Abstract

Results of the application of wavelet transform for signal processing in white-light interferometry are reported. The mother wavelet frequency is chosen to be the light-source correlogram 1’s, and accurate phase measurements are obtained from simple correlation computations. The fringe envelope is also addressed and permits a complete analysis of coherence-limited fringe patterns. Miscalibrations of phase shift and mean wavelength are also considered.

© 1997 Optical Society of America

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References

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  1. A. F. Ferscher, J. Biomed. Opt. 1, 157 (1996).
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    [CrossRef]
  7. P. Sandoz, J. Mod. Opt. 43, 1545 (1996).
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  11. J. M. Combes, A. Grossmann, and Ph. Tchamitchian, Wavelets, 2nd ed. (Springer-Verlag, Berlin, 1990).
    [CrossRef]

1997 (1)

P. Sandoz, R. Devillers, and A. Plata Gomez, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

1996 (4)

P. Sandoz, J. Mod. Opt. 43, 1545 (1996).

K. G. Larkin, J. Opt. Soc. Am. A 13, 832 (1996).
[CrossRef]

A. F. Ferscher, J. Biomed. Opt. 1, 157 (1996).
[CrossRef]

A. D. Kersey, Opt. Fiber Technol. 2, 291 (1996).
[CrossRef]

1995 (1)

P. de Groot and L. Deck, J. Mod. Opt. 42, 389 (1995).
[CrossRef]

1994 (2)

1993 (1)

1987 (1)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, Proc. SPIE 775, 233 (1987).
[CrossRef]

Biegen, J.

Caber, P. J.

Cohen, F.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, Proc. SPIE 775, 233 (1987).
[CrossRef]

Combes, J. M.

J. M. Combes, A. Grossmann, and Ph. Tchamitchian, Wavelets, 2nd ed. (Springer-Verlag, Berlin, 1990).
[CrossRef]

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, Proc. SPIE 775, 233 (1987).
[CrossRef]

de Groot, P.

P. de Groot and L. Deck, J. Mod. Opt. 42, 389 (1995).
[CrossRef]

L. Deck and P. de Groot, Appl. Opt. 33, 7334 (1994).
[CrossRef] [PubMed]

Deck, L.

P. de Groot and L. Deck, J. Mod. Opt. 42, 389 (1995).
[CrossRef]

L. Deck and P. de Groot, Appl. Opt. 33, 7334 (1994).
[CrossRef] [PubMed]

Devillers, R.

P. Sandoz, R. Devillers, and A. Plata Gomez, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

Ferscher, A. F.

A. F. Ferscher, J. Biomed. Opt. 1, 157 (1996).
[CrossRef]

Grossmann, A.

J. M. Combes, A. Grossmann, and Ph. Tchamitchian, Wavelets, 2nd ed. (Springer-Verlag, Berlin, 1990).
[CrossRef]

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, Proc. SPIE 775, 233 (1987).
[CrossRef]

Kersey, A. D.

A. D. Kersey, Opt. Fiber Technol. 2, 291 (1996).
[CrossRef]

Larkin, K. G.

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, Proc. SPIE 775, 233 (1987).
[CrossRef]

Plata Gomez, A.

P. Sandoz, R. Devillers, and A. Plata Gomez, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

Sandoz, P.

P. Sandoz, R. Devillers, and A. Plata Gomez, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

P. Sandoz, J. Mod. Opt. 43, 1545 (1996).

Tchamitchian, Ph.

J. M. Combes, A. Grossmann, and Ph. Tchamitchian, Wavelets, 2nd ed. (Springer-Verlag, Berlin, 1990).
[CrossRef]

Appl. Opt. (2)

J. Biomed. Opt. (1)

A. F. Ferscher, J. Biomed. Opt. 1, 157 (1996).
[CrossRef]

J. Mod. Opt. (3)

P. Sandoz, R. Devillers, and A. Plata Gomez, J. Mod. Opt. 44, 519 (1997).
[CrossRef]

P. de Groot and L. Deck, J. Mod. Opt. 42, 389 (1995).
[CrossRef]

P. Sandoz, J. Mod. Opt. 43, 1545 (1996).

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

Opt. Fiber Technol. (1)

A. D. Kersey, Opt. Fiber Technol. 2, 291 (1996).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, Proc. SPIE 775, 233 (1987).
[CrossRef]

Other (1)

J. M. Combes, A. Grossmann, and Ph. Tchamitchian, Wavelets, 2nd ed. (Springer-Verlag, Berlin, 1990).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

a, b, Typical interference signals recorded; c, d, modulus of the computed wavelet transform.

Fig. 2
Fig. 2

Errors made in the phase measurement.

Fig. 3
Fig. 3

Experimental results: a, absolute phase between the reference position and the top of the zero-order interference fringe; b, measured ϕ0 value.

Equations (10)

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Ix, y=Ibgx, y1+γx, ygzx, y×cos4πσ0zx, y+ϕ0,
Bσ=exp-σ-σ0/Δσ2,
gz=exp-z/Lc2,
Iz=Ibg+Ibgγexp-z/Lc2 cos4πσ0z+ϕ0.
Ψz=exp-z/Lw2expj4πσ0z,
Ψa, bz=a-1/2Ψz-b/a,
Wa,b=-+IzΨa,bzdz.
Ψk=exp-kδz/Lw2expj4πσ0kδz,
Wi, j=k=-NNΨkIzj+kδz.
Gz=exp-z/Lc2*exp-z/Lw2.

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