Abstract

A phase Ronchi grating-based real-time polarization phase-shifting method can be efficiently used for dynamic phase measurement in optical interferometry. A thorough error analysis is required for exhibiting how error sources influence phase-measurement results. We analyze the phase-measurement errors that are induced by the retardation error and azimuth angle error of the quarter-wave plate, the azimuth angle error of polarizers, the phase and intensity aberrations of diffractive wave fronts, and pixel mismatch of the interferometric patterns. The results will also be useful for evaluating the phase-measurement accuracy of other similar systems.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. W. Robinson, G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).
  2. M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  3. Y. Ichioka, M. Inuiya, “Direct phase detecting system,” Appl. Opt. 11, 1507–1514 (1972).
    [CrossRef] [PubMed]
  4. L. Merts, “Real-time fringe-pattern analysis,” Appl. Opt. 22, 1535–1539 (1983).
    [CrossRef]
  5. S. Toyooka, M. Tominaga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51, 68–70 (1984).
    [CrossRef]
  6. D. M. Shough, O. Y. Kwon, D. F. Leary, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 394–403 (1990).
    [CrossRef]
  7. R. Smythe, R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).
    [CrossRef]
  8. 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]
  9. A. L. Weijers, H. van Brug, H. J. Frankena, “Real-time deformation measurement using a transportable shearoghaphy system,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 76–81 (1996).
    [CrossRef]
  10. A. L. Weijiers, H. van Brug, H. J. Frankena, “Polarization phase stepping with a Savart element,” Appl. Opt. 37, 5150–5155 (1998).
    [CrossRef]
  11. M. Kujawinska, L. Salbut, K. Patorski, “Three-channel phase stepped system for moiré interferometry,” Appl. Opt. 30, 1633–1636 (1991).
    [CrossRef] [PubMed]
  12. J. Kranz, J. Lamprecht, A. Hettwer, J. Schwider, “Fiber optical single-frame speckle interferometer for measuring industrial surface,” in International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 328–331 (1998).
    [CrossRef]
  13. K. Qian, H. Miao, X. Wu, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
    [CrossRef]
  14. K. Qian, H. Miao, X. Wu, “A real-time polarization phase shifting technique for dynamic measurement,” Acta Opt. Sin. 21, 64–67 (2001) (in Chinese).
  15. O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984).
    [CrossRef] [PubMed]
  16. O. Y. Kwon, D. M. Shough, “Multichannel grating phase-shift interferometers,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. SPIE599, 273–278 (1985).
    [CrossRef]
  17. O. Y. Kwon, “Advanced wavefront sensing at Lockheed,” in Interferometric Metrology, N. A. Massie, ed., Proc. SPIE816, 196–211 (1987).
    [CrossRef]
  18. M. Kujawinska, D. W. Robinson, “Multichannel phase-stepped holographic interferometry,” Appl. Opt. 27, 312–320 (1988).
    [CrossRef] [PubMed]
  19. M. Kujawinska, J. Wojciak, “Spatial phase-shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).
  20. B. B. García, A. J. Moore, C. Pérez-López, L. Wang, T. Tschudi, “Transient deformation measurement with electronic speckle pattern interferometry by use of a holographic optical element for spatial phase stepping,” Appl. Opt. 38, 5944–5947 (1999).
    [CrossRef]
  21. H. Miao, “The studies on real-time phase measurement technique and its application to protein crystal growth,” Ph.D. dissertation (University of Science and Technology of China, Hefei, China, 1999).
  22. M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
    [CrossRef]
  23. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
    [CrossRef]
  24. J. van Wingerden, H. J. Frankena, C. Smorenburg, “Linear approximation for measurement errors in phase shifting interferometry,” Appl. Opt. 30, 2718–2729 (1991).
    [CrossRef] [PubMed]

2001 (1)

K. Qian, H. Miao, X. Wu, “A real-time polarization phase shifting technique for dynamic measurement,” Acta Opt. Sin. 21, 64–67 (2001) (in Chinese).

1999 (2)

1998 (1)

1994 (1)

1991 (2)

1988 (1)

1986 (1)

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

1984 (3)

O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984).
[CrossRef] [PubMed]

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

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

1983 (1)

1982 (1)

1972 (1)

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

Delisle, C.

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

Frankena, H. J.

García, B. B.

Hettwer, A.

J. Kranz, J. Lamprecht, A. Hettwer, J. Schwider, “Fiber optical single-frame speckle interferometer for measuring industrial surface,” in International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 328–331 (1998).
[CrossRef]

Hideki, I.

Ichioka, Y.

Inuiya, M.

Kobayashi, S.

Kothiyal, M. P.

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

Kranz, J.

J. Kranz, J. Lamprecht, A. Hettwer, J. Schwider, “Fiber optical single-frame speckle interferometer for measuring industrial surface,” in International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 328–331 (1998).
[CrossRef]

Kujawinska, M.

M. Kujawinska, L. Salbut, K. Patorski, “Three-channel phase stepped system for moiré interferometry,” Appl. Opt. 30, 1633–1636 (1991).
[CrossRef] [PubMed]

M. Kujawinska, D. W. Robinson, “Multichannel phase-stepped holographic interferometry,” Appl. Opt. 27, 312–320 (1988).
[CrossRef] [PubMed]

M. Kujawinska, J. Wojciak, “Spatial phase-shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).

Kwon, O. Y.

O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59–61 (1984).
[CrossRef] [PubMed]

O. Y. Kwon, D. M. Shough, “Multichannel grating phase-shift interferometers,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. SPIE599, 273–278 (1985).
[CrossRef]

O. Y. Kwon, “Advanced wavefront sensing at Lockheed,” in Interferometric Metrology, N. A. Massie, ed., Proc. SPIE816, 196–211 (1987).
[CrossRef]

D. M. Shough, O. Y. Kwon, D. F. Leary, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 394–403 (1990).
[CrossRef]

Lamprecht, J.

J. Kranz, J. Lamprecht, A. Hettwer, J. Schwider, “Fiber optical single-frame speckle interferometer for measuring industrial surface,” in International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 328–331 (1998).
[CrossRef]

Leary, D. F.

D. M. Shough, O. Y. Kwon, D. F. Leary, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 394–403 (1990).
[CrossRef]

Merts, L.

Miao, H.

K. Qian, H. Miao, X. Wu, “A real-time polarization phase shifting technique for dynamic measurement,” Acta Opt. Sin. 21, 64–67 (2001) (in Chinese).

K. Qian, H. Miao, X. Wu, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

H. Miao, “The studies on real-time phase measurement technique and its application to protein crystal growth,” Ph.D. dissertation (University of Science and Technology of China, Hefei, China, 1999).

Moore, A. J.

Moore, R.

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

Patorski, K.

Pérez-López, C.

Qian, K.

K. Qian, H. Miao, X. Wu, “A real-time polarization phase shifting technique for dynamic measurement,” Acta Opt. Sin. 21, 64–67 (2001) (in Chinese).

K. Qian, H. Miao, X. Wu, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

Reid, G. T.

D. W. Robinson, G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).

Robinson, D. W.

M. Kujawinska, D. W. Robinson, “Multichannel phase-stepped holographic interferometry,” Appl. Opt. 27, 312–320 (1988).
[CrossRef] [PubMed]

D. W. Robinson, G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).

Salbut, L.

Schwider, J.

J. Kranz, J. Lamprecht, A. Hettwer, J. Schwider, “Fiber optical single-frame speckle interferometer for measuring industrial surface,” in International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 328–331 (1998).
[CrossRef]

Shough, D. M.

D. M. Shough, O. Y. Kwon, D. F. Leary, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 394–403 (1990).
[CrossRef]

O. Y. Kwon, D. M. Shough, “Multichannel grating phase-shift interferometers,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. SPIE599, 273–278 (1985).
[CrossRef]

Smorenburg, C.

Smythe, R.

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

Takeda, M.

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]

Tschudi, T.

van Brug, H.

A. L. Weijiers, H. van Brug, H. J. Frankena, “Polarization phase stepping with a Savart element,” Appl. Opt. 37, 5150–5155 (1998).
[CrossRef]

A. L. Weijers, H. van Brug, H. J. Frankena, “Real-time deformation measurement using a transportable shearoghaphy system,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 76–81 (1996).
[CrossRef]

van Haasteren, A. J. P.

van Wingerden, J.

Wang, L.

Weijers, A. L.

A. L. Weijers, H. van Brug, H. J. Frankena, “Real-time deformation measurement using a transportable shearoghaphy system,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 76–81 (1996).
[CrossRef]

Weijiers, A. L.

Wojciak, J.

M. Kujawinska, J. Wojciak, “Spatial phase-shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).

Wu, X.

K. Qian, H. Miao, X. Wu, “A real-time polarization phase shifting technique for dynamic measurement,” Acta Opt. Sin. 21, 64–67 (2001) (in Chinese).

K. Qian, H. Miao, X. Wu, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

Acta Opt. Sin. (1)

K. Qian, H. Miao, X. Wu, “A real-time polarization phase shifting technique for dynamic measurement,” Acta Opt. Sin. 21, 64–67 (2001) (in Chinese).

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

Opt. Commun. (1)

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

Opt. Eng. (1)

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

Opt. Lasers Eng. (1)

K. Qian, H. Miao, X. Wu, “Real-time polarization phase shifting technique for dynamic deformation measurement,” Opt. Lasers Eng. 31, 289–295 (1999).
[CrossRef]

Opt. Lett. (1)

Other (9)

O. Y. Kwon, D. M. Shough, “Multichannel grating phase-shift interferometers,” in Optics in Engineering Measurement, W. F. Fagan, ed., Proc. SPIE599, 273–278 (1985).
[CrossRef]

O. Y. Kwon, “Advanced wavefront sensing at Lockheed,” in Interferometric Metrology, N. A. Massie, ed., Proc. SPIE816, 196–211 (1987).
[CrossRef]

J. Kranz, J. Lamprecht, A. Hettwer, J. Schwider, “Fiber optical single-frame speckle interferometer for measuring industrial surface,” in International Conference on Applied Optical Metrology, P. K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 328–331 (1998).
[CrossRef]

D. M. Shough, O. Y. Kwon, D. F. Leary, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 394–403 (1990).
[CrossRef]

D. W. Robinson, G. T. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).

A. L. Weijers, H. van Brug, H. J. Frankena, “Real-time deformation measurement using a transportable shearoghaphy system,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 76–81 (1996).
[CrossRef]

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

H. Miao, “The studies on real-time phase measurement technique and its application to protein crystal growth,” Ph.D. dissertation (University of Science and Technology of China, Hefei, China, 1999).

M. Kujawinska, J. Wojciak, “Spatial phase-shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Polarization phase-shifting interferometry schematic.

Fig. 2
Fig. 2

Arrangement of the GRPPSI system.

Fig. 3
Fig. 3

Theoretical (solid curves) and simulated (points) phase errors.

Tables (1)

Tables Icon

Table 1 Phase-Measurement Errors That Are Due to Various Error Sources

Equations (22)

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

Ix,y=0.5Ao2x, y+0.5Ar2x, y-Aox, yArx, ysinφx, y-2P.
φ=arctanI3-I1I2-I4.
ExiEyi=JPiJQToiUoTriUr, i=1, 2, 3, 4,
JQ=cos2 Q+sin2 Qexpjδsin Q cos Q1-expjδsin Q cos Q1-expjδsin2 Q+cos2Qexpjδ,JPi=cos2 Pisin Pi cos Pisin Pi cos Pisin2 Pi,
Ii=τoi2Ao2cos2 Pi+sin 2Q sin2Pi-Qsin2δ/2+τri2Ar2sin2 Pi-sin 2Q sin 2Pi-Qsin2δ/2+τoiτriAoAr cosφo-φr+φoi-φri×sin 2Pi-sin 2Pi-Qcos 2Q sin2δ/2+τoiτriAoAr sinφo-φr+φoi-φri×sin 2Pi-Qsin δ.
Δφ=cos2 φStt=toΔt =cos φΔt2τ2AoArI3t-I1tt=to+sin φΔt2τ2AoArI4t-I2tt=to,
I1=0.5τ2Ao21+cos δ+Ar21-cos δ-2AoAr sin φ sin δ, I1δδ=π/2=0.5τ2Ar2-Ao2,
Δφδ=Ao2-Ar2cos φ2AoArΔδ.
Δφδ0,
ΔφQ=1+Ao2-Ar2sin φAoAr+sin2φΔQ.
ΔφQΔQ.
ΔφP=-cos2 φΔP1+ΔP3-sin2 φΔP2+ΔP4
ΔφPΔPi.
Ii=0.5τ2Ao2+0.5τ2Ar2-τ2AoAr sinφ+Δφori-2Pi,
Δφφor=cos2 φ2Δφor1+Δφor3+sin2 φ2Δφor2+Δφor4.
Δφφor0.
Δφτ=Ao cos φ2τArΔτo3-Δτo1+Ao sin φ2τArΔτo4-Δτo2+Ar cos φ2τAoΔτr3-Δτr1+Ar sin φ2τAoΔτr4-Δτr2+sin 2φ4τΔτo3+Δτr3+Δτo1+Δτr1-Δτo4-Δτr4-Δτo2-Δτr2.
Δφτ=cos φ2τΔτo3+Δτr3-Δτo1-Δτr1+sin φ2τΔτo4+Δτr4-Δτo2-Δτr2+sin 2φ4τΔτo3+Δτr3+Δτo1+Δτr1-Δτo4-Δτr4-Δτo2-Δτr2.
Δφτ=cos φτΔτ3-Δτ1+sin φτΔτ4-Δτ2+sin 2φ2τΔτ3+Δτ1-Δτ4-Δτ2.
ΔφτΔτiτ.
ΔφΔx,Δy=- cos φ2bax-bx sin φ-bφx cos φΔx1+ay-by sin φ-bφy cos φΔy1-sin φ2bax+bx cos φ-bφx sin φΔx2+ay+by cos φ-bφy sin φΔy2+cos φ2bax+bx sin φ+bφx cos φΔx3+ay+by sin φ+bφy cos φΔy3+sin φ2bax-bx cos φ+bφx sin φΔx4+ay-by cos φ+bφy sin φΔy4,
ΔφΔx,Δy=cos2φ2φxΔx1+Δx3+φyΔy1+Δy3+sin2φ2φxΔx2+Δx4+φyΔy2+Δy4.

Metrics