Abstract

An analytic design of hybrid achromats that combine refractive and diffractive elements is presented. The design procedure does not rely on paraxial approximations and involves two separate stages. In the first stage the chromatic aberrations are corrected for the paraxial rays, and in the second stage the spherical aberrations are corrected by addition of an aspherical phase function to the diffractive element. The residual spherochromatic aberrations of the achromat are evaluated both analytically and numerically, with good agreement between the results. Finally, we illustrate the design procedure by designing a plano–convex achromat for IR radiation with little chromatic dispersion.

© 1993 Optical Society of America

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References

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  1. R. H. Katyal, “Compensating optical systems. Parts 1–3,” Appl. Opt. 11, 1241–1260 (1972).
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    [CrossRef] [PubMed]
  3. G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
  4. K. E. Spaulding, G. M. Morris, “Achromatic waveguide lenses,” Appl. Opt. 30, 2558–2569 (1991).
    [CrossRef] [PubMed]
  5. R. Kingslate, Lens Design Fundamentals (Academic, New York, 1978), p. 115.
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    [CrossRef]
  7. A. R. Peaker, Properties of Galluim Arsenide (Institute of Electrical Engineers, London, 1990), p. 250.
  8. D. H. Close, “Holographic optical elements,” Opt. Eng. 14, 408–413 (1975).
  9. E. Hasman, N. Davidson, A. A. Friesem, “Efficient multilevel phase holograms for CO2 lasers,” Opt. Lett. 16, 423–425 (1991).
    [CrossRef] [PubMed]

1991 (2)

1989 (1)

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

1988 (1)

1986 (1)

1975 (1)

D. H. Close, “Holographic optical elements,” Opt. Eng. 14, 408–413 (1975).

1972 (1)

Close, D. H.

D. H. Close, “Holographic optical elements,” Opt. Eng. 14, 408–413 (1975).

Davidson, N.

Felsen, L. B.

Friesem, A. A.

George, N.

Hasman, E.

Katyal, R. H.

Kingslate, R.

R. Kingslate, Lens Design Fundamentals (Academic, New York, 1978), p. 115.

Morris, G. M.

Peaker, A. R.

A. R. Peaker, Properties of Galluim Arsenide (Institute of Electrical Engineers, London, 1990), p. 250.

Spaulding, K. E.

Stone, T.

Swanson, G. J.

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

Veldkamp, W. B.

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

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

D. H. Close, “Holographic optical elements,” Opt. Eng. 14, 408–413 (1975).

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

Opt. Lett. (1)

Other (2)

A. R. Peaker, Properties of Galluim Arsenide (Institute of Electrical Engineers, London, 1990), p. 250.

R. Kingslate, Lens Design Fundamentals (Academic, New York, 1978), p. 115.

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of a hybrid diffractive–refractive achromat.

Fig. 2
Fig. 2

Variation of the focal distance as a function of the distance of the incoming ray from the optical axis of the GaAs singlet at wavelengths of 8 μm (solid curve), 10 μm (dashed curve), and 12 μm (dashed–dotted curve).

Fig. 3
Fig. 3

Variation of the focal distance as a function of the distance of the incoming ray from the optical axis of the simple paraxial (spherical) hybrid achromat at a 10-μm wavelength.

Fig. 4
Fig. 4

Variation of the focal distance as a function of distance of the incoming ray from the optical axis of the aspheric hybrid achromat at wavelengths of 8 μm (solid curve), 10 μm (dashed line), and 12 μm (dashed–dotted curve).

Fig. 5
Fig. 5

Variation of the focal distance as a function of the distance of the incoming ray from the optical axis of the improved aspheric hybrid achromat (chromatic aberrations corrected for the zonal ray) at wavelengths of 8 μm (solid curve), 10 μm (dashed line) and 12 μm (dashed–dotted curve).

Equations (18)

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V r = n d 1 n f n c ,
V d = λ d λ f λ c .
f d , 0 = F ( V d V r V d ) , f r , 0 = F ( V r V d V r ) .
S = y 2 f r , 0 2 ( G 1 c 3 G 2 c 2 c 1 + G 3 c 2 υ 1 + G 4 c c 1 2 G 5 c c 1 υ 1 + G 6 c υ 1 2 ) ,
S = y 2 ( n 1 ) 3 f r , 0 ( G 1 G 2 + G 4 ) ,
G 1 = 1 2 n 2 ( n 1 ) , G 2 = 1 2 ( 2 n + 1 ) ( n 1 ) , G 4 = 1 2 ( n + 2 ) ( n 1 ) / n .
f r ( y ) f r , 0 + a y 2 ,
a = ( G 1 G 2 + G 4 ) / f r , 0 ( n 1 ) 3 ,
1 f r ( y ) + 1 f d ( y ) = 1 F = const . ,
f d ( y ) = f r ( y ) F f r ( y ) F .
d ϕ ( y ) d y = 2 π λ d y [ y 2 + f d 2 ( y ) ] 1 / 2 .
f d ( y ) f d , 0 + a y 2 ,
a = a ( f d , 0 / f r , 0 ) 2 .
ϕ ( y ) = 2 π λ d a ln { 2 a [ a 2 y 4 + ( 2 f d , 0 a + 1 ) y 2 + f d , 0 2 ] 1 / 2 + 2 a 2 y 2 + 2 a f d , 0 + 1 } .
1 f additional ( M , λ d ) 1 F 1 F + S .
f additional ( M , λ ) = f additional ( M , λ d ) λ d / λ .
1 f aspheric ( M , λ ) 1 f spheric ( M ) + 1 f additional ( M , λ ) .
f aspheric ( M , λ c ) f aspheric ( M , λ f ) S δλ / λ d ,

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