Abstract

A more computationally tractable model of the kinoform lenses in hybrid refractive-diffractive systems is proposed by taking into consideration the actual phase function of the kinoform lenses for every wavelength. The principle and outline of this modified model are explained. We compare the results of this approach with the more conventional single order calculation and with the standard diffraction-order expansion by using a practical hybrid optical system example.

© 2008 Optical Society of America

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References

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  1. G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” Lincoln Laboratory, M.I.T. Tech. Rep. 854 , Aug. 14, 1989.
  2. P. P. Clark and C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39-40 (1989).
    [CrossRef]
  3. T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27, 2960-2971 (1988).
    [CrossRef] [PubMed]
  4. M. D. Missig and G. M. Morris, “Diffractive optics applied to eyepiece design,” Appl. Opt. 34, 2452-2461 (1995).
    [CrossRef] [PubMed]
  5. W. H. Southwell, “Ray tracing kinoform lens surfaces,” Appl. Opt. 31, 2244-2247 (1992).
    [CrossRef] [PubMed]
  6. H. Sauer, P. Chavel, and G. Erdei, “Diffractive optical elements in hybrid lenses: modeling and design by zone decomposition,” Appl. Opt. 38, 6482-6486 (1999).
    [CrossRef]
  7. C. Bigwood, “New infrared optical systems using diffractive optics,” Proc. SPIE 4767, 1-12 (2002).
    [CrossRef]
  8. D. A. Buralli and G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389-4396 (1992).
    [CrossRef] [PubMed]
  9. S. Thibault, N. Renaud, and M. Wang, “Effects and prediction of stray light produced by diffractive lenses,” Proc. SPIE 3779, 334-343 (1999).
    [CrossRef]
  10. Y. Han, L. N. Hazra and C. A. Delisle, “Exact surface-relief profile of a kinoform lens from its phase function,” J. Opt. Soc. Am. A 12, 524-529 (1995).
    [CrossRef]
  11. M. A. Golub, “Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements,” J. Opt. Soc. Am. A. 16, 1194-1201 (1999).
    [CrossRef]
  12. S. H. Yan, Y. F. Dai, H. B. Lu, and S. Y. Li, “Simulating research on dispersion performance of diffractive optical lenses,” Opt. Technique 29, 399-401 (2003).
  13. D. A. Buralli, G. M. Morris and J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976-983(1989).
    [CrossRef] [PubMed]
  14. M. Daniel and M. Zacarias, Handbook of Optical Design, 2nd ed. (Marecl Dekker, 2004), pp. 204-209.
  15. ZEMAX is a trademark of Zemax Development Corporation, Bellevue, Washington 98004.

2004 (1)

M. Daniel and M. Zacarias, Handbook of Optical Design, 2nd ed. (Marecl Dekker, 2004), pp. 204-209.

2003 (1)

S. H. Yan, Y. F. Dai, H. B. Lu, and S. Y. Li, “Simulating research on dispersion performance of diffractive optical lenses,” Opt. Technique 29, 399-401 (2003).

2002 (1)

C. Bigwood, “New infrared optical systems using diffractive optics,” Proc. SPIE 4767, 1-12 (2002).
[CrossRef]

1999 (3)

S. Thibault, N. Renaud, and M. Wang, “Effects and prediction of stray light produced by diffractive lenses,” Proc. SPIE 3779, 334-343 (1999).
[CrossRef]

M. A. Golub, “Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements,” J. Opt. Soc. Am. A. 16, 1194-1201 (1999).
[CrossRef]

H. Sauer, P. Chavel, and G. Erdei, “Diffractive optical elements in hybrid lenses: modeling and design by zone decomposition,” Appl. Opt. 38, 6482-6486 (1999).
[CrossRef]

1995 (2)

1992 (2)

1989 (2)

P. P. Clark and C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39-40 (1989).
[CrossRef]

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

1988 (1)

Bigwood, C.

C. Bigwood, “New infrared optical systems using diffractive optics,” Proc. SPIE 4767, 1-12 (2002).
[CrossRef]

Buralli, D. A.

Chavel, P.

Clark, P. P.

P. P. Clark and C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39-40 (1989).
[CrossRef]

Dai, Y. F.

S. H. Yan, Y. F. Dai, H. B. Lu, and S. Y. Li, “Simulating research on dispersion performance of diffractive optical lenses,” Opt. Technique 29, 399-401 (2003).

Daniel, M.

M. Daniel and M. Zacarias, Handbook of Optical Design, 2nd ed. (Marecl Dekker, 2004), pp. 204-209.

Delisle, C. A.

Erdei, G.

George, N.

Golub, M. A.

M. A. Golub, “Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements,” J. Opt. Soc. Am. A. 16, 1194-1201 (1999).
[CrossRef]

Han, Y.

Hazra, L. N.

Li, S. Y.

S. H. Yan, Y. F. Dai, H. B. Lu, and S. Y. Li, “Simulating research on dispersion performance of diffractive optical lenses,” Opt. Technique 29, 399-401 (2003).

Londono, C.

P. P. Clark and C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39-40 (1989).
[CrossRef]

Lu, H. B.

S. H. Yan, Y. F. Dai, H. B. Lu, and S. Y. Li, “Simulating research on dispersion performance of diffractive optical lenses,” Opt. Technique 29, 399-401 (2003).

Missig, M. D.

Morris, G. M.

Renaud, N.

S. Thibault, N. Renaud, and M. Wang, “Effects and prediction of stray light produced by diffractive lenses,” Proc. SPIE 3779, 334-343 (1999).
[CrossRef]

Rogers, J. R.

Sauer, H.

Southwell, W. H.

Stone, T.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” Lincoln Laboratory, M.I.T. Tech. Rep. 854 , Aug. 14, 1989.

Thibault, S.

S. Thibault, N. Renaud, and M. Wang, “Effects and prediction of stray light produced by diffractive lenses,” Proc. SPIE 3779, 334-343 (1999).
[CrossRef]

Wang, M.

S. Thibault, N. Renaud, and M. Wang, “Effects and prediction of stray light produced by diffractive lenses,” Proc. SPIE 3779, 334-343 (1999).
[CrossRef]

Yan, S. H.

S. H. Yan, Y. F. Dai, H. B. Lu, and S. Y. Li, “Simulating research on dispersion performance of diffractive optical lenses,” Opt. Technique 29, 399-401 (2003).

Zacarias, M.

M. Daniel and M. Zacarias, Handbook of Optical Design, 2nd ed. (Marecl Dekker, 2004), pp. 204-209.

Appl. Opt. (6)

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

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

M. A. Golub, “Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements,” J. Opt. Soc. Am. A. 16, 1194-1201 (1999).
[CrossRef]

Opt. News (1)

P. P. Clark and C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15, 39-40 (1989).
[CrossRef]

Opt. Technique (1)

S. H. Yan, Y. F. Dai, H. B. Lu, and S. Y. Li, “Simulating research on dispersion performance of diffractive optical lenses,” Opt. Technique 29, 399-401 (2003).

Proc. SPIE (2)

C. Bigwood, “New infrared optical systems using diffractive optics,” Proc. SPIE 4767, 1-12 (2002).
[CrossRef]

S. Thibault, N. Renaud, and M. Wang, “Effects and prediction of stray light produced by diffractive lenses,” Proc. SPIE 3779, 334-343 (1999).
[CrossRef]

Other (3)

M. Daniel and M. Zacarias, Handbook of Optical Design, 2nd ed. (Marecl Dekker, 2004), pp. 204-209.

ZEMAX is a trademark of Zemax Development Corporation, Bellevue, Washington 98004.

G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” Lincoln Laboratory, M.I.T. Tech. Rep. 854 , Aug. 14, 1989.

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Figures (7)

Fig. 1
Fig. 1

Wave surface of different wavelengths: (a) kinoform lens, (b) wave surface of nominal wavelength, (c) wave surface of different wavelength.

Fig. 2
Fig. 2

Layout of the hybrid miniature CCD camera system.

Fig. 3
Fig. 3

Phase plots versus radius of kinoform. Here only the first eight zones of the 37-zone kinoform are plotted. The dotted black curve is the ideal phase under nominal wavelength and the solid red curve is the actual phase under nonnominal wavelength.

Fig. 4
Fig. 4

Plots of optical path differences as a function of pupil coordinate: (a) original model and (b) modified model.

Fig. 5
Fig. 5

Onaxis monochromatic MTF of the hybrid system under different nonnominal wavelength.

Fig. 6
Fig. 6

(a) Onaxis polychromatic MTF of the hybrid system: solid line (1), diffraction limit; dotted line (2), conventional calculation; dashed line (3), modified model. (b) Magnified view of the low spatial frequency region.

Fig. 7
Fig. 7

(a) Onaxis polychromatic MTF of the hybrid system: solid line (1), diffraction limit; dotted line (2), standard diffraction-order expansion calculation; dashed line (3), modified model. (b) Magnified view of the low spatial frequency region.

Equations (13)

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ϕ 0 ( r ) = 2 π λ 0 i = 1 n a i r 2 i ,
d ( r ) = λ 0 2 π ( n 0 1 ) { ϕ 0 ( r ) mod 2 π } .
ϕ ( r ) = 2 π λ ( n 1 ) d ( r ) .
ϕ ( r ) = λ 0 λ 1 α { ϕ 0 ( r ) mod 2 π } ,
α = n 0 1 n 1 .
ϕ ( r ) = ϕ ( r ) { ϕ 0 ( r ) mod 2 π } , r i r < r i + 1 ,
ϕ 0 ( r i ) = ± m 2 π , m = 0 , 1 , 2 , 3     .
l = l + λ 2 π ϕ x = l + λ 2 π ( ϕ 0 x + ϕ x ) ,
m = m + λ 2 π ϕ y = m + λ 2 π ( ϕ 0 y + ϕ y ) .
P ( x , y ) = E ( x , y ) e i k W ( x , y ) = E ( x , y ) e i k ( W 0 + W ) ,
MTF ( λ i , v , u ) = | + P ( x , y ) P * ( x + λ i v R , y + λ i u R ) d x d y + | P ( x , y ) | 2 d x d y | ,
MTF ( λ i , v , u ) = | exp { i k [ W 0 ( x + λ i v R , y + λ i u R ) W 0 ( x , y ) ] } × exp { i k [ W ( x + λ i v R , y + λ i u R ) W ( x , y ) ] } d x d y | ,
MTF POLY = i = 1 N W i · MTF i i = 1 N W i ,

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