Abstract

Temporal fringe pattern analysis is invaluable in studies of transient phenomena but necessitates large data storage for two essential sets of data, i.e., fringe pattern intensity and deformation phase. We describe a compression scheme based on the Fourier-transform method for temporal fringe data storage that permits retrieval of both the intensity and the deformation phase. When the scheme was used with simulated temporal wavefront interferometry intensity fringe patterns, a high compression ratio of 10.77 was achieved, with a significant useful data ratio of 0.859. The average root-mean-square error in phase value restored was a low 0.0015 rad. With simulated temporal speckle interferometry intensity fringe patterns, the important paremeters varied with the modulation cutoff value applied. For a zero modulation cutoff value, the ratio of data points and the compression ratio values obtained were roughly the same as in wavelength interferometry, albeit the average root-mean-square error in the phase value restored was far higher. By increasing the modulation cutoff value we attained significant reduction and increase in the ratio of data points and the compression ratio, respectively, whereas the average root-mean-square error in the restored phase values was reduced only slightly.

© 2005 Optical Society of America

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References

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2003 (2)

D. Ambrosi, D. Paoletti, G. Schirripa Spagnalo, “Study of free-convective onset on a horizontal wire using speckle pattern interferometry,” Int. J. Heat Mass Transfer 46, 4145–4155 (2003).
[CrossRef]

V. D. Madjarova, H. Kadono, “Dynamic electronic speckle pattern interferometry (DESPI) phase analysis with temporal Hilbert transform,” Opt. Express 11, 617–623 (2003).
[CrossRef] [PubMed]

2002 (3)

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Sinusoidal least-squares fitting for temporal fringe pattern analysis,” J. Mod. Opt. 49, 2257–2266 (2002).
[CrossRef]

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Synchronous detection techniques for temporal fringe pattern analysis,” Opt. Commun. 204, 75–81 (2002).
[CrossRef]

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

2000 (2)

1998 (1)

K. M. Hung, T. Yamada, “Phase unwrapping by regions using least squares approach,” Opt. Eng. 37, 2965–2970 (1998).
[CrossRef]

1996 (1)

1995 (2)

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. of Am. A 12, 2393–2400 (1995).
[CrossRef]

T. W. Ng, “Carrier-modulated object step-loading method of automated analysis in digital speckle shearing interferometry,” J. Mod. Opt. 42, 2109–2118 (1995).
[CrossRef]

1994 (1)

T. W. Ng, F. S. Chau, “Automated analysis in digital speckle shearing interferometry using an object step-loading method,” Opt. Commun. 108, 214–218 (1994).
[CrossRef]

1993 (1)

1987 (1)

1986 (1)

1985 (1)

1983 (1)

1982 (1)

Ambrosi, D.

D. Ambrosi, D. Paoletti, G. Schirripa Spagnalo, “Study of free-convective onset on a horizontal wire using speckle pattern interferometry,” Int. J. Heat Mass Transfer 46, 4145–4155 (2003).
[CrossRef]

Ang, K. T.

T. W. Ng, K. T. Ang, “Data compression for speckle correlation interferometry temporal fringe pattern analysis,” submitted to Appl. Opt.

Astrakharchik-Farrimond, E.

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Barton, J. S.

Buckberry, C.

Carlsson, T. E.

Chau, F. S.

T. W. Ng, F. S. Chau, “Automated analysis in digital speckle shearing interferometry using an object step-loading method,” Opt. Commun. 108, 214–218 (1994).
[CrossRef]

Creath, K.

Galizzi, G. E.

Ghiglia, D. C.

Gomez-Pedrero, J. A.

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Sinusoidal least-squares fitting for temporal fringe pattern analysis,” J. Mod. Opt. 49, 2257–2266 (2002).
[CrossRef]

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Synchronous detection techniques for temporal fringe pattern analysis,” Opt. Commun. 204, 75–81 (2002).
[CrossRef]

Hung, K. M.

K. M. Hung, T. Yamada, “Phase unwrapping by regions using least squares approach,” Opt. Eng. 37, 2965–2970 (1998).
[CrossRef]

Huntley, J. M.

Ina, H.

Jones, J. D. C.

Kadono, H.

Kaufmann, G. H.

Kerr, D.

Kilpatrick, J. M.

Kobayashi, S.

Madjarova, V. D.

Marroquin, J. L.

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. of Am. A 12, 2393–2400 (1995).
[CrossRef]

Mastin, G. A.

Moore, A. J.

Morgan, S. P.

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Ng, T. W.

T. W. Ng, “Carrier-modulated object step-loading method of automated analysis in digital speckle shearing interferometry,” J. Mod. Opt. 42, 2109–2118 (1995).
[CrossRef]

T. W. Ng, F. S. Chau, “Automated analysis in digital speckle shearing interferometry using an object step-loading method,” Opt. Commun. 108, 214–218 (1994).
[CrossRef]

T. W. Ng, K. T. Ang, “Data compression for speckle correlation interferometry temporal fringe pattern analysis,” submitted to Appl. Opt.

Paoletti, D.

D. Ambrosi, D. Paoletti, G. Schirripa Spagnalo, “Study of free-convective onset on a horizontal wire using speckle pattern interferometry,” Int. J. Heat Mass Transfer 46, 4145–4155 (2003).
[CrossRef]

Quiroga, J. A.

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Synchronous detection techniques for temporal fringe pattern analysis,” Opt. Commun. 204, 75–81 (2002).
[CrossRef]

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Sinusoidal least-squares fitting for temporal fringe pattern analysis,” J. Mod. Opt. 49, 2257–2266 (2002).
[CrossRef]

Reeves, M.

Rivera, M.

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. of Am. A 12, 2393–2400 (1995).
[CrossRef]

Robinson, D. W.

Romero, L. A.

Saldner, H.

Sawyer, N. B. E.

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Schirripa Spagnalo, G.

D. Ambrosi, D. Paoletti, G. Schirripa Spagnalo, “Study of free-convective onset on a horizontal wire using speckle pattern interferometry,” Int. J. Heat Mass Transfer 46, 4145–4155 (2003).
[CrossRef]

See, C. W.

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Shekunov, B. Y.

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Slettemoen, G. A.

Somekh, M. G.

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Takeda, M.

Villa, J.

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Sinusoidal least-squares fitting for temporal fringe pattern analysis,” J. Mod. Opt. 49, 2257–2266 (2002).
[CrossRef]

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Synchronous detection techniques for temporal fringe pattern analysis,” Opt. Commun. 204, 75–81 (2002).
[CrossRef]

Wei, A.

Wyant, J. C.

Yamada, T.

K. M. Hung, T. Yamada, “Phase unwrapping by regions using least squares approach,” Opt. Eng. 37, 2965–2970 (1998).
[CrossRef]

York, P.

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Appl. Opt. (5)

Exp. Fluids (1)

E. Astrakharchik-Farrimond, B. Y. Shekunov, P. York, N. B. E. Sawyer, S. P. Morgan, M. G. Somekh, C. W. See, “Dynamic measurements in supercritical flow using instantaneous phase-shift interferometry,” Exp. Fluids 33, 307–314 (2002).
[CrossRef]

Int. J. Heat Mass Transfer (1)

D. Ambrosi, D. Paoletti, G. Schirripa Spagnalo, “Study of free-convective onset on a horizontal wire using speckle pattern interferometry,” Int. J. Heat Mass Transfer 46, 4145–4155 (2003).
[CrossRef]

J. Mod. Opt. (2)

T. W. Ng, “Carrier-modulated object step-loading method of automated analysis in digital speckle shearing interferometry,” J. Mod. Opt. 42, 2109–2118 (1995).
[CrossRef]

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Sinusoidal least-squares fitting for temporal fringe pattern analysis,” J. Mod. Opt. 49, 2257–2266 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

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

J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. of Am. A 12, 2393–2400 (1995).
[CrossRef]

Opt. Commun. (2)

T. W. Ng, F. S. Chau, “Automated analysis in digital speckle shearing interferometry using an object step-loading method,” Opt. Commun. 108, 214–218 (1994).
[CrossRef]

J. Villa, J. A. Gomez-Pedrero, J. A. Quiroga, “Synchronous detection techniques for temporal fringe pattern analysis,” Opt. Commun. 204, 75–81 (2002).
[CrossRef]

Opt. Eng. (1)

K. M. Hung, T. Yamada, “Phase unwrapping by regions using least squares approach,” Opt. Eng. 37, 2965–2970 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

T. W. Ng, K. T. Ang, “Data compression for speckle correlation interferometry temporal fringe pattern analysis,” submitted to Appl. Opt.

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Figures (7)

Fig. 1
Fig. 1

Wavefront interferometry intensity fringe patterns with carrier modulation generated for (a) no deformation and (b) deformation. Intensity fringe patterns with carrier modulation recovered by use of the compression scheme for (c) no deformation and (d) deformation.

Fig. 2
Fig. 2

Speckle interferometry intensity fringe patterns with carrier modulation generated for (a) a single frame and (b) two subtracted frames, one with deformation. Intensity fringe patterns with the carrier modulation recovered by use of the compression scheme for (c) a single frame and (d) two subtracted frames, one with deformation.

Fig. 3
Fig. 3

Intensity distribution retrieved from a spatial point.

Fig. 4
Fig. 4

A, wrapped phase and B, unwrapped phase retrieved from the same spatial point as in Fig. 3. The phase corresponding to the constant carrier is marked C.

Fig. 5
Fig. 5

Deformation phase obtained by subtraction of the carrier phase from the unwrapped phase in Fig. 4.

Fig. 6
Fig. 6

Deformation phase retrieved for frames (a) 100 and (b) 391 for a rectangular region taken about the center of the wavefront interferometry fringe patterns.

Fig. 7
Fig. 7

Ratio of data points and average root-mean-square error of the phase retrieved, computed against the moduation cutoff value introduced by compression of the speckle interferometry fringe data set.

Equations (11)

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i ( x , y , k ) = r ( x , y ) + s ( x , y ) cos [ ϕ ( x , y ) + Δ ( x , y , k ) + ψ ( x , y , k ) ] .
i ( x , y , k ) = r ( x , y ) + t ( x , y , k ) + t * ( x , y , k ) ,
t ( x , y , k ) = ½ s ( x , y ) exp { i [ ϕ ( x , y ) + Δ ( x , y , k ) + ψ ( x , y , k ) ] }
I ( x , y , w ) = R ( x , y ) + T ( x , y , w ) + T * ( x , y , w ) .
Δ ( x , y , k ) + ψ ( x , y , k ) = tan 1 { Im [ t ( x , y , k ) ] Re [ t ( x , y , k ) ] } Δ ( x , y , 0 ) .
ratio of data points = N c / N o .
compression ratio = original file size / compressed file size .
original file size = N o * K * [ bit size ( intensity ) + bit size ( phase ) ] ,
compressed file size = N c * [ ( filter size × 32 bits ) + 16 bits ] + overhead .
compression ratio = 9.253 / ratio of data points .
e ( ) rms = { 1 N c K [ Δ ( x , y , k ) r Δ ( x , y , k ) ] 2 } 1 / 2 .

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