Abstract

We have developed a fringe analyzer that delivers the phase distribution at a video rate from a fringe pattern containing a spatial carrier. It is based on parallel generations of three phase-shifted moiré patterns through electronic multiplication with computer-generated reference gratings and low-pass filtering. The phase distribution is derived by the subsequent parallel processing of these patterns on the basis of a three-step phase-shifting algorithm. By modification of the bias phase distribution of the reference gratings, several functions, such as correction of an initial wave-front error, are realized in real time. The usefulness of this analyzer is demonstrated experimentally for phase measurements by grating-projection surface topography and interferometry.

© 1997 Optical Society of America

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References

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  1. J. H. Brunning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wave front measuring interferometer for testing optical surface and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef]
  2. See, for example, K. Creath, “Phase measurement interferometric techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
  3. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  4. R. Smythe, R. Moor, “Instantaneous phase measuring interferometer,” Opt. Eng. 23, 361–364 (1984).
    [CrossRef]
  5. P. L. Wizinowich, “Phase shifting interferometry in the presence of vibration: a new algorithm and system,” Appl. Opt. 29, 3271–3279 (1990).
    [CrossRef] [PubMed]
  6. A. J. P. van Haasteren, H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. 33, 4137–4142 (1994).
    [CrossRef]
  7. Y. Ichioka, M. Inuiya, “Direct phase detecting system,” Appl. Opt. 11, 1507–1514 (1972).
    [CrossRef] [PubMed]
  8. K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984).
    [CrossRef]
  9. L. Merts, “Real-time fringe-pattern analysis,” Appl. Opt. 22, 1535–1539 (1983).
    [CrossRef]
  10. L. Merts, “Optical homodyne phase metrology,” Appl. Opt. 28, 1011–1014 (1989).
    [CrossRef]
  11. S. Toyooka, M. Tominaga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51, 68–70 (1984).
    [CrossRef]
  12. J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
    [CrossRef]
  13. J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).
  14. M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
    [CrossRef]
  15. Y. Arai, S. Yokozeki, K. Shiraki, T. Yamada, “High-speed fringe analysis method using frequency demodulation technology,” Opt. Eng. 35, 2341–2344 (1996).
    [CrossRef]
  16. M. Küchel, “The new Zeiss interferometer,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. SPIE1332, 655–663 (1990).
  17. M. Idesawa, T. Yatagai, T. Soma, “Scanning moiré and automatic measurement of 3-D shapes,” Appl. Opt. 16, 2152–2162 (1977).
    [CrossRef] [PubMed]
  18. Although a similar idea has been reported in M. Servin, D. Malacara, F. J. Cuevas, “Direct-phase detection of modulated Ronchi rulings using a phase-locked loop,” Opt. Eng. 33, 1193–1199 (1994), our technique was developed independently (see Ref. 20).
  19. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982).
    [CrossRef] [PubMed]
  20. J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiréand its applications,” in Fringe ’93: Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptnerand, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 66–71.
  21. I. Yamaguchi, J.-Y. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 35, 2930–2937 (1996).
    [CrossRef]

1996 (2)

Y. Arai, S. Yokozeki, K. Shiraki, T. Yamada, “High-speed fringe analysis method using frequency demodulation technology,” Opt. Eng. 35, 2341–2344 (1996).
[CrossRef]

I. Yamaguchi, J.-Y. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 35, 2930–2937 (1996).
[CrossRef]

1994 (2)

Although a similar idea has been reported in M. Servin, D. Malacara, F. J. Cuevas, “Direct-phase detection of modulated Ronchi rulings using a phase-locked loop,” Opt. Eng. 33, 1193–1199 (1994), our technique was developed independently (see Ref. 20).

A. J. P. van Haasteren, H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. 33, 4137–4142 (1994).
[CrossRef]

1993 (2)

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

1990 (1)

1989 (1)

1984 (3)

S. Toyooka, M. Tominaga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51, 68–70 (1984).
[CrossRef]

R. Smythe, R. Moor, “Instantaneous phase measuring interferometer,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984).
[CrossRef]

1983 (1)

1982 (2)

1977 (1)

1974 (1)

1972 (1)

Arai, Y.

Y. Arai, S. Yokozeki, K. Shiraki, T. Yamada, “High-speed fringe analysis method using frequency demodulation technology,” Opt. Eng. 35, 2341–2344 (1996).
[CrossRef]

Brangaccio, D. J.

Brunning, J. H.

Creath, K.

See, for example, K. Creath, “Phase measurement interferometric techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.

Cuevas, F. J.

Although a similar idea has been reported in M. Servin, D. Malacara, F. J. Cuevas, “Direct-phase detection of modulated Ronchi rulings using a phase-locked loop,” Opt. Eng. 33, 1193–1199 (1994), our technique was developed independently (see Ref. 20).

Frankena, H. J.

Fujita, K.

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
[CrossRef]

Furutani, R.

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

Gallagher, J. E.

Herriott, D. R.

Ichioka, Y.

Idesawa, M.

Ina, H.

Inuiya, M.

Itoh, K.

Kato, J.

I. Yamaguchi, J.-Y. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 35, 2930–2937 (1996).
[CrossRef]

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
[CrossRef]

J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiréand its applications,” in Fringe ’93: Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptnerand, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 66–71.

Kobayashi, S.

Küchel, M.

M. Küchel, “The new Zeiss interferometer,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. SPIE1332, 655–663 (1990).

Liu, J.-Y.

I. Yamaguchi, J.-Y. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 35, 2930–2937 (1996).
[CrossRef]

Malacara, D.

Although a similar idea has been reported in M. Servin, D. Malacara, F. J. Cuevas, “Direct-phase detection of modulated Ronchi rulings using a phase-locked loop,” Opt. Eng. 33, 1193–1199 (1994), our technique was developed independently (see Ref. 20).

Merts, L.

Moor, R.

R. Smythe, R. Moor, “Instantaneous phase measuring interferometer,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

Ozono, S.

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
[CrossRef]

Rodriguez-Vera, R.

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

Rosenfeld, D. P.

Servin, M.

Although a similar idea has been reported in M. Servin, D. Malacara, F. J. Cuevas, “Direct-phase detection of modulated Ronchi rulings using a phase-locked loop,” Opt. Eng. 33, 1193–1199 (1994), our technique was developed independently (see Ref. 20).

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

Shiraki, K.

Y. Arai, S. Yokozeki, K. Shiraki, T. Yamada, “High-speed fringe analysis method using frequency demodulation technology,” Opt. Eng. 35, 2341–2344 (1996).
[CrossRef]

Shizawa, M.

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
[CrossRef]

Smythe, R.

R. Smythe, R. Moor, “Instantaneous phase measuring interferometer,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

Soma, T.

Takamasu, K.

J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
[CrossRef]

Takeda, M.

Tanaka, T.

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
[CrossRef]

Tominaga, M.

S. Toyooka, M. Tominaga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51, 68–70 (1984).
[CrossRef]

Toyooka, S.

S. Toyooka, M. Tominaga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51, 68–70 (1984).
[CrossRef]

van Haasteren, A. J. P.

White, A. D.

Wizinowich, P. L.

Womack, K. H.

K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984).
[CrossRef]

Yamada, T.

Y. Arai, S. Yokozeki, K. Shiraki, T. Yamada, “High-speed fringe analysis method using frequency demodulation technology,” Opt. Eng. 35, 2341–2344 (1996).
[CrossRef]

Yamaguchi, I.

I. Yamaguchi, J.-Y. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 35, 2930–2937 (1996).
[CrossRef]

J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiréand its applications,” in Fringe ’93: Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptnerand, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 66–71.

Yatagai, T.

Yokozeki, S.

Y. Arai, S. Yokozeki, K. Shiraki, T. Yamada, “High-speed fringe analysis method using frequency demodulation technology,” Opt. Eng. 35, 2341–2344 (1996).
[CrossRef]

Appl. Opt. (8)

J. Mod. Opt. (1)

M. Servin, R. Rodriguez-Vera, “Two-dimensional phase locked loop demodulation of interferograms,” J. Mod. Opt. 40, 2087–2094 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. Soc. Prec. Eng. (1)

J. Kato, K. Fujita, T. Tanaka, M. Shizawa, R. Furutani, S. Ozono, “A real-time profile restoration method from fringe patterns using digital phase-locked loop,” Jpn. Soc. Prec. Eng. 59, 141–146 (1993) (in Japanese).

Opt. Commun. (1)

S. Toyooka, M. Tominaga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51, 68–70 (1984).
[CrossRef]

Opt. Eng. (5)

Y. Arai, S. Yokozeki, K. Shiraki, T. Yamada, “High-speed fringe analysis method using frequency demodulation technology,” Opt. Eng. 35, 2341–2344 (1996).
[CrossRef]

Although a similar idea has been reported in M. Servin, D. Malacara, F. J. Cuevas, “Direct-phase detection of modulated Ronchi rulings using a phase-locked loop,” Opt. Eng. 33, 1193–1199 (1994), our technique was developed independently (see Ref. 20).

R. Smythe, R. Moor, “Instantaneous phase measuring interferometer,” Opt. Eng. 23, 361–364 (1984).
[CrossRef]

K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984).
[CrossRef]

I. Yamaguchi, J.-Y. Liu, J. Kato, “Active phase-shifting interferometers for shape and deformation measurements,” Opt. Eng. 35, 2930–2937 (1996).
[CrossRef]

Other (4)

J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiréand its applications,” in Fringe ’93: Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptnerand, W. Osten, eds. (Akademie Verlag, Berlin, 1993), pp. 66–71.

See, for example, K. Creath, “Phase measurement interferometric techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.

M. Küchel, “The new Zeiss interferometer,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed., Proc. SPIE1332, 655–663 (1990).

J. Kato, T. Tanaka, S. Ozono, K. Fujita, M. Shizawa, K. Takamasu, “Real-time phase detection for fringe-pattern analysis using digital signal processing,” in Eighteenth International Congress on High Speed Photographyand Photonics, W. Daheng, ed., Proc. SPIE1032, 791–796 (1988).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of real-time fringe analyzer based on the phase-shifting electronic moiré-pattern technique.

Fig. 2
Fig. 2

Phase-shifting electronic moiré-pattern generator: (a) conceptual illustration and (b) detailed electronic circuit. LPF, low-pass filter.

Fig. 3
Fig. 3

Diagram of parallel signal processor for implementing the phase-shifting algorithm. ROM, read-only memory.

Fig. 4
Fig. 4

(a) Frequency transmission characteristics of the low-pass filter, and (b) the result of the estimation of the leakage error for various spatial frequencies of the reference gratings. The cutoff frequency was set to 150 kHz.

Fig. 5
Fig. 5

Calculated errors for the phase delay, the amplitude deviation,and the bias difference. The total error summing them all up is shown as the solid curve.

Fig. 6
Fig. 6

Experimental setup for profile measurement by use of the projection-grating method. The grating pattern, recorded on a slide transparency, was projected on the object with a slide projector.

Fig. 7
Fig. 7

Profile measurement of a ceramic mask: (a) input fringe, (b) one of the electronically generated phase-shifted moiré patterns, (c) wrapped phase output from the analyzer at video rates, (d) unwrapping process of (b), and (e) shading display of the measured profile.

Fig. 8
Fig. 8

Experimental setup for measuring the deformation of an acrylic plate. HM: half-mirror; M: mirror.

Fig. 9
Fig. 9

Initial error compensation by modification of the reference phase: (a) input fringe pattern containing the initial phase error, (b) phase distribution of (a), (c) one of the compensated phase-shifted reference gratings calculated with Eq. (6), and (d) the phase distribution after compensation.

Fig. 10
Fig. 10

Results of the phase measurements for the loaded plate: Wrapped phase distributions (a) before and (c) after compensation. Unwrapped 3-D displays (b) of view (a) and (d) of view (c).

Equations (16)

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IOx, y=Ax, y+Bx, ycos2πfsx+ϕOx, y,
IRix, y=D cos2πfrx-ψi, i=1, 2, 3,
IOIRi=A cos2πfrx-ψi+12B cos2πfs+frx+ϕO-ψi+12B cos2πfs-frx+ϕO+ψi.
Iix, y=αx, y+βx, y×cos2πfs-fr)x+ϕOx, y+ψi, i=1, 2, 3, ψi=π4, 3π4, 5π4,
ϕOx, y=tan-1I3-I2I1-I2.
IRix, y=D cos2πfrx+ϕDx, y-ψi, i=1, 2, 3, ψi=π4, 3π4, 5π4.
VoutVin=1iffc2+2 2iffc+1,
Ci=βx, ycos ϕOx, y, Si=βx, ysin ϕOx, y.
Δ tan-1SiCi=Citan-1SiCiΔCi+Sitan-1SiCiΔSi=CiΔSi-SiΔCiCi2+Si2.
ΔCi=0, ΔSi=β sinϕO+Δϕ-β sin ϕO,
Δ tan-1SiCi=12sin Δϕ+sinΔϕ2cos2ϕO+Δϕ2.
ΔCi=0, ΔSi=1+β sin ϕO-β sin ϕO=β sin ϕO,
Δ tan-1SiCi=12 sin 2ϕO.
ΔCi=ηCβ+β cos ϕO-β cos ϕO=ηCβ, ΔSi=ηSβ,
Δ tan-1SiCi=-ηC2+ηS21/2sinϕO-tan-1ηSηC.
hX, Y=ϕX, Yp2π tan θ.

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