Abstract

We investigated the design of two broadband hybrid diffractive–refractive optical systems, a landscape lens, and a Schmidt telescope. The systems were achromatized by using the characteristically large negative dispersion of kinoforms. In the scalar wave regime kinoforms can approach 100% efficiency but only for one object point and wavelength. We evaluated polychromatic image quality, accounting for diffraction efficiency, by constructing weighted geometric point-spread functions from several diffracted orders and then calculating modulation transfer functions (MTF’s). The MTF’s of the hybrid achromats were improved at high spatial frequencies but were reduced at low frequencies because of diffraction into nondesign orders.

© 1992 Optical Society of America

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References

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  1. J. L. Soret, “Concerning the diffraction phenomena generated by means of circular gratings,” Ann Phys. 156, 99–113 (1875).
    [CrossRef]
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    [CrossRef] [PubMed]
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  6. M. J. Hayford, “Optical design of holographic optical element (HOE) construction optics,” in 1985 International Lens Design Conference, D. T. Moore, W. Taylor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.554, 502–509 (1985).
    [CrossRef]
  7. W. C. Sweatt, “Describing holographic optical elements as lenses,” J. Opt. Soc. Am. 67, 803 (1977).
    [CrossRef]
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    [CrossRef] [PubMed]

1989 (1)

1985 (1)

K. Firth, “Recent developments in diffractive optics,” GEC J. Res. 3, 1–10 (1985).

1977 (1)

1975 (1)

1875 (1)

J. L. Soret, “Concerning the diffraction phenomena generated by means of circular gratings,” Ann Phys. 156, 99–113 (1875).
[CrossRef]

Buralli, D. A.

Firth, K.

K. Firth, “Recent developments in diffractive optics,” GEC J. Res. 3, 1–10 (1985).

Hayford, M. J.

M. J. Hayford, “Optical design of holographic optical element (HOE) construction optics,” in 1985 International Lens Design Conference, D. T. Moore, W. Taylor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.554, 502–509 (1985).
[CrossRef]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).

Morris, G. M.

Plummer, W. T.

Rogers, J. R.

Soret, J. L.

J. L. Soret, “Concerning the diffraction phenomena generated by means of circular gratings,” Ann Phys. 156, 99–113 (1875).
[CrossRef]

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854, MIT Lincoln Laboratory (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1989).

Sweatt, W. C.

Ann Phys. (1)

J. L. Soret, “Concerning the diffraction phenomena generated by means of circular gratings,” Ann Phys. 156, 99–113 (1875).
[CrossRef]

Appl. Opt. (2)

GEC J. Res. (1)

K. Firth, “Recent developments in diffractive optics,” GEC J. Res. 3, 1–10 (1985).

J. Opt. Soc. Am. (1)

Other (3)

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854, MIT Lincoln Laboratory (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1989).

M. J. Hayford, “Optical design of holographic optical element (HOE) construction optics,” in 1985 International Lens Design Conference, D. T. Moore, W. Taylor, eds., Proc. Soc. Photo-Opt. Instrum. Eng.554, 502–509 (1985).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Hybrid (refractive–diffractive) model of a blazed grating that is used to derive efficiency behavior of a kinoform.

Fig. 2
Fig. 2

Diffraction efficiency varies with diffracted order and wavelength. The light in nondesign orders affects image quality.

Fig. 3
Fig. 3

Transverse ray aberration of the Fresnel (or blaze) surface superimposed upon those of three diffracted orders.

Fig. 4
Fig. 4

How diffraction efficiency can be calculated from ray trace data.

Fig. 5
Fig. 5

Two design examples of hybrid achromatized systems. For the landscape lens the material is acrylic (PMMA), nd = 1.4917, VF,C = 57.2, the effective focal length is 114.3 mm, the f-number is 9.2, the field of view is ± 18°, and the wavelengths are 656, 588, and 546 nm. For the Schmidt telescope the material is BK7 glass, nd = 1.5168, VF,C = 64.2, the effective focal length is 500 mm, the f-number is 2.0, the field of view is ±5°, and the wavelengths are 656, 688, and 486 nm.

Fig. 6
Fig. 6

On-axis transverse ray aberration for the design order m = 1. For the landscape lens (a) the wavelengths are 546, 588, and 656 nm, which are represented by the dashed, solid, and dotted curves, respectively. For the Schmidt telescope (b) the wavelengths are 486, 588, and 656 nm, which are represented by the dash ed, solid, and dotted curves, respectively.

Fig. 7
Fig. 7

Superimposed transverse aberrations for on-axis object point.

Fig. 8
Fig. 8

Geometric MTF curves for on-axis field points.

Tables (1)

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Table I Geometric Spot Sizes and Diffraction Efficiencies (On Axis)

Equations (7)

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n sin ( α - θ ) = n sin ( α - θ 0 ) ,
d [ n sin ( α - θ ) - n sin ( α - θ m ) ] = m λ ,
n sin ( α - β - θ ) = n sin ( α - β - θ β ) .
( m , λ ) = sinc 2 { π [ m - m 0 λ 0 Δ n ( λ 0 ) Δ n ( λ ) λ ] } ,
m = sinc 2 [ 2 π Δ m F Δ 02 ] .
MTF corr ¯ MTF 012             for frequencies > 0 , MTF corr = 1             for frequency = 0.
MTF x ( ν ) 1 - 2 π 2 B x 2 ν 2 .

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