Abstract

Based on the matrix description of the fractional Talbot effect, a new and effective method to numerically optimize diffractive optical elements that work in the Fresnel diffraction regime is described. When the investigation is restricted to spatially quantized phase-only gratings, diffraction can be described in terms of the fractional Talbot effect and the diffraction amplitude is efficiently evaluated from a finite set of sampling points. As an illustrating example we numerically optimize Talbot array illuminators. Our results show that a limited number of discrete phase levels does not imply a limited compression ratio but does lead to a reduced diffraction efficiency. Experimental results obtained from lithographically fabricated surface-relief gratings are compared with our theoretical designs.

© 1999 Optical Society of America

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1998 (2)

1997 (1)

1996 (7)

1995 (3)

1994 (4)

1990 (2)

1989 (1)

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. (Bellingham) 28, 605–608 (1989).
[CrossRef]

1988 (1)

A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. (Bellingham) 19, 297–305 (1980).
[CrossRef]

1971 (1)

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

1967 (1)

1965 (1)

Arimoto, Y.

Arrizón, V.

Bryngdahl, O.

O. Bryngdahl, F. Wyrowski, “Digital holography—computer generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.

Dammann, H.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

Dorsch, R. G.

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. (Bellingham) 19, 297–305 (1980).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Goncharenko, A. M.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 57–76.

Görtler, K.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Hamam, H.

Ibarra, J. G.

V. Arrizón, J. G. Ibarra, A. Serrano-Heredia, “Split Talbot array illuminators,” Opt. Commun. 123, 63–70 (1996).
[CrossRef]

V. Arrizón, J. G. Ibarra, J. Ojeda-Castañeda, “Matrix formulation of the Fresnel transform of complex transmittance gratings,” J. Opt. Soc. Am. A 13, 2414–2422 (1996).
[CrossRef]

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

Jahns, J.

M. Testorf, J. Jahns, “Planar-integrated Talbot array illuminators,” Appl. Opt. 37, 5399–5407 (1998).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

Khilo, N. A.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

Klaus, W.

Kodate, K.

Leger, J. R.

Lohmann, A. W.

López-Olazagasti, E.

Mait, J. N.

Ojeda-Castañeda, J.

Paris, D. P.

Pellat-Finet, P.

Piestun, R.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Serrano-Heredia, A.

V. Arrizón, J. G. Ibarra, A. Serrano-Heredia, “Split Talbot array illuminators,” Opt. Commun. 123, 63–70 (1996).
[CrossRef]

V. Arrizón, E. López-Olazagasti, A. Serrano-Heredia, “Talbot array illuminators with optimum compression ratio,” Opt. Lett. 21, 233–235 (1996).
[CrossRef] [PubMed]

Shamir, J.

Sinzinger, S.

Spektor, B.

Suleski, T. J.

Swanson, G. J.

J. R. Leger, G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional Talbot planes,” Opt. Lett. 15, 288–290 (1990).
[CrossRef] [PubMed]

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. (Bellingham) 28, 605–608 (1989).
[CrossRef]

Testorf, M.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. (Bellingham) 28, 605–608 (1989).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Winthrop, J. T.

Worthington, C. R.

Wyrowski, F.

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990).
[CrossRef]

O. Bryngdahl, F. Wyrowski, “Digital holography—computer generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Opt. Commun. (5)

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

H. Hamam, “Design of Talbot array illuminators,” Opt. Commun. 131, 359–370 (1996).
[CrossRef]

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

V. Arrizón, J. G. Ibarra, A. Serrano-Heredia, “Split Talbot array illuminators,” Opt. Commun. 123, 63–70 (1996).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

Opt. Eng. (Bellingham) (2)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer generated holograms,” Opt. Eng. (Bellingham) 19, 297–305 (1980).
[CrossRef]

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. (Bellingham) 28, 605–608 (1989).
[CrossRef]

Opt. Lett. (4)

Optik (Stuttgart) (1)

A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).

Other (3)

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 57–76.

O. Bryngdahl, F. Wyrowski, “Digital holography—computer generated holograms,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1990), Vol. XXVIII.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

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