Abstract

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik’s coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. J. A. Davis and M. D. Nowak, Appl. Opt. 41, 4835 (2002).
    [CrossRef] [PubMed]
  4. P. P. Banerjee, D. Cao, T.-C. Poon, Appl. Opt. 37, 7532 (1998).
    [CrossRef]
  5. P. Hariharan, Optical Holography (Cambridge U. Press, Cambridge, 1996).
    [CrossRef]
  6. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Springer-Verlag, Berlin, 1997).
  7. S. K. Case, Opt. Lett. 4, 286 (1979).
    [CrossRef] [PubMed]
  8. D. Peri and A. A. Friesem, Opt. Lett. 3, 124 (1978).
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  9. H. J. Coufal, D. Psaltis, and B. T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000).
    [CrossRef]
  10. S. Blaya, L. Carretero, R. Mallavia, A. Fimia, R. F. Madrigal, M. Ulibarrena, and D. Levy, Appl. Opt. 37, 7604 (1998).
    [CrossRef]
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    [CrossRef]
  12. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
    [CrossRef]

2002 (2)

J. A. Davis and M. D. Nowak, Appl. Opt. 41, 4835 (2002).
[CrossRef] [PubMed]

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

1998 (3)

1996 (1)

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, Opt. Commun. 128, 1 (1996).
[CrossRef]

1979 (1)

1978 (1)

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Banerjee, P. P.

Beléndez, A.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

Blaya, S.

Cao, D.

Carretero, L.

Case, S. K.

Coufal, H. J.

H. J. Coufal, D. Psaltis, and B. T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000).
[CrossRef]

Davis, J. A.

Dunn, D. B.

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, Opt. Commun. 128, 1 (1996).
[CrossRef]

Fimia, A.

Friesem, A. A.

Gallego, S.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

García, C.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Holography (Cambridge U. Press, Cambridge, 1996).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Levy, D.

Madrigal, R. F.

Mallavia, R.

Neipp, C.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

Nowak, M. D.

Ortuño, M.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

Pascual, I.

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

Peri, D.

Poon, T.-C.

Psaltis, D.

H. J. Coufal, D. Psaltis, and B. T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000).
[CrossRef]

Sincerbox, B. T.

H. J. Coufal, D. Psaltis, and B. T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000).
[CrossRef]

Turunen, J.

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Springer-Verlag, Berlin, 1997).

Ulibarrena, M.

Wyrowski, F.

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Springer-Verlag, Berlin, 1997).

Xia, J.

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, Opt. Commun. 128, 1 (1996).
[CrossRef]

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Opt. Commun. (2)

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, Opt. Commun. 128, 1 (1996).
[CrossRef]

S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, Opt. Commun. 215, 263 (2002).
[CrossRef]

Opt. Lett. (2)

Other (3)

H. J. Coufal, D. Psaltis, and B. T. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000).
[CrossRef]

P. Hariharan, Optical Holography (Cambridge U. Press, Cambridge, 1996).
[CrossRef]

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Springer-Verlag, Berlin, 1997).

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Figures (4)

Fig. 1
Fig. 1

Setup for image formation with a holographic grating. We show the deviation of the transmitted and the diffracted images caused by the grating.

Fig. 2
Fig. 2

Angular response in intensity, from experiment and from Kogelnik’s fit, for the photopolymer grating used. We used a He–Ne laser beam λ=633 nm. Bragg angle, 20.8°; Q300.

Fig. 3
Fig. 3

Simulated results of the effect of the zero-order transfer function on an input image: (a) object, a slit of 70µm width; (b) frequency content of the object as a function of angle θo (scaled with λ=633 nm); (c) zero-order transfer function of the photopolymer; (d) resultant filtered image.

Fig. 4
Fig. 4

Experimental images: (a) direct image with no grating, (b) zero-order filtered image.

Equations (6)

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

R=exp-jξcosv2+ξ2+jξ sincv2+ξ2,
S=exp-jξ-jvsincv2+ξ2,
v=πΔndλ0 cos θr, ξ=πdΛ cos θrsin θr-λ02n0Λ,
ξ=QΛ4πp, v=πΔndλ0,
H0p=exp-jQΛ4πpcosQΛ4πp+πΔndλ021/2+jQΛ4πpsincQΛ4πp2+πΔndλ021/2,
H1p=exp-jQΛ4πp-jπΔndλ0×sincQΛ4πp2+πΔndλ021/2.

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