Abstract

We point out that all formulas for calculating the phase map of object deformations in one step can be described by the same simple formalism of a complex division.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. T. Bothe, J. Burke, H. Helmers, “Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors,” Appl. Opt. 36, 5310–5316 (1997).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. H. O. Saldner, N. E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
    [CrossRef] [PubMed]
  6. H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
    [CrossRef] [PubMed]
  7. K. A. Stetson, W. R. Brohinsky, “Electrooptic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985).
    [CrossRef] [PubMed]
  8. K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.
  9. J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 512–598.
  10. B. Stroebel, “Processing of interferometric phase maps as complex-valued phasor images,” Appl. Opt. 35, 2192–2198 (1996).
    [CrossRef]

1997

1996

1993

J. M. Huntley, H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[CrossRef] [PubMed]

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40.1, 89–96 (1993).
[CrossRef]

1985

Bothe, T.

Brohinsky, W. R.

Bruning, J. H.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 512–598.

Burke, J.

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 512–598.

Helmers, H.

Huntley, J. M.

Molin, N. E.

Nakadate, S.

Pedrini, G.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40.1, 89–96 (1993).
[CrossRef]

Pfister, B.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40.1, 89–96 (1993).
[CrossRef]

Saito, H.

Saldner, H. O.

Stetson, K. A.

H. O. Saldner, N. E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

K. A. Stetson, W. R. Brohinsky, “Electrooptic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985).
[CrossRef] [PubMed]

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

Stroebel, B.

Tiziani, H.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40.1, 89–96 (1993).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40.1, 89–96 (1993).
[CrossRef]

Other

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 512–598.

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Equations (10)

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I i x ,   y = I 0 x ,   y 1 + γ x ,   y cos φ x ,   y + α i , I i x ,   y = I 0 x ,   y 1 + γ x ,   y cos φ x ,   y + α i ,
φ = arctan Δ I 42 Δ I 13     φ = arctan Δ I 42 Δ I 13 .
Δ φ = arctan Δ I 42 Δ I 13 - Δ I 42 Δ I 13 Δ I 13 Δ I 13 + Δ I 42 Δ I 42 ,
z = cos   φ + i   sin   φ     z = cos   φ + i   sin   φ .
φ = arg z = arctan Im z Re z = arctan sin   φ cos   φ .
Δ φ = φ - φ = arg z - arg z = arg z z ,
z z = sin   φ   sin   φ   +   cos   φ   cos   φ cos 2   φ   +   sin 2   φ + i   sin   φ   cos   φ   +   sin   φ   cos   φ cos 2   φ   -   sin 2   φ .
Δ φ = arg z z = arctan sin   φ   cos   φ   -   sin   φ   cos   φ sin   φ   sin   φ   +   cos   φ   cos   φ .
φ = arctan 3 I 1 - I 3 2 I 2 - I 1 - I 3 ,
Δ φ = arctan 3 I 1 - I 3 2 I 2 - I 1 - I 3 - 3 I 1 - I 3 2 I 2 - I 1 - I 3 3 I 1 - I 3 I 1 - I 3 + 2 I 2 - I 1 - I 3 2 I 2 - I 1 - I 3 .

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