Abstract

Design procedures for simple two- and three-element diffractive telescopes, suitable for monochromatic applications, are described. We obtained the basic configuration for the two-element design analytically by solving design equations to set the Seidel aberrations to target values. Computer optimization is used to complete the design of the doublet and triplet telescopes. The two- and three-element designs exhibit similar optical performance and diffraction efficiency. We show that diffraction-limited performance can be obtained from these all-diffractive systems.

© 1992 Optical Society of America

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References

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  1. P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); see also J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 142–149 (1989); G. M. Morris, D. A. Buralli, “Wide field diffractive lenses for imaging, scanning, and Fourier transformation,” Opt. News 15, 41–42 (1989).
    [CrossRef]
  2. L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
    [CrossRef]
  3. V. P. Koronkevich, “Computer synthesis of diffraction optical elements,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, San Diego, Calif., 1989), pp. 277–313.
  4. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969); see also J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
    [CrossRef] [PubMed]
  5. W. B. Veldkamp, G. J. Swanson, D. C. Shaver, “High efficiency binary lenses,” Opt. Commun. 53, 353–358 (1985); see also G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. 24, 791–795 (1985); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
    [CrossRef]
  6. K. Miyamoto, “The phase Fresnel lens,” J. Opt. Soc. Am. 51, 17–20 (1961).
    [CrossRef]
  7. H. Madjidi-Zolbanine, C. Froehly, “Holographic correction of both chromatic and spherical aberrations of single glass lenses,” Appl. Opt. 18, 2385–2393 (1979).
    [CrossRef] [PubMed]
  8. G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017–2025 (1981).
    [CrossRef] [PubMed]
  9. T. Stone, N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27, 2960–2971 (1988).
    [CrossRef] [PubMed]
  10. D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 77–83.
  12. W. T. Welford, Aberrations of Optical Systems (Hilger, London, 1986), pp. 130–140.
  13. W. C. Sweatt, “Describing holographic optical elements as lenses,” J. Opt. Soc. Am. 67, 803–808 (1977).
    [CrossRef]
  14. W. A. Kleinhans, “Aberrations of curved zone plates and Fresnel lenses,” Appl. Opt. 16, 1701–1704 (1977).
    [CrossRef] [PubMed]
  15. D. A. Buralli, G. M. Morris, “Design of diffractive singlets for monochromatic imaging,” Appl. Opt. 30, 2151–2158 (1991).
    [CrossRef] [PubMed]
  16. Reference 12, pp. 148–152.
  17. W. B. Wetherell, “Afocal lenses,” in Applied Optics and Optical Engineering, R. Shannon, J. Wyant, eds. (Academic, San Diego, Calif., 1987), Vol. 10, pp. 109–192.
  18. Ref. 12, pp. 147–148.
  19. super-oslo is a product of Sinclair Optics, Inc., 6780 Palmyra Road, Fairport, N.Y. 14450.
  20. These equations are modified to conform to our notation and are derived from formulas presented in C. G. Wynne, “Thin-lens aberration theory,” Opt. Acta 8, 255–265 (1961).
    [CrossRef]
  21. T. H. Jamieson, “Refracting afocal systems in thermal imagers,” Opt. Eng. 19, 888–893 (1980).
    [CrossRef]
  22. W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT/Lincoln Laboratory Project Rep. ODT-20 (Massachusetts Institute of Technology, Lexington, Mass., 23August1989).

1991 (1)

1989 (2)

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); see also J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 142–149 (1989); G. M. Morris, D. A. Buralli, “Wide field diffractive lenses for imaging, scanning, and Fourier transformation,” Opt. News 15, 41–42 (1989).
[CrossRef]

D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
[CrossRef]

1988 (1)

1985 (1)

W. B. Veldkamp, G. J. Swanson, D. C. Shaver, “High efficiency binary lenses,” Opt. Commun. 53, 353–358 (1985); see also G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. 24, 791–795 (1985); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

1981 (1)

1980 (1)

T. H. Jamieson, “Refracting afocal systems in thermal imagers,” Opt. Eng. 19, 888–893 (1980).
[CrossRef]

1979 (1)

1977 (2)

1972 (1)

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

1969 (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969); see also J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef] [PubMed]

1961 (2)

These equations are modified to conform to our notation and are derived from formulas presented in C. G. Wynne, “Thin-lens aberration theory,” Opt. Acta 8, 255–265 (1961).
[CrossRef]

K. Miyamoto, “The phase Fresnel lens,” J. Opt. Soc. Am. 51, 17–20 (1961).
[CrossRef]

Buralli, D. A.

Chen, C-L.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT/Lincoln Laboratory Project Rep. ODT-20 (Massachusetts Institute of Technology, Lexington, Mass., 23August1989).

Clark, P. P.

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); see also J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 142–149 (1989); G. M. Morris, D. A. Buralli, “Wide field diffractive lenses for imaging, scanning, and Fourier transformation,” Opt. News 15, 41–42 (1989).
[CrossRef]

d’Auria, L.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Faklis, D.

D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
[CrossRef]

Froehly, C.

Gaither, S. A.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT/Lincoln Laboratory Project Rep. ODT-20 (Massachusetts Institute of Technology, Lexington, Mass., 23August1989).

George, N.

Goodman, J. W.

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

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969); see also J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef] [PubMed]

Huignard, J. P.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Jamieson, T. H.

T. H. Jamieson, “Refracting afocal systems in thermal imagers,” Opt. Eng. 19, 888–893 (1980).
[CrossRef]

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969); see also J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef] [PubMed]

Kleinhans, W. A.

Koronkevich, V. P.

V. P. Koronkevich, “Computer synthesis of diffraction optical elements,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, San Diego, Calif., 1989), pp. 277–313.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969); see also J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef] [PubMed]

Londono, C.

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); see also J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 142–149 (1989); G. M. Morris, D. A. Buralli, “Wide field diffractive lenses for imaging, scanning, and Fourier transformation,” Opt. News 15, 41–42 (1989).
[CrossRef]

Madjidi-Zolbanine, H.

Miyamoto, K.

Morris, G. M.

Osborne, T. R.

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT/Lincoln Laboratory Project Rep. ODT-20 (Massachusetts Institute of Technology, Lexington, Mass., 23August1989).

Roy, A. M.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Shaver, D. C.

W. B. Veldkamp, G. J. Swanson, D. C. Shaver, “High efficiency binary lenses,” Opt. Commun. 53, 353–358 (1985); see also G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. 24, 791–795 (1985); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Spitz, E.

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

Stone, T.

Swanson, G. J.

W. B. Veldkamp, G. J. Swanson, D. C. Shaver, “High efficiency binary lenses,” Opt. Commun. 53, 353–358 (1985); see also G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. 24, 791–795 (1985); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT/Lincoln Laboratory Project Rep. ODT-20 (Massachusetts Institute of Technology, Lexington, Mass., 23August1989).

Sweatt, W. C.

Veldkamp, W. B.

W. B. Veldkamp, G. J. Swanson, D. C. Shaver, “High efficiency binary lenses,” Opt. Commun. 53, 353–358 (1985); see also G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. 24, 791–795 (1985); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT/Lincoln Laboratory Project Rep. ODT-20 (Massachusetts Institute of Technology, Lexington, Mass., 23August1989).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, London, 1986), pp. 130–140.

Wetherell, W. B.

W. B. Wetherell, “Afocal lenses,” in Applied Optics and Optical Engineering, R. Shannon, J. Wyant, eds. (Academic, San Diego, Calif., 1987), Vol. 10, pp. 109–192.

Wynne, C. G.

These equations are modified to conform to our notation and are derived from formulas presented in C. G. Wynne, “Thin-lens aberration theory,” Opt. Acta 8, 255–265 (1961).
[CrossRef]

Appl. Opt. (5)

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, 150–155 (1969); see also J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

Opt. Acta (1)

These equations are modified to conform to our notation and are derived from formulas presented in C. G. Wynne, “Thin-lens aberration theory,” Opt. Acta 8, 255–265 (1961).
[CrossRef]

Opt. Commun. (2)

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[CrossRef]

W. B. Veldkamp, G. J. Swanson, D. C. Shaver, “High efficiency binary lenses,” Opt. Commun. 53, 353–358 (1985); see also G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. 24, 791–795 (1985); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Opt. Eng. (2)

D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
[CrossRef]

T. H. Jamieson, “Refracting afocal systems in thermal imagers,” Opt. Eng. 19, 888–893 (1980).
[CrossRef]

Opt. News (1)

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); see also J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 142–149 (1989); G. M. Morris, D. A. Buralli, “Wide field diffractive lenses for imaging, scanning, and Fourier transformation,” Opt. News 15, 41–42 (1989).
[CrossRef]

Other (8)

W. B. Veldkamp, G. J. Swanson, S. A. Gaither, C-L. Chen, T. R. Osborne, “Binary optics: a diffraction analysis,” MIT/Lincoln Laboratory Project Rep. ODT-20 (Massachusetts Institute of Technology, Lexington, Mass., 23August1989).

V. P. Koronkevich, “Computer synthesis of diffraction optical elements,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, San Diego, Calif., 1989), pp. 277–313.

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

W. T. Welford, Aberrations of Optical Systems (Hilger, London, 1986), pp. 130–140.

Reference 12, pp. 148–152.

W. B. Wetherell, “Afocal lenses,” in Applied Optics and Optical Engineering, R. Shannon, J. Wyant, eds. (Academic, San Diego, Calif., 1987), Vol. 10, pp. 109–192.

Ref. 12, pp. 147–148.

super-oslo is a product of Sinclair Optics, Inc., 6780 Palmyra Road, Fairport, N.Y. 14450.

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Figures (7)

Fig. 1
Fig. 1

Layout of the two-element diffractive telescope.

Fig. 2
Fig. 2

Wave-front aberration as a function of the pupil coordinate for the two-element telescope corrected for Seidel aberrations: (a) on axis; (b) an object field point 4 deg off-axis.

Fig. 3
Fig. 3

Root-mean-square wave-front error for the optimized two-element telescope with an additional sixth-order phase term.

Fig. 4
Fig. 4

Magnitude of the image space chief ray angle as a function of the magnitude of the object space chief ray angle for the optimized two-element telescope.

Fig. 5
Fig. 5

Layout of the three-element diffractive telescope.

Fig. 6
Fig. 6

The f-numbers of the two eyepiece lenses, normalized to the f-number of the singlet eyepiece lens, as a function of the back focal distance of the doublet eyepiece.

Fig. 7
Fig. 7

Root-mean-square wave-front error for the optimized three-element telescope.

Equations (39)

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Φ ( r ) = 2 π ( A r 2 + G r 4 + ) ,
ϕ = 2 λ A ,
W ( h , ρ, cos ϕ p ) = 1 8 S I ρ 4 + 1 2 S II h ρ 3 cos ϕ p + 1 2 S III h 2 ρ 2 cos 2 ϕ p + 1 4 ( S III + S IV ) h 2 ρ 2 + 1 2 S V h 3 ρ cos 2 ϕ p ,
S I = y 4 ϕ 3 4 ( 1 + B 2 + 4 B T + 3 T 2 ) 8 λ G y 4 ;
S II = y 2 ϕ 2 H 2 ( B + 2 T ) ,
S III = H 2 ϕ ;
S IV = 0 ;
S V = 0 .
B = 2 c sub ϕ ,
T = u + u u u ,
S I * = S I ,
S II * = S II + y ¯ y S I ,
S III * = S III + 2 y ¯ y S II + ( y ¯ y ) 2 S I ,
S IV * = S IV ,
S V * = S V + y ¯ y ( 3 S III + S IV ) + 3 ( y ¯ y ) 2 S II + ( y ¯ y ) 3 S I .
y ¯ y = u ¯ ( M 1 ) y obj ϕ obj ,
α = M θ tan 1 ( M u ¯ h ) = M tan 1 ( u ¯ h ) tan 1 ( M u ¯ h ) .
α = M ( u ¯ h u ¯ 3 h 3 3 + ) ( M u ¯ h M 3 u ¯ 3 h 3 3 + ) = 1 3 M ( M 2 1 ) u ¯ 3 h 3 + .
S V = 2 3 y obj u ¯ 3 ( 1 M 2 ) .
S I = S II = S III = 0 , S V = 2 3 y obj u ¯ 3 ( 1 M 2 ) ,
B obj = ( 2 + 8 M ) 3 3 M ,
B eye = 2 ( 4 + M ) 3 ( 1 M ) ,
G obj = ϕ obj 3 ( M 2 7 M + 1 ) 72 λ ( 1 M ) 2 ,
G eye = ϕ eye 3 ( M 2 7 M + 1 ) 72 λ ( 1 M ) 2 .
S ¯ I = 0 ;
S ¯ II = 0 ;
S ¯ III = 0 ;
S ¯ V = 1 2 H y 2 ϕ 2 B .
S ¯ I * = S ¯ I + y ¯ y ( 3 S ¯ II + S V ) + ( y ¯ y ) 2 ( 3 S ¯ III + 2 S IV + 3 S III ) + ( y ¯ y ) 3 ( S ¯ V + 3 S II ) + ( y ¯ y ) 4 S I ,
S ¯ II * = S ¯ II + y ¯ y ( 2 S ¯ III + S IV + S III ) + ( y ¯ y ) 2 ( S ¯ V + 2 S II ) + ( y ¯ y ) 3 S I ,
S ¯ III * = S ¯ III + y ¯ y ( S ¯ V + S II ) + ( y ¯ y ) 2 S I ,
S ¯ V * = S ¯ V + y ¯ y S I .
S ¯ I * = u ¯ 4 ( 1 M ) 2 ( 2 M ) 3 ϕ obj ,
S ¯ II * = y obj u ¯ 3 3 ( M 2 1 ) .
¯ y = 1 2 u ¯ S ¯ I * h 3 = u ¯ 3 ( 1 M ) 2 ( 2 M ) 6 M ϕ obj h 3 .
s min 2 λ 0 f / # ,
r f = λ 0 s .
η local ( r f ) 1 0 . 32 ( r f ) .
on-axis η doublet = 0 . 896 , η triplet = 0 . 897 ; 4 degrees off-axis η doublet = 0 . 814 , η triplet = 0 . 818 .

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