwata, “Profile measurement by an active light source,” in Proceedings of The Far East Conference on Nondestructive Testing and the Republic of China’s Society for Nondestructive Testing Ninth Annual Conference, W.-H. Chen, T.-T. Wu, K.-C. Wu, eds. (The Republic of China’s Society for Nondestructive Testing, Taipai, Taiwan, 1994), pp. 237–242.

R. A. Andrade, B. S. Gilbert, S. C. Cahall, S. Kozaitis, J. Blatt, “Real-time optically processed target recognition system based on arbitrary moiré contours,” in Imaging and Illumination for Metrology and Inspection, Svetkoff, ed., Proc. SPIE2348, 170–180 (1994).
[CrossRef]

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1988), Vol. 26, Chap. 5, pp. 348–393.

S. Kakunai, K. Iwata, M. Hasegawa, T. Sakamoto, “Profile measurement by projecting phase-shifted interference fringes,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. SPIE1163, 128–136 (1989).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Optical system.

Fig. 2
Fig. 2

Measurement principle of surface with steps: (a) relationship between calculated fractional height δn i P i and true height H; (b) relationship between the difference in calculated height S = δn 1 P 1 - δn 2 P 2 and true height H.

Fig. 3
Fig. 3

Schematic of the experimental setup for measurement of the surface with steps.

Fig. 4
Fig. 4

Intensity for the digital output level of the computer.

Fig. 5
Fig. 5

Sinusoidal intensity change at a point.

Fig. 6
Fig. 6

Intensity distribution of (a) a composed grating and (b), (c) gratings separated by red and blue filters.

Fig. 7
Fig. 7

Experimental verification of an object with steps: (a) profile of a cross section A–A′; (b) measurement-error distribution.

Fig. 8
Fig. 8

Profile measurement of an object with steps.

Fig. 9
Fig. 9

Intensity distribution for a surface with different reflectivities: (a) intensity distribution with a white-light grating; (b) intensity distribution with a blue grating.

Fig. 10
Fig. 10

Profile measurement with three-primary-color gratings: (a) measurement-error distribution with a white-light grating; (b) measurement-error distribution with composed red, green, and blue gratings.

Equations (5)

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

z0=atan α-tan ξ.
tan ξ=xz.
α=n+δnαp,
δn=12πtan-1I3-I1I4-I2.
P=P1P2P2-P1.

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