Abstract

The accuracy of phase shifting interferometry is limited by reference phase errors caused by nonlinearities in the phase shifter movements, calibration errors of this device, phase drifts during the measuring interval, and low frequency mechanical vibrations. Since the error depends on the phase to be measured in a sinusoidal fashion one can greatly reduce its influence on the measuring results. For this purpose a function also containing the characteristic error function, is fitted to the measured data. In a second step the error function is subtracted from the measured phase values. In most cases an error reduction by 1 order of magnitude seems achievable as has been demonstrated by computer simulations.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. S. Fritz, “Absolute Calibration of an Optical Flat,” Opt. Eng. 23, 379–383 (1984).
    [Crossref]
  2. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digitial Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [Crossref] [PubMed]
  3. M. Kuchel, E. Heynacher, “Testing as an Integral Tool for Fabrication of Large Mirrors, ESO-NTT 3.5m Prime Mirror,” in Proceedings, ESO Conference on Very Large Telescopes and Their Instrumentation, Garching (21–24 Mar. 1988).
  4. P. Hariharan, B. F. Oreb, C. H. Freund, “Stroboscopic Holographic Interferometry: Measurements of Vector Components of a Vibration,” Appl. Opt. 26, 3899–3903 (1987).
    [Crossref] [PubMed]
  5. R. Daendliker, “Heterodyne Holographic Interferometry,” Prog. Opt. 17, 1–84 (1980).
    [Crossref]
  6. C.-C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365–370 (1984).
  7. F. M. Mottier, “Microprocessor-Based Automatic Heterodyne Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 146–149 (1978).
  8. J. Mastner, V. Masek, “Electronic Instrumentation for Heterodyne Holographic Interferometry,” Rev. Sci. Instrum. 51, 926–930 (1980).
    [Crossref]
  9. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421–3432 (1983).
    [Crossref] [PubMed]
  10. P. Carre, “Installation et utilisation du comparateur photoelectrque et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
    [Crossref]
  11. K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 350–393 (1988).
  12. K. Kinnstaetter, A. W. Lohmann, J. Schwider, N. Streibl, “Accuracy of Phase Shifting Interferometry,” Appl. Opt. 27, 5082–5089 (1988).
    [Crossref] [PubMed]
  13. J. Schwider, K.-E. Elssner, J. Grzanna, R. Spolaczyk, “Results and Error Sources in Absolute Sphericity Measurements,” presented at IMEKO Laser Measurement Working Group Symposium, Budapest (Nov. 1986).

1988 (2)

1987 (1)

1984 (2)

B. S. Fritz, “Absolute Calibration of an Optical Flat,” Opt. Eng. 23, 379–383 (1984).
[Crossref]

C.-C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365–370 (1984).

1983 (1)

1980 (2)

R. Daendliker, “Heterodyne Holographic Interferometry,” Prog. Opt. 17, 1–84 (1980).
[Crossref]

J. Mastner, V. Masek, “Electronic Instrumentation for Heterodyne Holographic Interferometry,” Rev. Sci. Instrum. 51, 926–930 (1980).
[Crossref]

1978 (1)

F. M. Mottier, “Microprocessor-Based Automatic Heterodyne Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 146–149 (1978).

1974 (1)

1966 (1)

P. Carre, “Installation et utilisation du comparateur photoelectrque et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[Crossref]

Brangaccio, D. J.

Bruning, J. H.

Burow, R.

Carre, P.

P. Carre, “Installation et utilisation du comparateur photoelectrque et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[Crossref]

Creath, K.

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 350–393 (1988).

Daendliker, R.

R. Daendliker, “Heterodyne Holographic Interferometry,” Prog. Opt. 17, 1–84 (1980).
[Crossref]

Elssner, K.-E.

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421–3432 (1983).
[Crossref] [PubMed]

J. Schwider, K.-E. Elssner, J. Grzanna, R. Spolaczyk, “Results and Error Sources in Absolute Sphericity Measurements,” presented at IMEKO Laser Measurement Working Group Symposium, Budapest (Nov. 1986).

Freund, C. H.

Fritz, B. S.

B. S. Fritz, “Absolute Calibration of an Optical Flat,” Opt. Eng. 23, 379–383 (1984).
[Crossref]

Gallagher, J. E.

Grzanna, J.

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421–3432 (1983).
[Crossref] [PubMed]

J. Schwider, K.-E. Elssner, J. Grzanna, R. Spolaczyk, “Results and Error Sources in Absolute Sphericity Measurements,” presented at IMEKO Laser Measurement Working Group Symposium, Budapest (Nov. 1986).

Hariharan, P.

Herriott, D. R.

Heynacher, E.

M. Kuchel, E. Heynacher, “Testing as an Integral Tool for Fabrication of Large Mirrors, ESO-NTT 3.5m Prime Mirror,” in Proceedings, ESO Conference on Very Large Telescopes and Their Instrumentation, Garching (21–24 Mar. 1988).

Huang, C.-C.

C.-C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365–370 (1984).

Kinnstaetter, K.

Kuchel, M.

M. Kuchel, E. Heynacher, “Testing as an Integral Tool for Fabrication of Large Mirrors, ESO-NTT 3.5m Prime Mirror,” in Proceedings, ESO Conference on Very Large Telescopes and Their Instrumentation, Garching (21–24 Mar. 1988).

Lohmann, A. W.

Masek, V.

J. Mastner, V. Masek, “Electronic Instrumentation for Heterodyne Holographic Interferometry,” Rev. Sci. Instrum. 51, 926–930 (1980).
[Crossref]

Mastner, J.

J. Mastner, V. Masek, “Electronic Instrumentation for Heterodyne Holographic Interferometry,” Rev. Sci. Instrum. 51, 926–930 (1980).
[Crossref]

Merkel, K.

Mottier, F. M.

F. M. Mottier, “Microprocessor-Based Automatic Heterodyne Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 146–149 (1978).

Oreb, B. F.

Rosenfeld, D. P.

Schwider, J.

Spolaczyk, R.

J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421–3432 (1983).
[Crossref] [PubMed]

J. Schwider, K.-E. Elssner, J. Grzanna, R. Spolaczyk, “Results and Error Sources in Absolute Sphericity Measurements,” presented at IMEKO Laser Measurement Working Group Symposium, Budapest (Nov. 1986).

Streibl, N.

White, A. D.

Appl. Opt. (4)

Metrologia (1)

P. Carre, “Installation et utilisation du comparateur photoelectrque et interferentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[Crossref]

Opt. Eng. (2)

C.-C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365–370 (1984).

B. S. Fritz, “Absolute Calibration of an Optical Flat,” Opt. Eng. 23, 379–383 (1984).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

F. M. Mottier, “Microprocessor-Based Automatic Heterodyne Interferometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 146–149 (1978).

Prog. Opt. (2)

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 350–393 (1988).

R. Daendliker, “Heterodyne Holographic Interferometry,” Prog. Opt. 17, 1–84 (1980).
[Crossref]

Rev. Sci. Instrum. (1)

J. Mastner, V. Masek, “Electronic Instrumentation for Heterodyne Holographic Interferometry,” Rev. Sci. Instrum. 51, 926–930 (1980).
[Crossref]

Other (2)

M. Kuchel, E. Heynacher, “Testing as an Integral Tool for Fabrication of Large Mirrors, ESO-NTT 3.5m Prime Mirror,” in Proceedings, ESO Conference on Very Large Telescopes and Their Instrumentation, Garching (21–24 Mar. 1988).

J. Schwider, K.-E. Elssner, J. Grzanna, R. Spolaczyk, “Results and Error Sources in Absolute Sphericity Measurements,” presented at IMEKO Laser Measurement Working Group Symposium, Budapest (Nov. 1986).

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 (5)

Fig. 1
Fig. 1

Zernike polynomial used in the simulation of Fig. 3.

Fig. 2
Fig. 2

Phase error for a linear phase deviation of about four fringes across the aperture. The sinusoid gives the error before and the more irregular curve shows the remaining error after the first reduction method has been used: (a) A = 0; (b) A = π/2.

Fig. 3
Fig. 3

Same as Fig. 2 but with a combination of Zernike and a linear phase function. The more irregular curve gives the remaining error after reduction.

Fig. 4
Fig. 4

Removal after the second method. All the parameters as in Fig. 2.

Fig. 5
Fig. 5

Error reduction for only one fringe per interferometer aperture. The influence of the piston phase A can be seen more clearly: (a) A = 0; (b) A = π/2.

Equations (7)

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

Δ Φ = tan 1 [ ( A C cos 2 Φ S sin 2 Φ ) / 1 C sin 2 Φ + S cos 2 Φ ] ,
A = 1 / R r = 1 R ɛ r , C = 1 / R r = 1 R ɛ r cos 2 φ r , S = 1 / R r = 1 R ɛ r sin 2 φ r ,
Δ Φ = A ( C AS ) cos 2 Φ ( S AC ) sin 2 Φ + higher terms in C 2 , S 2 , and CS .
Δ Φ = a + b cos 2 Φ + s sin 2 Φ .
Φ = tan 1 [ ( r = 1 R I r sin φ r ) / ( r = 1 R I r cos φ r ) ] .
l ( ρ ) = A + B ρ ,
z ( ρ ) = 70 ρ 8 160 ρ 6 + 90 ρ 4 10 ρ 2 + 1 ,

Metrics