Abstract

A new method for phase retrieval of optical fringe patterns is presented. This method is based on a wavelet transform and is capable of extracting the full 2D phase distribution from a single fringe pattern. An important conclusion that the phase of the optical fringe pattern is equal to the phase of its wavelet transform on the ridge of the wavelet transform is theoretically clarified. The method is compared with the Fourier transform and the integration methods. A numerical simulation and an experimental example of phase retrieval are shown.

© 2005 Optical Society of America

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References

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2005

2004

2003

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, Exp. Mech. 43, 45 (2003).
[CrossRef]

1999

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

1997

1996

P. Guillemain and R. Kroland-Martinet, Proc. IEEE 84, 561 (1996).
[CrossRef]

1992

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

1983

Barnes, T. H.

Chen, L.

Cherbuliez, M.

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

Colonna de Lega, X.

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

Delprat, N.

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Escudié, B.

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Guillemain, P.

P. Guillemain and R. Kroland-Martinet, Proc. IEEE 84, 561 (1996).
[CrossRef]

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Jacquot, P.

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

Kadooka, K.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, Exp. Mech. 43, 45 (2003).
[CrossRef]

Kroland-Martinet, R.

P. Guillemain and R. Kroland-Martinet, Proc. IEEE 84, 561 (1996).
[CrossRef]

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Kunoo, K.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, Exp. Mech. 43, 45 (2003).
[CrossRef]

Mutoh, K.

Nagayasu, T.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, Exp. Mech. 43, 45 (2003).
[CrossRef]

Ono, K.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, Exp. Mech. 43, 45 (2003).
[CrossRef]

Quan, C.

Takeda, M.

Tan, S. M.

Tay, C.-J.

Tchamitchian, P.

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Torrésani, B.

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Uda, N.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, Exp. Mech. 43, 45 (2003).
[CrossRef]

Watkins, L. R.

Weng, J.

Zhong, J.

Appl. Opt.

Exp. Mech.

K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, Exp. Mech. 43, 45 (2003).
[CrossRef]

IEEE Trans. Inf. Theory

N. Delprat, B. Escudié, P. Guillemain, R. Kroland-Martinet, P. Tchamitchian, and B. Torrésani, IEEE Trans. Inf. Theory 38, 644 (1992).
[CrossRef]

Opt. Lett.

Proc. IEEE

P. Guillemain and R. Kroland-Martinet, Proc. IEEE 84, 561 (1996).
[CrossRef]

Proc. SPIE

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, Proc. SPIE 3813, 692 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Deformed fringe pattern.

Fig. 2
Fig. 2

(a) Amplitudes and (b) phases of the WT to the 128th row.

Fig. 3
Fig. 3

Comparison of the phase distribution of the 128th row obtained by the RWT, FT, and integration methods.

Fig. 4
Fig. 4

Comparison of the errors of the 128th row obtained by the RWT, FT, and integration methods.

Fig. 5
Fig. 5

(a) Deformed grating pattern on the surface of a hand. (b) Phase distribution obtained by the RWT method.

Equations (13)

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W ( a , b ) = I ( x ) M a , b * ( x ) d x ,
M ( x ) = 1 π 4 2 π γ exp [ ( 2 π γ ) 2 x 2 2 + j 2 π x ] ,
I ( x ) = A ( x ) + B ( x ) cos φ ( x ) = A ( x ) + 1 2 B ( x ) exp [ j φ ( x ) ] + 1 2 B ( x ) exp [ j φ ( x ) ] ,
φ ( x ) = φ ( b ) + φ ( b ) ( x b ) + φ ( b ) 2 ! ( x b ) 2 + .
W ( a , b ) = I ( x ) M a , b * ( x ) d x = { A + 1 2 B exp [ j φ ( x ) ] + 1 2 B exp [ j φ ( x ) ] } M a , b * ( x ) d x = W 1 ( a , b ) + W 2 ( a , b ) + W 3 ( a , b ) .
W 1 ( a , b ) = A M a , b * ( x ) d x = 1 π 4 γ 3 A e γ 2 ,
W 2 ( a , b ) = 1 2 B exp { j [ φ ( b ) + φ ( b ) ( x b ) ] } M a , b * ( x ) d x = 1 π 4 γ 3 B exp [ j φ ( b ) ] exp { γ 2 [ φ ( b ) a 2 π 1 ] 2 } ,
W 3 ( a , b ) = 1 2 B exp { j [ φ ( b ) + φ ( b ) ( x b ) ] } M a , b * ( x ) d x = 1 π 4 γ 3 B exp [ j φ ( b ) ] exp { γ 2 [ φ ( b ) a 2 π + 1 ] 2 } .
a = 2 π φ ( b ) = 1 f b .
W ( 1 f b , b ) = 1 π 4 γ 3 { A e γ 2 + B exp [ j φ ( b ) ] + B exp [ j φ ( b ) ] e 4 γ 2 } 1 π 4 γ 3 B exp [ j φ ( b ) ] .
ψ ( a , b ) = arctan { imag [ W ( a , b ) ] real [ W ( a , b ) ] } ,
W ( a , b ) = ( { imag [ W ( a , b ) ] } 2 + { real [ W ( a , b ) ] } 2 ) 1 2 .
φ ( b ) = ψ ( 1 f b , b ) .

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