Abstract

Interferometers often encode the information on the measurand in the phase of a fringe pattern, which is usually recorded by an imaging device. Accuracy of measurements carried out by interferometric techniques is thus strongly dependent on the accuracy with which the underlying phase distribution of these fringe patterns is estimated. Fringe analysis methods, which have been developed to accomplish this task, are in general characterized by their performance in terms of both accuracy of phase estimation and associated computational complexity. We propose an improved high-order ambiguity-function-based fringe-analysis method that is demonstrated to provide an accurate and direct estimation of the unwrapped phase distribution in a highly computationally efficient manner. Presented simulation and experimental results in digital holographic interferometry depict the potential utility of the proposed method.

© 2009 Optical Society of America

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S. S. Gorthi and P. Rastogi, J. Mod. Opt. 56, 949 (2009).
[CrossRef]

S. S. Gorthi and P. Rastogi, J. Opt. A 11, 065405 (2009).
[CrossRef]

2008 (1)

2006 (1)

2005 (1)

E. Aboutanios and B. Mulgrew, IEEE Trans. Signal Process. 53, 1237 (2005).
[CrossRef]

2004 (3)

2003 (1)

2002 (1)

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

2001 (1)

J. A. Quiroga, J. Antonio Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

1999 (1)

1998 (1)

S. Golden and B. Friedlander, IEEE Trans. Signal Process. 46, 1452 (1998).
[CrossRef]

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1989 (1)

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[CrossRef]

1986 (1)

R. O. Schmidt, IEEE Trans. Antennas Propag. AP-34, 276 (1986).
[CrossRef]

1982 (1)

Aboutanios, E.

E. Aboutanios and B. Mulgrew, IEEE Trans. Signal Process. 53, 1237 (2005).
[CrossRef]

Antonio Gomez-Pedrero, J.

J. A. Quiroga, J. Antonio Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

Asundi, A.

Barnes, T. H.

Burton, D. R.

Cuevas, F. J.

Dalmau-Cedeno, O. S.

Dursun, A.

A. Dursun, S. Ozder, and F. N. Ecevit, Meas. Sci. Technol. 15, 1768 (2004).
[CrossRef]

Ecevit, F. N.

A. Dursun, S. Ozder, and F. N. Ecevit, Meas. Sci. Technol. 15, 1768 (2004).
[CrossRef]

Friedlander, B.

S. Golden and B. Friedlander, IEEE Trans. Signal Process. 46, 1452 (1998).
[CrossRef]

Garcia-Botella, A.

J. A. Quiroga, J. Antonio Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

Gdeisat, M. A.

Golden, S.

S. Golden and B. Friedlander, IEEE Trans. Signal Process. 46, 1452 (1998).
[CrossRef]

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, J. Opt. A 11, 065405 (2009).
[CrossRef]

S. S. Gorthi and P. Rastogi, J. Mod. Opt. 56, 949 (2009).
[CrossRef]

Ina, H.

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

Kailath, T.

R. Roy and T. Kailath, IEEE Trans. Acoust. Speech Signal Process. 37, 984 (1989).
[CrossRef]

Kemao, Q.

Kobayashi, S.

Lalor, M. J.

Legarda-Saenz, R.

Marroquin, J. L.

Mulgrew, B.

E. Aboutanios and B. Mulgrew, IEEE Trans. Signal Process. 53, 1237 (2005).
[CrossRef]

Ozder, S.

A. Dursun, S. Ozder, and F. N. Ecevit, Meas. Sci. Technol. 15, 1768 (2004).
[CrossRef]

Qian, K.

Quiroga, J. A.

J. A. Quiroga, J. Antonio Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

Rastogi, P.

S. S. Gorthi and P. Rastogi, J. Mod. Opt. 56, 949 (2009).
[CrossRef]

S. S. Gorthi and P. Rastogi, J. Opt. A 11, 065405 (2009).
[CrossRef]

Rivera, M.

Roy, R.

R. Roy and T. Kailath, IEEE Trans. Acoust. Speech Signal Process. 37, 984 (1989).
[CrossRef]

Schmidt, R. O.

R. O. Schmidt, IEEE Trans. Antennas Propag. AP-34, 276 (1986).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

Servin, M.

Soon, S. H.

Takeda, M.

Tan, S. M.

Watkins, L. R.

Weng, J.

Zhong, J.

Appl. Opt. (4)

IEEE Trans. Acoust. Speech Signal Process. (1)

R. Roy and T. Kailath, IEEE Trans. Acoust. Speech Signal Process. 37, 984 (1989).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. O. Schmidt, IEEE Trans. Antennas Propag. AP-34, 276 (1986).
[CrossRef]

IEEE Trans. Signal Process. (2)

E. Aboutanios and B. Mulgrew, IEEE Trans. Signal Process. 53, 1237 (2005).
[CrossRef]

S. Golden and B. Friedlander, IEEE Trans. Signal Process. 46, 1452 (1998).
[CrossRef]

J. Mod. Opt. (1)

S. S. Gorthi and P. Rastogi, J. Mod. Opt. 56, 949 (2009).
[CrossRef]

J. Opt. A (1)

S. S. Gorthi and P. Rastogi, J. Opt. A 11, 065405 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Meas. Sci. Technol. (2)

U. Schnars and W. P. O. Juptner, Meas. Sci. Technol. 13, R85 (2002).
[CrossRef]

A. Dursun, S. Ozder, and F. N. Ecevit, Meas. Sci. Technol. 15, 1768 (2004).
[CrossRef]

Opt. Commun. (1)

J. A. Quiroga, J. Antonio Gomez-Pedrero, and A. Garcia-Botella, Opt. Commun. 197, 43 (2001).
[CrossRef]

Opt. Lett. (2)

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Figures (2)

Fig. 1
Fig. 1

(a) Simulated fringe pattern at SNR of 30 dB ( 512 × 512 ) , (b) estimated phase along the middle row using the IHAF method ( N w = 8 , M = 4 ), (c) 3-D plot of the estimated phase over the whole image, (d) error in phase estimation.

Fig. 2
Fig. 2

(a) Real part of the reconstructed interference field corresponding to the loading of a circularly clamped object ( 256 × 256 ) , (b) 3D mesh plot of the phase distribution estimated using the IHAF method, (c) wrapped phase map generated from (b) for the purpose of illustration.

Tables (2)

Tables Icon

Table 1 Optimal Set of Delay Parameters of IHAF as Fractions of the Number of Samples ( N ) Present in the Signal

Tables Icon

Table 2 Evaluation of Computational Time

Equations (5)

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

A ( x , y ) = b ( x , y ) exp [ j Δ ϕ ( x , y ) ] + η ( x , y ) ,
A i = b i exp [ j ( q = 0 M a i q x q ) ] + η i ,
P M [ A i ( x ) , τ q ] = q = 0 M 1 [ A i q ( x q τ q ) ] ( M 1 q ) ,
A i q ( x ) = { A i ( x ) if q is even A i * ( x ) if q is odd } .
a ̂ i M = ω i 0 M ! γ ,

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