Abstract

An experimental study of the use of an S-transform to evaluate the phase distribution from a two-dimensional fringe pattern by introducing the carrier frequencies in two spatial directions, x and y, is presented. The phase distribution is extracted from the optical fringe pattern by using an S-transform gradient and S-transform phase methods. The experimental result for the Fourier transform profilometry algorithm is compared with the results of the S-transform analysis.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2003

C. R. Pinnegar and L. Mansinha, Fluct. Noise Lett. 3, L357 (2003).
[CrossRef]

2002

L. D. Acquisto, L. Frantini, and A. M. Siddiolo, Meas. Sci. Technol. 13, 613 (2002).
[CrossRef]

2001

X. Su and W. Chen, Opt. Lasers Eng. 35, 263 (2001).
[CrossRef]

1996

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process. 44, 998 (1996).
[CrossRef]

1994

1988

R. J. Green and J. G. Walker, Opt. Lasers Eng. 8, 29 (1988).
[CrossRef]

1983

Acquisto, L. D.

L. D. Acquisto, L. Frantini, and A. M. Siddiolo, Meas. Sci. Technol. 13, 613 (2002).
[CrossRef]

Chen, W.

X. Su and W. Chen, Opt. Lasers Eng. 35, 263 (2001).
[CrossRef]

Frantini, L.

L. D. Acquisto, L. Frantini, and A. M. Siddiolo, Meas. Sci. Technol. 13, 613 (2002).
[CrossRef]

Green, R. J.

R. J. Green and J. G. Walker, Opt. Lasers Eng. 8, 29 (1988).
[CrossRef]

Lowe, R. P.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process. 44, 998 (1996).
[CrossRef]

Mansinha, L.

C. R. Pinnegar and L. Mansinha, Fluct. Noise Lett. 3, L357 (2003).
[CrossRef]

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process. 44, 998 (1996).
[CrossRef]

Mutoh, K.

Pinnegar, C. R.

C. R. Pinnegar and L. Mansinha, Fluct. Noise Lett. 3, L357 (2003).
[CrossRef]

Siddiolo, A. M.

L. D. Acquisto, L. Frantini, and A. M. Siddiolo, Meas. Sci. Technol. 13, 613 (2002).
[CrossRef]

Singh, H.

Sirkis, J. S.

Stockwell, R. G.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process. 44, 998 (1996).
[CrossRef]

R. G. Stockwell, 'S-transform analysis of gravity wave activity from a small scale network of airglow imagers' (Faculty of Graduate Studies, the University of Western Ontario, 1999), pp. 52-100. The S-transform subroutine is available at URL: http://www.cora.nwra.com/~stockwel/.

Su, X.

X. Su and W. Chen, Opt. Lasers Eng. 35, 263 (2001).
[CrossRef]

Takeda, M.

Walker, J. G.

R. J. Green and J. G. Walker, Opt. Lasers Eng. 8, 29 (1988).
[CrossRef]

Appl. Opt.

Fluct. Noise Lett.

C. R. Pinnegar and L. Mansinha, Fluct. Noise Lett. 3, L357 (2003).
[CrossRef]

IEEE Trans. Signal Process.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, IEEE Trans. Signal Process. 44, 998 (1996).
[CrossRef]

Meas. Sci. Technol.

L. D. Acquisto, L. Frantini, and A. M. Siddiolo, Meas. Sci. Technol. 13, 613 (2002).
[CrossRef]

Opt. Lasers Eng.

R. J. Green and J. G. Walker, Opt. Lasers Eng. 8, 29 (1988).
[CrossRef]

X. Su and W. Chen, Opt. Lasers Eng. 35, 263 (2001).
[CrossRef]

Other

R. G. Stockwell, 'S-transform analysis of gravity wave activity from a small scale network of airglow imagers' (Faculty of Graduate Studies, the University of Western Ontario, 1999), pp. 52-100. The S-transform subroutine is available at URL: http://www.cora.nwra.com/~stockwel/.

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Figures (2)

Fig. 1
Fig. 1

Sinusoidal fringe projected image of the relief of Atatürk.

Fig. 2
Fig. 2

Recovered phase distribution of the relief of Atatürk by (a) the S-transform phase gradient method, (b) the S-transform phase method, (c) the FTP method.

Equations (9)

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h ( x ) = I 0 ( x ) [ 1 + V ( x ) cos ( 2 π f 0 x + φ ( x ) ) ] ,
2 π f 0 > d φ d x max .
S ( b , f ) = + h ( x ) w ( b x , f ) exp ( i 2 π f x ) d x ,
w ( b x , f ) = f 2 π exp ( f 2 ( b x ) 2 2 ) ;
S ( b , f ) = + H ( α + f ) W ( α , f ) exp ( i 2 π α b ) d α = I F T { H ( α + f ) W ( α , f ) } .
H ( α ) = I 0 ( b ) π { 2 δ ( α ) + V ( b ) [ δ ( α f 0 φ ( b ) 2 π ) exp ( i ( φ ( b ) b φ ( b ) ) ) + δ ( α + f 0 + φ ( b ) 2 π ) exp ( i ( φ ( b ) b φ ( b ) ) ) ] } .
S ( b , f ) = I 0 ( b ) π V ( b ) exp ( 2 π 2 f 2 ( f + f 0 + φ ( b ) 2 π ) 2 ) exp ( i ( φ + 2 π b f 0 2 π b f ) ) .
f max ( b ) = f 0 + φ ( b ) 2 π .
h ( x , y ) = I 0 ( x , y ) [ 1 + V ( x , y ) cos ( 2 π f 0 x + 2 π f 0 y + φ ( x , y ) ) ] .

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