Abstract

High-speed in-line holography is used to visualize the trajectories of glass fibers being drawn out in a turbulent flame. To improve the signal-to-noise ratio, the images are not observed by a conventional reconstruction setup, but the holographic plate is placed directly on the input plane of a wavelet-transform optical system. This processing system is based on a VanderLugt correlator with inclusion of an electrically addressed spatial light modulator. The shape of the matched filters is deduced by successive rotation and dilatation operations of wavelet functions in the Fourier domain. We estimate the three-dimensional location of a fiber element and its orientation by searching for the daughter wavelet that yields the maximum intensity on the output plane of the correlator, which also contains the reconstructed image. The results are compared with those obtained by conventional optical reconstruction. The signal-to-noise ratios of the images observed on the output plane are improved. Moreover, it is shown that the axis coordinate accuracy is improved to Δz = ±50 µm, instead of ±0.5 mm for holographic reconstruction.

© 1999 Optical Society of America

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References

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  1. S. Belaïd, D. Lebrun, C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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1997 (1)

S. Belaïd, D. Lebrun, C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997).
[Crossref]

1996 (3)

1995 (3)

1994 (1)

1993 (4)

1992 (1)

C. Özkul, D. Lebrun, D. Allano, “Trajectographie automatique 3-D de fibres de verre restituées par holographie,” J. Opt. (Paris) 23, 207–214 (1992).
[Crossref]

1987 (1)

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[Crossref]

1976 (1)

R. Bexon, J. Gibbs, G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[Crossref]

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Allano, D.

C. Özkul, D. Lebrun, D. Allano, “Trajectographie automatique 3-D de fibres de verre restituées par holographie,” J. Opt. (Paris) 23, 207–214 (1992).
[Crossref]

Anderson, W. L.

Arneodo, A.

J. F. Muzy, E. Bacry, A. Arneodo, “Wavelets and multifractal formalism for singular signals: application to turbulence data,” Phys. Rev. Lett. 67, 3515–3518 (1996).
[Crossref]

Bacry, E.

J. F. Muzy, E. Bacry, A. Arneodo, “Wavelets and multifractal formalism for singular signals: application to turbulence data,” Phys. Rev. Lett. 67, 3515–3518 (1996).
[Crossref]

Belaïd, S.

S. Belaïd, D. Lebrun, C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997).
[Crossref]

Bexon, R.

R. Bexon, J. Gibbs, G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[Crossref]

Bishop, G. D.

R. Bexon, J. Gibbs, G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[Crossref]

Diao, H.

Francis, T. S. Y.

W. Meiyuan, Y. Shizhuo, P. Pursumarto, T. S. Y. Francis, “Wavelet matched filtering using a photorefractive crystal,” Opt. Commun. 99, 325–330 (1993).
[Crossref]

Garcia, J.

Gibbs, J.

R. Bexon, J. Gibbs, G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[Crossref]

Goodman, J. W.

Heddle, S.

S. Heddle, D. G. Vass, R. M. Sillitto, “Reduction of aliasing in correlation using a pixelated spatial light modulator,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE1772, 116–127 (1992).
[Crossref]

Joseph, J.

Kocatepe, M.

L. Onural, M. Kocatepe, “Family of scaling chirp functions, diffraction and holography,” IEEE Trans. Signal Process. 43, 1568–1578 (1995).
[Crossref]

Konforti, N.

Lebrun, D.

S. Belaïd, D. Lebrun, C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997).
[Crossref]

C. Özkul, D. Lebrun, D. Allano, “Trajectographie automatique 3-D de fibres de verre restituées par holographie,” J. Opt. (Paris) 23, 207–214 (1992).
[Crossref]

Lu, T.

Meiyuan, W.

W. Meiyuan, Y. Shizhuo, P. Pursumarto, T. S. Y. Francis, “Wavelet matched filtering using a photorefractive crystal,” Opt. Commun. 99, 325–330 (1993).
[Crossref]

Mendlovic, D.

Minemoto, T.

Muzy, J. F.

J. F. Muzy, E. Bacry, A. Arneodo, “Wavelets and multifractal formalism for singular signals: application to turbulence data,” Phys. Rev. Lett. 67, 3515–3518 (1996).
[Crossref]

Onural, L.

L. Onural, M. Kocatepe, “Family of scaling chirp functions, diffraction and holography,” IEEE Trans. Signal Process. 43, 1568–1578 (1995).
[Crossref]

L. Onural, “Diffraction from a wavelet point of view,” Opt. Lett. 18, 846–848 (1993).
[Crossref] [PubMed]

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[Crossref]

Our, T.

Ouzieli, I.

Özkul, C.

S. Belaïd, D. Lebrun, C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997).
[Crossref]

C. Özkul, D. Lebrun, D. Allano, “Trajectographie automatique 3-D de fibres de verre restituées par holographie,” J. Opt. (Paris) 23, 207–214 (1992).
[Crossref]

Pursumarto, P.

W. Meiyuan, Y. Shizhuo, P. Pursumarto, T. S. Y. Francis, “Wavelet matched filtering using a photorefractive crystal,” Opt. Commun. 99, 325–330 (1993).
[Crossref]

Roberge, D.

Scott, P. D.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[Crossref]

Sheng, Y.

Shizhuo, Y.

W. Meiyuan, Y. Shizhuo, P. Pursumarto, T. S. Y. Francis, “Wavelet matched filtering using a photorefractive crystal,” Opt. Commun. 99, 325–330 (1993).
[Crossref]

Sillitto, R. M.

S. Heddle, D. G. Vass, R. M. Sillitto, “Reduction of aliasing in correlation using a pixelated spatial light modulator,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE1772, 116–127 (1992).
[Crossref]

Szu, H.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Vass, D. G.

S. Heddle, D. G. Vass, R. M. Sillitto, “Reduction of aliasing in correlation using a pixelated spatial light modulator,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE1772, 116–127 (1992).
[Crossref]

Weaver, C. S.

Zalevsky, Z.

Appl. Opt. (7)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

IEEE Trans. Signal Process. (1)

L. Onural, M. Kocatepe, “Family of scaling chirp functions, diffraction and holography,” IEEE Trans. Signal Process. 43, 1568–1578 (1995).
[Crossref]

J. Aerosol Sci. (1)

R. Bexon, J. Gibbs, G. D. Bishop, “Automatic assessment of aerosol holograms,” J. Aerosol Sci. 7, 397–407 (1976).
[Crossref]

J. Opt. (Paris) (1)

C. Özkul, D. Lebrun, D. Allano, “Trajectographie automatique 3-D de fibres de verre restituées par holographie,” J. Opt. (Paris) 23, 207–214 (1992).
[Crossref]

Opt. Commun. (1)

W. Meiyuan, Y. Shizhuo, P. Pursumarto, T. S. Y. Francis, “Wavelet matched filtering using a photorefractive crystal,” Opt. Commun. 99, 325–330 (1993).
[Crossref]

Opt. Eng. (2)

S. Belaïd, D. Lebrun, C. Özkul, “Application of two dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947–1951 (1997).
[Crossref]

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

J. F. Muzy, E. Bacry, A. Arneodo, “Wavelets and multifractal formalism for singular signals: application to turbulence data,” Phys. Rev. Lett. 67, 3515–3518 (1996).
[Crossref]

Other (1)

S. Heddle, D. G. Vass, R. M. Sillitto, “Reduction of aliasing in correlation using a pixelated spatial light modulator,” in Optical Information Processing Systems and Architectures IV, B. Javidi, ed., Proc. SPIE1772, 116–127 (1992).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Reconstruction of a hologram by optical WT.

Fig. 2
Fig. 2

Reconstruction of an in-line hologram. (a) Intensity distribution recorded by the holographic plate, (b) reconstruction of the nearest fiber (z 1 = 9.0 mm), (c) reconstruction of the farthest fiber (z 2 = 18.5 mm).

Fig. 3
Fig. 3

Optical WT of an image represented by Fig. 2(a). (a) θ = 72.5°, a = 41.0 µm; (b) θ = 41°, a = 63.3 µm; (c) θ = 34°, a = 62.6 µm; (d) θ = 30°, a = 62.1 µm.

Fig. 4
Fig. 4

Three-dimensional representation of a trajectory.

Equations (16)

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Azx, y=1jλzexp2jπzλ  Aξ, ηexpjπλzx-ξ2+y-η2dξdη,
Aξ, η=1-rectξ|d=0  if -d/2ξd/2,=1  elsewhere
Azx=1λzexp-jπ4-+ Aξexpjπλzx-ξ2dξ.
hzx=exp-jπ/4λzexpjπx2λz.
Azx=Ax * hzx,
Izx=1-rectxd*hzx+h¯zx+rectxd * hzx2
tzx=p+rectxd * hzx+h¯zx,
tzx=p+rectxd * 2λzcosπx2λz-π4.
WTsa, b, c, θ=1a  sξ, ηψ¯rθξ-ba, η-cadξdη.
tzx=p+2πWTrecta, x, θ,
a=λzπ1/2.
ψGx, y=cosx2-π4-Mψexp-x2σx2+y2σy2.
WTtza, x=p+rectxd * h2zx+h¯2zx+2δx,
WTtza, x=2p+rectxd+12λz1/2rectxd * cosπx22λz-π4.
ψˆGu, v=σyπ cosπ2u2+12σx2exp-π2u2σx2+v2σy2-Mψσxσyπ exp-π2σx2u2+σy2v2,
ψˆGa,θu, v=aψˆGrθau, av.

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