Abstract

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.

© 1995 Optical Society of America

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References

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  1. K. Miyamoto, “The phase Fresnel lens,” J. Opt. Soc. Am. 51, 17–20 (1961).
    [CrossRef]
  2. D. Faklis, G. M. Morris, “Optical design with diffractive lenses,” Photon. Spectra. 25(11), 205–208 (1991).
  3. P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. 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]
  4. L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
    [CrossRef]
  5. D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photon. Spectra, 25(12), 131–134 (1991).
  6. G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.
  7. H. Dammann, “Color separation gratings,” Appl. Opt. 17, 2273–2279 (1978).
    [CrossRef] [PubMed]
  8. H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409 (1979).
  9. J. A. Futhey, “Diffractive lens,” U.S. Patent4,936,666, (26June1990).
  10. J. A. Futhey, M. Beal, S. Saxe, “Superzone diffractive optics,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.
  11. J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).
  12. D. W. Sweeney, G. Sommargren, “Single element achromatic diffractive lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.
  13. D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).
  14. D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
    [CrossRef] [PubMed]
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  16. Ref. 15, Chap. 6, Eq. (6-37).
  17. D. A. Buralli, G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389–4396 (1992).
    [CrossRef] [PubMed]
  18. J. P. Bowen, C. G. Blough, V. Wong, “Fabrication of optical surfaces by laser pattern generation,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 153–156.
  19. W. J. Smith, Modern Lens Design (McGraw-Hill, New York, 1992), p. 44.
  20. D. A. Buralli, G. M. Morris, “Design of diffractive singlets for monochromatic imaging,” Appl. Opt. 30, 2151–2158 (1991).
    [CrossRef] [PubMed]

1992 (1)

1991 (3)

D. A. Buralli, G. M. Morris, “Design of diffractive singlets for monochromatic imaging,” Appl. Opt. 30, 2151–2158 (1991).
[CrossRef] [PubMed]

D. Faklis, G. M. Morris, “Optical design with diffractive lenses,” Photon. Spectra. 25(11), 205–208 (1991).

D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photon. Spectra, 25(12), 131–134 (1991).

1989 (2)

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. 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. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
[CrossRef] [PubMed]

1979 (1)

H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409 (1979).

1978 (1)

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

1961 (1)

Angell, D. K.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

Beal, M.

J. A. Futhey, M. Beal, S. Saxe, “Superzone diffractive optics,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

Blough, C. G.

J. P. Bowen, C. G. Blough, V. Wong, “Fabrication of optical surfaces by laser pattern generation,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 153–156.

Bowen, J. P.

J. P. Bowen, C. G. Blough, V. Wong, “Fabrication of optical surfaces by laser pattern generation,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 153–156.

Buralli, D. A.

Clark, P. P.

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. 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); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Dammann, H.

H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409 (1979).

H. Dammann, “Color separation gratings,” Appl. Opt. 17, 2273–2279 (1978).
[CrossRef] [PubMed]

Faklis, D.

D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photon. Spectra, 25(12), 131–134 (1991).

D. Faklis, G. M. Morris, “Optical design with diffractive lenses,” Photon. Spectra. 25(11), 205–208 (1991).

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

Futhey, J. A.

J. A. Futhey, “Diffractive lens,” U.S. Patent4,936,666, (26June1990).

J. A. Futhey, M. Beal, S. Saxe, “Superzone diffractive optics,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

Goodman, J. W.

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

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

Judd, D. B.

D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).

Londono, C.

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. 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]

Marron, J. C.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

Miyamoto, K.

Morris, G. M.

D. A. Buralli, G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389–4396 (1992).
[CrossRef] [PubMed]

D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photon. Spectra, 25(12), 131–134 (1991).

D. Faklis, G. M. Morris, “Optical design with diffractive lenses,” Photon. Spectra. 25(11), 205–208 (1991).

D. A. Buralli, G. M. Morris, “Design of diffractive singlets for monochromatic imaging,” Appl. Opt. 30, 2151–2158 (1991).
[CrossRef] [PubMed]

D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
[CrossRef] [PubMed]

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

Rogers, J. R.

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

Saxe, S.

J. A. Futhey, M. Beal, S. Saxe, “Superzone diffractive optics,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

Smith, W. J.

W. J. Smith, Modern Lens Design (McGraw-Hill, New York, 1992), p. 44.

Sommargren, G.

D. W. Sweeney, G. Sommargren, “Single element achromatic diffractive lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.

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

Sweeney, D. W.

D. W. Sweeney, G. Sommargren, “Single element achromatic diffractive lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.

Tai, A. M.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

Wong, V.

J. P. Bowen, C. G. Blough, V. Wong, “Fabrication of optical surfaces by laser pattern generation,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 153–156.

Wyszecki, G.

D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

L. d’Auria, J. P. Huignard, A. M. Roy, E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972); G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Opt. News (1)

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39–40 (1989); J. A. Futhey, “Diffractive bifocal intraocular lens,” in Holographic Optics: Optically and Computer Generated, I. 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]

Optik (1)

H. Dammann, “Spectral characteristics of stepped-phase gratings,” Optik 53, 409 (1979).

Photon. Spectra (1)

D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photon. Spectra, 25(12), 131–134 (1991).

Photon. Spectra. (1)

D. Faklis, G. M. Morris, “Optical design with diffractive lenses,” Photon. Spectra. 25(11), 205–208 (1991).

Other (10)

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

J. A. Futhey, “Diffractive lens,” U.S. Patent4,936,666, (26June1990).

J. A. Futhey, M. Beal, S. Saxe, “Superzone diffractive optics,” in Annual Meeting, Vol. 17 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper TuS2.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

D. W. Sweeney, G. Sommargren, “Single element achromatic diffractive lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.

D. B. Judd, G. Wyszecki, Color in Business, Science and Industry (Wiley, New York, 1975).

J. P. Bowen, C. G. Blough, V. Wong, “Fabrication of optical surfaces by laser pattern generation,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 153–156.

W. J. Smith, Modern Lens Design (McGraw-Hill, New York, 1992), p. 44.

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

Ref. 15, Chap. 6, Eq. (6-37).

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Figures (6)

Fig. 1
Fig. 1

Diffractive lens construction: (a) conventional refractive lens, (b) diffractive lens with continuous quadratic blaze profile, (c) phase-reversal (or Wood) lens, (d) four-level approximation to quadratic blaze profile.

Fig. 2
Fig. 2

Diffraction efficiency of the mth diffracted order versus wavelength for a MOD lens with p = 10.

Fig. 3
Fig. 3

Diffraction efficiency as a function of wavelength for p = m.

Fig. 4
Fig. 4

MTF for p = 2 and m = 2. The design wavelength, 640 nm, is represented in (b) and a wavelength detuning of ±5 nm is represented in (a) and (c). The diffraction limit is the same in all three cases. The tangential MTF is displayed by a dashed curve, and the sagittal MTF is illustrated by a solid curve. The theoretical tangential performance at 635 and 645 nm is also illustrated as a dotted–dashed curve.

Fig. 5
Fig. 5

MTF for p = 2 and m = 3. The design wavelength, 427 nm, is represented in (b) and a wavelength detuning of ±5 nm is represented in (a) and (c). The diffraction limit is the same in all three cases. The tangential MTF is displayed by a dashed curve, and the sagittal MTF is illustrated by a solid curve. The theoretical tangential performance at 422 and 432 nm is also illustrated as dotted–dashed curve.

Fig. 6
Fig. 6

Strehl ratio as a function of wavelength. The graph in (a) illustrates the performance at p = 2 and m = 3 and (b) at p = 2 and m = 2. Note that a Strehl ratio of 0.8 or greater denotes diffraction-limited performance.

Equations (18)

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r j 2 = 2 j p λ 0 F 0 .
ϕ ( r ) = 2 πα p ( j r 2 2 p λ 0 F 0 ) , r j r < r j + 1 ,
α = λ 0 λ [ n ( λ ) 1 n ( λ 0 ) 1 ] ,
h max ( r ) = p λ 0 n ( λ 0 ) 1 .
t ( r ) = m = exp [ i π ( α p m ) ] × sinc ( α p m ) exp ( i π m r 2 p λ 0 F 0 ) ,
t ( r ) = exp ( i π r 2 λ F ) ,
F ( λ ) = p λ 0 F 0 m λ .
η m = sinc 2 ( α p m ) .
λ peak = p λ 0 m .
U II ( u , v ; λ ) = i λ F 0 U I ( x , y ; λ ) P ( x , y ; λ ) × exp { i π λ F 0 [ ( u x ) 2 + ( v y ) 2 ] } d x d y ,
U II ( u , v ; λ ) = i exp [ i π λ F 0 ( u 2 + v 2 ) ] λ F 0 m = × exp [ i π ( α p m ) ] sinc ( α p m ) × P ( x , y ; λ ) exp [ i π λ ( x 2 + y 2 ) ] × exp [ i 2 π λ F 0 ( u x + v y ) ] d x d y ,
= 1 F 0 ( m λ p λ 0 1 ) .
OTF ( f X , f y ) = H ( ξ + f x 2 , η + f y 2 ) H * ( ξ f x 2 , η f y 2 ) d ξ d η | H ( ξ , η ) | 2 d ξ d η ,
OTF ( f x , f y ) = Λ ( f x 2 f 0 ) Λ ( f y 2 f 0 ) m = sinc 2 ( α p m ) × sinc [ l 2 λ ( f x 2 f 0 ) ( 1 | f x | 2 f 0 ) ] × sinc [ l 2 λ ( f y 2 f 0 ) ( 1 | f y | 2 f 0 ) ] ,
f 0 = l 2 λ F 0
OTF ( f x , f y ) = Λ ( f x 2 f 0 ) Λ ( f y 2 f 0 ) ,
D = OTF ( f x , f y ) | aberrated d f x d f y [ OTF ( f x , f y ) | unaberrated m = sinc 2 ( α p m ) ] d f x d f y .
D = 1 4 f 0 2 m = sinc 2 ( α p m ) × [ Λ ( f x 2 f 0 ) sinc [ l 2 λ ( f x 2 f 0 ) ( 1 | f x | 2 f 0 ) ] d f x ] 2 .

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