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References

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  1. J. H. Bruning, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, D. R. Herriott, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  2. J. C. Wyant, “Use of an ac Heterodyne Lateral Shear Interferometer with Real-Time Wavefront Correction Systems,” Appl. Opt. 14, 2622 (1975).
    [CrossRef] [PubMed]
  3. L. M. Frantz, A. A. Sawchuk, W. van der Ohe, “Optical Phase Measurement in Real Time,” Appl. Opt. 18, 3301 (1979).
    [CrossRef] [PubMed]
  4. P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393 (1982).
    [CrossRef]
  5. 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 (1983).
    [CrossRef] [PubMed]
  6. P. Carré, “Installation et Utilisation du Comparateur Photoelectrique et Interferentiel du Bureau International des Poids et Measures,” Metrologia 2, 13 (1966).
    [CrossRef]
  7. Y.-Y. Cheng, J. C. Wyant, “Phase Shifter Calibration in Phase-Shifting Interferometry,” Appl. Opt. 24, 3049 (1985).
    [CrossRef] [PubMed]

1985 (1)

1983 (1)

1982 (1)

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393 (1982).
[CrossRef]

1979 (1)

1975 (1)

1974 (1)

1966 (1)

P. Carré, “Installation et Utilisation du Comparateur Photoelectrique et Interferentiel du Bureau International des Poids et Measures,” Metrologia 2, 13 (1966).
[CrossRef]

Brangaccio, D. J.

Brown, N.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393 (1982).
[CrossRef]

Bruning, J. H.

Burow, R.

Carré, P.

P. Carré, “Installation et Utilisation du Comparateur Photoelectrique et Interferentiel du Bureau International des Poids et Measures,” Metrologia 2, 13 (1966).
[CrossRef]

Cheng, Y.-Y.

Elssner, K-E.

Frantz, L. M.

Gallagher, J. E.

Grzanna, J.

Hariharan, P.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393 (1982).
[CrossRef]

Herriott, D. R.

Merkel, K.

Oreb, B. F.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393 (1982).
[CrossRef]

Rosenfeld, D. P.

Sawchuk, A. A.

Schwider, J.

Spolaczyk, R.

van der Ohe, W.

White, A. D.

Wyant, J. C.

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Figures (3)

Fig. 1
Fig. 1

Phase error plotted against the phase difference for an error in the phase step of 5° (phase step of 95° instead of 90°).

Fig. 2
Fig. 2

Movement of the PZT as a function of the voltage applied to it showing typical errors: (a) simple nonlinearity; (b) hysteresis; and (c) linear drift.

Fig. 3
Fig. 3

Phase error plotted against the phase difference for a PZT with deviations from linearity of ±1° at nominal phase shifts of ±90°.

Equations (8)

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

tan 2 α = 3 I 2 - 3 I 3 - I 1 + I 4 I 1 + I 2 - I 3 - I 4 ,
tan 2 φ = ( 3 I 2 - 3 I 3 - I 1 + I 4 ) ( I 1 + I 2 - I 3 - I 4 ) ( I 1 - I 2 - I 3 + I 4 ) 2 .
I 1 = A + B + 2 ( A B ) 1 / 2 cos ( φ - 2 α ) , I 2 = A + B + 2 ( A B ) 1 / 2 cos ( φ - α ) , I 3 = A + B + 2 ( A B ) 1 / 2 cos φ , I 4 = A + B + 2 ( A B ) 1 / 2 cos ( φ + α ) , I 5 = A + B + 2 ( A B ) 1 / 2 cos ( φ + 2 α ) ,
I 2 - I 4 ( 2 I 3 - I 5 - I 1 ) = sin α sin φ ( 1 - cos 2 α ) cos φ .
tan φ = 2 ( I 2 - I 4 ) 2 I 3 - I 5 - I 1 .
tan φ = [ 1 + ( 2 / 2 ) ] tan φ .
Δ φ = φ - φ = ( 2 / 4 ) sin 2 φ .
cos α = I 5 - I 1 2 ( I 4 - I 2 ) .

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