Abstract

We propose a new approach for estimating the phase in the presence of a nonlinear response of a phase-shifting device: a piezoelectric transducer (PZT). The method is complemented well by the high resolution and the maximum likelihood estimation techniques in the estimation of the phase step and the nonlinear coefficient. The advantage of the proposed method is that it can be extended to the extraction of multiple phases in configurations involving multiple PZTs in the presence of nonlinearity. Symmetricity in the phase steps is not required in this method. Hence hysteresis of the PZT does not have any influence on the accuracy of the phase estimation. The effectiveness of the method is shown by experimental results.

© 2006 Optical Society of America

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References

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2005 (2)

1998 (1)

1997 (1)

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

1995 (2)

1984 (1)

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).

1982 (1)

1970 (1)

V. Cizek, IEEE Trans. Audio Electroacoust. 18, 340 (1970).
[CrossRef]

Cizek, V.

V. Cizek, IEEE Trans. Audio Electroacoust. 18, 340 (1970).
[CrossRef]

Creath, K.

de Groot, P.

Farrant, D. I.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Greivenkamp, J. E.

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).

Gutmann, B.

Hibino, K.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Kay, S. M.

S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice-Hall, 1998).

Larkin, K. G.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Morgan, C. J.

Oreb, B. F.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Patil, A.

Raphael, B.

Rastogi, P.

Schmit, J.

Weber, H.

Appl. Opt. (4)

IEEE Trans. Audio Electroacoust. (1)

V. Cizek, IEEE Trans. Audio Electroacoust. 18, 340 (1970).
[CrossRef]

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

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Opt. Eng. (1)

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).

Opt. Express (1)

Opt. Lett. (1)

Other (1)

S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice-Hall, 1998).

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Figures (3)

Fig. 1
Fig. 1

(a) Holography fringe, (b) lattice representation using Gutmann and Weber method.[10]

Fig. 2
Fig. 2

Histogram representation of the phase step and the nonlinear coefficient (in degrees).

Fig. 3
Fig. 3

Comparison of the actual PZT response with the estimated PZT responses for N = 15 and N = 25 data frames.

Equations (8)

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I ¯ n = I dc [ 1 + γ cos ( φ + α n ) ] + η n ,
α n = n α ( 1 + ϵ 1 ) + ϵ 2 ( n α ) 2 π , 0 n N 1 ,
I ¯ n = I dc [ 1 + γ cos ( n α ¯ + n 2 β ¯ + φ ) ] + η n .
I d ( n ) = A exp [ j ( φ + n α ¯ + n 2 β ¯ ) ] + ζ n ,
I d ( n ) I d * ( n k ) = A 2 exp [ j ( 2 k β ¯ n + k α ¯ k 2 β ¯ ) ] ,
I ¯ = I + η + S ( ξ ) C + η ,
p ( I ¯ ; ξ ) = 1 π N σ N exp [ 1 σ 2 ( I ¯ S C ) H ( I ¯ S C ) ] ,
ξ = max I ¯ H [ S ( S H S ) 1 S H ] I ¯ .

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