Abstract

A phase-shifting algorithm is proposed and experimentally demonstrated for phase-difference analysis. The method involves only three steps, the original and two equal in amount but unknown phase steps for each stage. Only six frames of data are thus sufficient for the phase-difference analysis between two stages. Real-time holographic interferometry with a concentration change in a sugar-water solution in a test cell is presented for experimental verification.

© 1993 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, Amsterdam, 1988), Vol. 26, pp. 349–393.
    [CrossRef]
  2. J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14, pp. 501–598.
  3. R. S. Sirohi, Optical Components, Systems, and Measurement Techniques (Dekker, New York, 1991), Chap. 6, pp. 219–246.
  4. P. L. Wizinowich, “Phase shifting interferometry in the presence of vibration: a new algorithm and system,” Appl. Opt. 29, 3271–3279 (1990).
    [CrossRef] [PubMed]
  5. K. Creath, “Phase-measurement interferometry techniques for nondestructive testing,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554B, 701–707 (1991).
  6. G. Lai, T. Yatagai, “Generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 8, 822–827 (1991).
    [CrossRef]
  7. K. Creath, “Phase-measurement interferometry: beware these errors,” in Laser Interferometry TV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 213–220 (1992).
  8. 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]
  9. B. Ovryn, E. M. Haacke, “Temporal averaging in a turbulent environment: compensation for phase drifts in phase shifting interferometry,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 221–230 (1992).
  10. P. K. Rastogi, “Phase shifting applied to four-wave holographic interferometers,” Appl. Opt. 31, 1680–1681 (1992).
    [CrossRef] [PubMed]
  11. C. Joenathan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
    [CrossRef]
  12. C. Joenathan, B. M. Khorana, “Phase measurement by differentiating interferometric fringes,” J. Mod. Opt. 39, 2075–2087 (1992).
    [CrossRef]
  13. T. A. W. M. Lanen, P. G. Bakker, P. J. Bryanston-Cross, “Digital holographic interferometry in high-speed flow research,” Exp. Fluids 13, 56–62 (1992).
    [CrossRef]
  14. Q. R. J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).
  15. P. K. Rastogi, “Modification of the Carré phase-stepping method to suit four-wave holographic interferometry,” Opt. Eng. 32, 190–191 (1993).
    [CrossRef]
  16. G. H. Kaufmann, P. Jacquot, “Phase shifting of whole field speckle photography fringes,” Appl. Opt. 29, 3570–3572 (1990).
    [CrossRef] [PubMed]
  17. “Polarimetry, saccharimetry of the sugars,” Natl. Bur. Stand. (U.S.) Circ. 440, 652 (1942).
  18. J. C. Wyant, C. L. Koliopoulos, B. Bhushan, O. E. George, “An optical profilometer for surface characterization of magnetic media,” ASLE Trans. 27, 101–113 (1984).
    [CrossRef]

1993 (1)

P. K. Rastogi, “Modification of the Carré phase-stepping method to suit four-wave holographic interferometry,” Opt. Eng. 32, 190–191 (1993).
[CrossRef]

1992 (5)

P. K. Rastogi, “Phase shifting applied to four-wave holographic interferometers,” Appl. Opt. 31, 1680–1681 (1992).
[CrossRef] [PubMed]

C. Joenathan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

C. Joenathan, B. M. Khorana, “Phase measurement by differentiating interferometric fringes,” J. Mod. Opt. 39, 2075–2087 (1992).
[CrossRef]

T. A. W. M. Lanen, P. G. Bakker, P. J. Bryanston-Cross, “Digital holographic interferometry in high-speed flow research,” Exp. Fluids 13, 56–62 (1992).
[CrossRef]

Q. R. J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

1991 (2)

1990 (2)

1984 (1)

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, O. E. George, “An optical profilometer for surface characterization of magnetic media,” ASLE Trans. 27, 101–113 (1984).
[CrossRef]

1942 (1)

“Polarimetry, saccharimetry of the sugars,” Natl. Bur. Stand. (U.S.) Circ. 440, 652 (1942).

Bakker, P. G.

T. A. W. M. Lanen, P. G. Bakker, P. J. Bryanston-Cross, “Digital holographic interferometry in high-speed flow research,” Exp. Fluids 13, 56–62 (1992).
[CrossRef]

Bhushan, B.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, O. E. George, “An optical profilometer for surface characterization of magnetic media,” ASLE Trans. 27, 101–113 (1984).
[CrossRef]

Bruning, J. H.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14, pp. 501–598.

Bryanston-Cross, P. J.

T. A. W. M. Lanen, P. G. Bakker, P. J. Bryanston-Cross, “Digital holographic interferometry in high-speed flow research,” Exp. Fluids 13, 56–62 (1992).
[CrossRef]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques for nondestructive testing,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554B, 701–707 (1991).

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

K. Creath, “Phase-measurement interferometry: beware these errors,” in Laser Interferometry TV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 213–220 (1992).

Endo, Q. R. J.

Q. R. J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

Frankena, H. J.

George, O. E.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, O. E. George, “An optical profilometer for surface characterization of magnetic media,” ASLE Trans. 27, 101–113 (1984).
[CrossRef]

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14, pp. 501–598.

Haacke, E. M.

B. Ovryn, E. M. Haacke, “Temporal averaging in a turbulent environment: compensation for phase drifts in phase shifting interferometry,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 221–230 (1992).

Jacquot, P.

Joenathan, C.

C. Joenathan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

C. Joenathan, B. M. Khorana, “Phase measurement by differentiating interferometric fringes,” J. Mod. Opt. 39, 2075–2087 (1992).
[CrossRef]

Kaufmann, G. H.

Khorana, B. M.

C. Joenathan, B. M. Khorana, “Phase measurement by differentiating interferometric fringes,” J. Mod. Opt. 39, 2075–2087 (1992).
[CrossRef]

C. Joenathan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

Koliopoulos, C. L.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, O. E. George, “An optical profilometer for surface characterization of magnetic media,” ASLE Trans. 27, 101–113 (1984).
[CrossRef]

Lai, G.

Lanen, T. A. W. M.

T. A. W. M. Lanen, P. G. Bakker, P. J. Bryanston-Cross, “Digital holographic interferometry in high-speed flow research,” Exp. Fluids 13, 56–62 (1992).
[CrossRef]

Ovryn, B.

B. Ovryn, E. M. Haacke, “Temporal averaging in a turbulent environment: compensation for phase drifts in phase shifting interferometry,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 221–230 (1992).

Rastogi, P. K.

P. K. Rastogi, “Modification of the Carré phase-stepping method to suit four-wave holographic interferometry,” Opt. Eng. 32, 190–191 (1993).
[CrossRef]

P. K. Rastogi, “Phase shifting applied to four-wave holographic interferometers,” Appl. Opt. 31, 1680–1681 (1992).
[CrossRef] [PubMed]

Sirohi, R. S.

R. S. Sirohi, Optical Components, Systems, and Measurement Techniques (Dekker, New York, 1991), Chap. 6, pp. 219–246.

Smorenburg, C.

Tanji, T.

Q. R. J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

Tonomura, A.

Q. R. J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

van Wingerden, J.

Wizinowich, P. L.

Wyant, J. C.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, O. E. George, “An optical profilometer for surface characterization of magnetic media,” ASLE Trans. 27, 101–113 (1984).
[CrossRef]

Yatagai, T.

Appl. Opt. (4)

ASLE Trans. (1)

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, O. E. George, “An optical profilometer for surface characterization of magnetic media,” ASLE Trans. 27, 101–113 (1984).
[CrossRef]

Exp. Fluids (1)

T. A. W. M. Lanen, P. G. Bakker, P. J. Bryanston-Cross, “Digital holographic interferometry in high-speed flow research,” Exp. Fluids 13, 56–62 (1992).
[CrossRef]

J. Mod. Opt. (1)

C. Joenathan, B. M. Khorana, “Phase measurement by differentiating interferometric fringes,” J. Mod. Opt. 39, 2075–2087 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

Natl. Bur. Stand. (U.S.) Circ. (1)

“Polarimetry, saccharimetry of the sugars,” Natl. Bur. Stand. (U.S.) Circ. 440, 652 (1942).

Opt. Eng. (2)

P. K. Rastogi, “Modification of the Carré phase-stepping method to suit four-wave holographic interferometry,” Opt. Eng. 32, 190–191 (1993).
[CrossRef]

C. Joenathan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

Optik (1)

Q. R. J. Endo, T. Tanji, A. Tonomura, “High resolution and precision measurement of electron wave by phase-shifting electron holography,” Optik 92, 51–55 (1992).

Other (6)

K. Creath, “Phase-measurement interferometry: beware these errors,” in Laser Interferometry TV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 213–220 (1992).

B. Ovryn, E. M. Haacke, “Temporal averaging in a turbulent environment: compensation for phase drifts in phase shifting interferometry,” in Laser Interferometry IV: Computer-Aided Interferometry, R. J. Pryputniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1553, 221–230 (1992).

K. Creath, “Phase-measurement interferometry techniques for nondestructive testing,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554B, 701–707 (1991).

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

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14, pp. 501–598.

R. S. Sirohi, Optical Components, Systems, and Measurement Techniques (Dekker, New York, 1991), Chap. 6, pp. 219–246.

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Figures (1)

Fig. 1
Fig. 1

Observation of a real-time holographic fringe pattern for the analysis of optical path variations of fluid in the test cell. A He–Ne laser with a wavelength of 632.8 nm was used.

Equations (13)

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

I 1 = A + B cos ϕ ,
I 2 = A + B cos ( ϕ + α ) ,
I 3 = A + B cos ( ϕ α ) ,
I 4 = A + B cos ( ϕ + δ ) ,
I 5 = A + B cos ( ϕ + δ + α ) ,
I 6 = A + B cos ( ϕ + δ α ) .
P = I 6 I 5 I 3 I 2 = sin ( ϕ + δ ) sin ϕ .
Q = ( I 6 I 4 ) + ( I 5 I 4 ) ( I 2 I 1 ) + ( I 3 I 1 ) = cos ( ϕ + δ ) cos ϕ .
cos δ = P Q + 1 P + Q = ( I 6 I 5 ) [ ( I 6 I 4 ) + ( I 5 I 4 ) ] + ( I 3 I 2 ) [ ( I 2 I 1 ) + ( I 3 I 1 ) ] ( I 6 I 5 ) [ ( I 2 I 1 ) + ( I 3 I 1 ) ] + ( I 3 I 2 ) [ ( I 6 I 4 ) + ( I 5 I 4 ) ] .
I 3 + I 2 2 I 1 = 2 B cos ϕ ( cos α 1 )
I 3 I 2 = 2 B sin ϕ sin α ,
P = cos δ + cot ϕ sin δ
Q = cos δ tan ϕ sin δ ,

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