Abstract

We demonstrate an imaging diffractive optical element (DOE) that is free of coma and other first-order aberrations. The DOE was holographically recorded on a properly curved surface and thereby satisfies the Abbe sine (aplanatic) condition. Experimental results as well as numerical ray-tracing simulations indicate that the off-axis aberrations of the curved DOE are much smaller than those of a flat DOE. Because the recording of the DOE involves a single step and only readily available spherical and plane waves, it is extremely simple.

© 2001 Optical Society of America

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References

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2000 (1)

1998 (1)

1992 (1)

A. Talatinian, “Aberration characteristics of curved holographic optical elements for Fourier transform,” Optik (Stuttgart) 89, 151–158 (1992).

1991 (2)

E. Jagoszewski, A. Talatinian, “Design considerations for Fourier transform holographic elements recorded on a curved substrate,” Optik (Stuttgart) 88, 20–24 (1991).

Y. Amitai, I. A. Erteza, J. W. Goodman, “Recursive design of a holographic focusing grating coupler,” Appl. Opt. 30, 3886–3890 (1991).
[CrossRef] [PubMed]

1990 (1)

Y. Amitai, J. W. Goodman, “Recording an efficient holographic optical element from computer generated holograms,” Opt. Commun. 80, 107–109 (1990).
[CrossRef]

1989 (1)

1988 (1)

1987 (1)

Y. Amitai, A. A. Friesem, “Recursive design techniques for Fourier transform holographic lenses,” Opt. Eng. 26, 1133–1139 (1987).
[CrossRef]

1986 (1)

H. P. Herzig, “Holographic optical elements (HOEs) for semiconductor lasers,” Opt. Commun. 58, 144–148 (1986).
[CrossRef]

1984 (1)

1983 (1)

1982 (1)

R. C. Fairchild, R. J. Fienup, “Computer-originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).

1979 (1)

1975 (2)

D. H. Close, “Holographic optical elements,” Opt. Eng. 14, 408–419 (1975).
[CrossRef]

W. T. Welford, “Practical design of an aplanatic hologram lens for focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

1973 (1)

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

1970 (1)

Amitai, Y.

Close, D. H.

D. H. Close, “Holographic optical elements,” Opt. Eng. 14, 408–419 (1975).
[CrossRef]

Davidson, N.

Erteza, I. A.

Fairchild, R. C.

R. C. Fairchild, R. J. Fienup, “Computer-originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).

Fienup, J. R.

Fienup, R. J.

R. C. Fairchild, R. J. Fienup, “Computer-originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).

Friesem, A. A.

Goodman, J. W.

Y. Amitai, I. A. Erteza, J. W. Goodman, “Recursive design of a holographic focusing grating coupler,” Appl. Opt. 30, 3886–3890 (1991).
[CrossRef] [PubMed]

Y. Amitai, J. W. Goodman, “Recording an efficient holographic optical element from computer generated holograms,” Opt. Commun. 80, 107–109 (1990).
[CrossRef]

Guedalia, J. L.

Hasman, E.

Herzig, H. P.

H. P. Herzig, “Holographic optical elements (HOEs) for semiconductor lasers,” Opt. Commun. 58, 144–148 (1986).
[CrossRef]

Hirsch, P. M.

Jagoszewski, E.

E. Jagoszewski, A. Talatinian, “Design considerations for Fourier transform holographic elements recorded on a curved substrate,” Optik (Stuttgart) 88, 20–24 (1991).

Jordan, J. A.

Kedmi, J.

Kritchman, E. M.

Lee, W. H.

W. H. Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. XVI, pp. 119–232.
[CrossRef]

Lesem, L. B.

Oron, R.

Reinhorn, S.

Talatinian, A.

A. Talatinian, “Aberration characteristics of curved holographic optical elements for Fourier transform,” Optik (Stuttgart) 89, 151–158 (1992).

E. Jagoszewski, A. Talatinian, “Design considerations for Fourier transform holographic elements recorded on a curved substrate,” Optik (Stuttgart) 88, 20–24 (1991).

Van Rooy, D. L.

Welford, W. T.

W. T. Welford, “Practical design of an aplanatic hologram lens for focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

W. T. Welford, “Aplanatism and isoplanatism,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIII, pp. 267–296.
[CrossRef]

Winick, K. A.

Yekutieli, G.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (4)

Y. Amitai, J. W. Goodman, “Recording an efficient holographic optical element from computer generated holograms,” Opt. Commun. 80, 107–109 (1990).
[CrossRef]

H. P. Herzig, “Holographic optical elements (HOEs) for semiconductor lasers,” Opt. Commun. 58, 144–148 (1986).
[CrossRef]

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

W. T. Welford, “Practical design of an aplanatic hologram lens for focal length 50 mm and numerical aperture 0.5,” Opt. Commun. 15, 46–49 (1975).
[CrossRef]

Opt. Eng. (3)

Y. Amitai, A. A. Friesem, “Recursive design techniques for Fourier transform holographic lenses,” Opt. Eng. 26, 1133–1139 (1987).
[CrossRef]

R. C. Fairchild, R. J. Fienup, “Computer-originated hologram lenses,” Opt. Eng. 21, 133–140 (1982).

D. H. Close, “Holographic optical elements,” Opt. Eng. 14, 408–419 (1975).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (2)

E. Jagoszewski, A. Talatinian, “Design considerations for Fourier transform holographic elements recorded on a curved substrate,” Optik (Stuttgart) 88, 20–24 (1991).

A. Talatinian, “Aberration characteristics of curved holographic optical elements for Fourier transform,” Optik (Stuttgart) 89, 151–158 (1992).

Other (2)

W. T. Welford, “Aplanatism and isoplanatism,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIII, pp. 267–296.
[CrossRef]

W. H. Lee, “Computer generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. XVI, pp. 119–232.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Configuration of an imaging system: a and b are the object and the image distances, respectively, from the surface I. A and B are the on-axis object and image points, respectively, and α and β are arbitrary angles of the input and the output beams, respectively.

Fig. 2
Fig. 2

Geometrical arrangements for recording a curved DOE that satisfies the Abbe sine condition. MO, microscope objective.

Fig. 3
Fig. 3

Setup for measuring the reconstruction performance of the curved and the flat DOEs. A, movable aperture; RD, rotating diffuser; S, white screen.

Fig. 4
Fig. 4

Experimental results for focusing with flat and curved diffractive elements: (a) flat DOE with Θ = 0°, (b) flat DOE with Θ = 5°, (c) curved DOE with Θ = 0°, (d) curved DOE with Θ = 5°. The entrance aperture of the imaging system was 60 mm, and the focal length was 35 mm.

Fig. 5
Fig. 5

Spot sizes for flat (squares) and curved (diamonds) DOEs plotted as functions of Θ x . The entrance aperture of the imaging system was 60 mm, and the focal length was 35 mm, for both cases.

Fig. 6
Fig. 6

Focal spots obtained from ray-tracing simulations for (a) a flat and (b) a curved DOE with NA = 0.7, a focal length of F = 35 mm, and an angular separation of 2° between adjacent spots.

Fig. 7
Fig. 7

Ratio between the combined aberrations of the flat and the curved DOEs plotted as a function of the NA for Θ x = 2° (solid curve) and Θ x = 5° (dashed curve), as obtained from ray-tracing simulations.

Equations (2)

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sin α/sin β=constant=-b/a=-M,
R=ab/a+b,

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