Abstract

The optical properties of holographic kinoforms are described. It is shown that paraxial designs are not adequate for f /Nos. less than ~F/10. A nonparaxial design is introduced that retains the high diffraction efficiency of the paraxial designs, yet also produces an unaberrated diffracted wavefront for the design wavelength. Aberration calculations and computer calculations, based on the Huygens-Fresnel principle, of the point spread functions for these elements show the necessity of using the nonparaxial design. Specifications for a surface profile that takes account of the finite thickness of the diffracting surface are given. A model for kinoforms which can be used in optical design programs is proposed.

© 1989 Optical Society of America

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References

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  1. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  2. J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L Van Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883 (1970).
    [PubMed]
  3. G. G. Sliusarev, “Optical Systems with Phase Layers,” Sov. Phys. Dok. 2, 161 (1957).
  4. A. I. Tudorovskii, “An Objective with a Phase Plate,” Opt. Spectrosc. 6, 126 (1959).
  5. K. Miyamoto, “The Phase Fresnel Lens,” J. Opt. Soc. Am. 51, 17 (1961).
    [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 77–83.
  7. H. Dammann, “Blazed Synthetic Phase Only Holograms,” Op-tik 31, 95 (1970).
  8. L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolitho-graphic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232 (1972).
    [CrossRef]
  9. G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791 (1985).
    [CrossRef]
  10. W. C. Sweatt, “Describing Holographic Optical Elements as Lenses,” J. Opt. Soc. Am. 67, 803 (1977).
    [CrossRef]
  11. W. A. Kleinhans, “Aberrations of Curved Zone Plates and Fresnel Lenses,” Appl. Opt. 16, 1701 (1977).
    [CrossRef] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 370–375.
  13. R. Tatchyn, P. Csonka, I. Lindau, “A Unified Approach to the Theory and Design of Optimum Transmission Diffraction Systems in the Soft X-Ray Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 168 (1984).
  14. R. Kingslake, Lens Design Fundamentals (Academic, Orlando, 1978), pp. 112–113.
  15. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, 1986), pp. 152–153 and 226–234.
  16. Ref. 15, pp. 234–235.
  17. See, for example, H. H. Hopkins, “The Airy Disk Formula for Systems of High Relative Aperture,” Proc. Phys. Soc. London 55, 116 (1943);M. Mansuripur, “Distribution of Light at and Near the Focus of High-Numerical-Aperture Objectives,” J. Opt. Soc. Am. A 3, 2086 (1986).
    [CrossRef]
  18. ACCOS V is a trademark of Scientific Calculations, Inc., 7635 Main St., Fishers, New York 14453.

1985 (1)

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791 (1985).
[CrossRef]

1984 (1)

R. Tatchyn, P. Csonka, I. Lindau, “A Unified Approach to the Theory and Design of Optimum Transmission Diffraction Systems in the Soft X-Ray Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 168 (1984).

1977 (2)

1972 (1)

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolitho-graphic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232 (1972).
[CrossRef]

1970 (2)

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L Van Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883 (1970).
[PubMed]

H. Dammann, “Blazed Synthetic Phase Only Holograms,” Op-tik 31, 95 (1970).

1969 (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

1961 (1)

1959 (1)

A. I. Tudorovskii, “An Objective with a Phase Plate,” Opt. Spectrosc. 6, 126 (1959).

1957 (1)

G. G. Sliusarev, “Optical Systems with Phase Layers,” Sov. Phys. Dok. 2, 161 (1957).

1943 (1)

See, for example, H. H. Hopkins, “The Airy Disk Formula for Systems of High Relative Aperture,” Proc. Phys. Soc. London 55, 116 (1943);M. Mansuripur, “Distribution of Light at and Near the Focus of High-Numerical-Aperture Objectives,” J. Opt. Soc. Am. A 3, 2086 (1986).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 370–375.

Csonka, P.

R. Tatchyn, P. Csonka, I. Lindau, “A Unified Approach to the Theory and Design of Optimum Transmission Diffraction Systems in the Soft X-Ray Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 168 (1984).

d’Auria, L.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolitho-graphic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232 (1972).
[CrossRef]

Dammann, H.

H. Dammann, “Blazed Synthetic Phase Only Holograms,” Op-tik 31, 95 (1970).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 77–83.

Hirsch, P. M.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L Van Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883 (1970).
[PubMed]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Hopkins, H. H.

See, for example, H. H. Hopkins, “The Airy Disk Formula for Systems of High Relative Aperture,” Proc. Phys. Soc. London 55, 116 (1943);M. Mansuripur, “Distribution of Light at and Near the Focus of High-Numerical-Aperture Objectives,” J. Opt. Soc. Am. A 3, 2086 (1986).
[CrossRef]

Huignard, J. P.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolitho-graphic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232 (1972).
[CrossRef]

Jordan, J. A.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L Van Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883 (1970).
[PubMed]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, Orlando, 1978), pp. 112–113.

Kleinhans, W. A.

Lesem, L. B.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L Van Rooy, “Kinoform Lenses,” Appl. Opt. 9, 1883 (1970).
[PubMed]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Lindau, I.

R. Tatchyn, P. Csonka, I. Lindau, “A Unified Approach to the Theory and Design of Optimum Transmission Diffraction Systems in the Soft X-Ray Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 168 (1984).

Miyamoto, K.

Roy, A. M.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolitho-graphic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232 (1972).
[CrossRef]

Sliusarev, G. G.

G. G. Sliusarev, “Optical Systems with Phase Layers,” Sov. Phys. Dok. 2, 161 (1957).

Spitz, E.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolitho-graphic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232 (1972).
[CrossRef]

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791 (1985).
[CrossRef]

Sweatt, W. C.

Tatchyn, R.

R. Tatchyn, P. Csonka, I. Lindau, “A Unified Approach to the Theory and Design of Optimum Transmission Diffraction Systems in the Soft X-Ray Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 168 (1984).

Tudorovskii, A. I.

A. I. Tudorovskii, “An Objective with a Phase Plate,” Opt. Spectrosc. 6, 126 (1959).

Van Rooy, D. L

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791 (1985).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, 1986), pp. 152–153 and 226–234.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 370–375.

Appl. Opt. (2)

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The Kinoform: a New Wavefront Reconstruction Device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

Op-tik (1)

H. Dammann, “Blazed Synthetic Phase Only Holograms,” Op-tik 31, 95 (1970).

Opt. Commun. (1)

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolitho-graphic Fabrication of Thin Film Lenses,” Opt. Commun. 5, 232 (1972).
[CrossRef]

Opt. Eng. (1)

G. J. Swanson, W. B. Veldkamp, “Binary Lenses for Use at 10.6 Micrometers,” Opt. Eng. 24, 791 (1985).
[CrossRef]

Opt. Spectrosc. (1)

A. I. Tudorovskii, “An Objective with a Phase Plate,” Opt. Spectrosc. 6, 126 (1959).

Proc. Phys. Soc. London (1)

See, for example, H. H. Hopkins, “The Airy Disk Formula for Systems of High Relative Aperture,” Proc. Phys. Soc. London 55, 116 (1943);M. Mansuripur, “Distribution of Light at and Near the Focus of High-Numerical-Aperture Objectives,” J. Opt. Soc. Am. A 3, 2086 (1986).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. Tatchyn, P. Csonka, I. Lindau, “A Unified Approach to the Theory and Design of Optimum Transmission Diffraction Systems in the Soft X-Ray Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 503, 168 (1984).

Sov. Phys. Dok. (1)

G. G. Sliusarev, “Optical Systems with Phase Layers,” Sov. Phys. Dok. 2, 161 (1957).

Other (6)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 77–83.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 370–375.

R. Kingslake, Lens Design Fundamentals (Academic, Orlando, 1978), pp. 112–113.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, 1986), pp. 152–153 and 226–234.

Ref. 15, pp. 234–235.

ACCOS V is a trademark of Scientific Calculations, Inc., 7635 Main St., Fishers, New York 14453.

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Figures (6)

Fig. 1
Fig. 1

Point spread functions for 50-mm focal length, paraxial design kinoforms. The solid line is an F/10 element; the dashed line is an F/5 element. Each curve is normalized such that the peak intensity for an unaberrated diffracted wavefront is 1.0.

Fig. 2
Fig. 2

Point spread functions for nonparaxial design kinoforms, λ = λ0 = 0.58756 μm; (a) F/10 kinoform; (b) F/2.5 kinoform.

Fig. 3
Fig. 3

Diffraction efficiency as a function of wavelength for diffracted orders n = 0,1, and 2. The design wavelength is λ0 = 0.58756 μm. Note that η = 1.0 for n = 1 and λ = λ0.

Fig. 4
Fig. 4

Point spread functions for nonparaxial design kinoforms for three wavelengths. Each PSF was calculated in the paraxial focal plane for the wavelength of interest; (a) F/10 kinoform; (b) F/5 kinoform.

Fig. 5
Fig. 5

Geometry and notation for the design of a finite thickness kinoform.

Fig. 6
Fig. 6

Comparison of Huygens-Fresnel and ultrahigh index model calculations of point spread functions. The solid line is the Huygens-Fresnel result and the dashed line is the ACCOS v calculation; (a) nonparaxial design, F/5 kinoform, λ = 0.48613 μm (hydrogen-F line); (b) paraxial design, F/5 kinoform, λ =λ0 = 0.58756 μm.

Equations (37)

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t lens ( x , y ; λ ) = exp [ i π ( x 2 + y 2 ) λ f ] .
r m 2 = 2 m λ 0 f + ( m λ 0 ) 2 .
r m ,paraxial 2 = 2 m λ 0 f .
d max = λ 0 n ( λ 0 ) 1 .
ϕ ( r ) = α 2 π ( m r 2 2 λ 0 f )  , for  r m r < r m + 1  ,
ϕ ( ξ ) = α 2 π ( m ξ ) , for  m ξ < m + 1.
α = λ 0 n ( λ ) 1 λ n ( λ 0 ) 1 .
t ( ξ ) = exp [ i ϕ ( ξ ) ] = n = c n exp ( i 2 π n ξ )  ,
c n = exp [ i π ( α + n ) ] π ( α + n ) sin [ π ( α + n ) ] .
t ( r ) = n = exp [ i π ( α n ) ] sin c ( α n ) exp [ i π r 2 λ 0 ( f / n ) ]  ,
sin c ( x ) = sin ( π x ) π x .
f kinoform = λ 0 λ f n .
η = c n c n * = sin c 2 ( α n ) .
ϕ sph ( r ) = 2 π λ [ ζ ζ 2 + r 2 ] = 2 π λ ( r 2 2 ζ + r 4 8 ζ 3 + )  ,
π 1 ( λ ) = h ( 4 f / # ) 3 ( λ λ 0 ) 3 ,
Ψ II ( x , y , z ) = i λ   Ψ I ( ξ , η , 0 ) exp ( i k R ) R X ( θ ) d ξ d η  ,
R Fres = z + x 2 + y 2 + ξ 2 + η 2 2 x ξ 2 y η 2 z .
Ψ I I Fres ( x , y , z ) = i exp [ i k z + i k 2 z ( x 2 + y 2 ) ] λ z × FT { Ψ I ( ξ , η , 0 ) X ( θ ) exp [ i π λ z ( ξ 2 + η 2 ) ] }  ,
exp ( i k R ) = exp [ i 2 π λ z ( x ξ + y η ) ] exp [ i 2 π λ z ( x ξ + y η ) ] exp ( i k R ) .
Ψ II ( x , y , z ) = 1 λ z FT { Ψ I ( ξ , η , 0 ) X ( θ ) exp [ i k R + i 2 π ( f ξ ξ + f η η ) ] } .
ϕ ( r ) = α 2 π ( m f 2 + r 2 f λ 0 )  , for  r m r < r m + 1  ,
π 1 ( λ ) = h ( 4 f / No . ) 3 ( λ 3 λ λ 0 2 λ 0 3 ) .
s min = 2 λ 0 f / No .
n ( λ 0 ) s ( r ) + ( f + m λ 0 ) = [ f s ( r ) ] 2 + r 2 .
[ s ( r ) s 0 ] 2 a 2 r 2 b 2 = 1 ,
s 0 = n ( λ 0 ) [ f + m λ 0 ] f n 2 ( λ 0 ) 1 ,
a 2 = [ n ( λ 0 ) f f m λ 0 ] 2 [ n 2 ( λ 0 ) 1 ] 2 ,
b 2 = [ n ( λ 0 ) f f m λ 0 ] 2 n 2 ( λ 0 ) 1 .
e = a 2 + b 2 a = n ( λ 0 ) .
s ( r ) = m λ 0 n ( λ 0 ) 1 + c r 2 1 + 1 ( κ + 1 ) c 2 r 2 .
c = 1 f [ 1 n ( λ 0 ) ] + m λ 0 ,
κ = n 2 ( λ 0 ) .
c thin = 1 f [ 1 n ( λ 0 ) ]  ,
κ thin = [ n ( λ 0 ) 1 ] 2 1.
c = 1 f [ 1 n s ( λ 0 ) ] .
I ( 0 , 0 , z ) = sin 2 ( π λ 0 f N λ z ) ( π N ) 2 ( 1 α λ z λ 0 f ) 2 { cos ( α π ) sin ( α π ) tan [ ( π λ 0 f ) / ( λ z ) ] } 2 .
I ( 0 , 0 , λ 0 f λ n ) = n 2 sin c 2 ( α n ) = n 2 η .

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