Abstract

The parametric relationships of achromatized transmissive and reflective diffractive optical elements (DOEs) are explored for a number of configuration classes as a function of diffraction order, focal ratio, wavelength, and field angle. The necessity for blazing high-diffraction-order DOEs is elucidated. The ray image sizes are presented in dimensionless imaging space and thus are applicable to any size of optical system. Several aplanatic configurations are evaluated.

© 2002 Optical Society of America

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References

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  1. A. B. Meinel, M. P. Meinel, “Large membrane space optics: imagery and aberrations of lachromatized diffractive and holographic optical elements of high diffraction order,” Opt. Eng. 41, 1995–2007 (2002).
    [CrossRef]
  2. D. Faklis, G. M. Morris, “Spectral properties of multi-order diffractive lenses,” Appl. Opt. 27, 2960–2971 (1988).
  3. D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
    [CrossRef]
  4. N. M. Ceglio, A. M. Hawryluk, D. P. Gaines, R. A. London, L. G. Seppala, “Broadband diffractive lens,” Internal unnumbered report (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).
  5. W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
    [CrossRef]
  6. H. Sauer, P. Chavel, G. Erdai, “Diffractive optical elements in hybrid lenses: modeling and design by zone decomposition,” Appl. Opt. 38, 6482–6486 (1999).
    [CrossRef]
  7. S. Sinzinger, M. Testorf, “Transition between diffractive and refractive micro-optical components,” Appl. Opt. 34, 5970–5796 (1995).
    [CrossRef] [PubMed]
  8. D. Faklis, G. M. Morris, “Broadband imaging with holographic lenses,” Opt. Eng. 28, 592–598 (1989).
    [CrossRef]
  9. S. Bennett, “Achromatic combinations of holographic optical elements,” Appl. Opt. 15, 542–545 (1976).
    [CrossRef] [PubMed]
  10. R. E. Hufnagel, “Achromatic holographic optical systems,” U.S. patent4,550,973 (5November1985).
  11. R. A. Hyde, “Eyeglass. 1. Very large aperture diffractive telescopes,” Appl. Opt. 38, 4198–4212 (1999).
    [CrossRef]
  12. W. S. Rockward, D. C. O’Shea, “Crossed phase gratings with diffractive optical elements,” Appl. Opt. 37, 5075–5086 (1998).
    [CrossRef]
  13. G. H. Derrick, R. C. McPhedian, D. Maystre, M. Neviere, “Crossed gratings: a theory and its applications,” Appl. Opt. 18, 39–52 (1979).
  14. M. Lampton, BEAM 4-3.01 (Stellar Software, Berkeley, Calif., 1998).
  15. M. C. Hettrick, C. S. Bowyer, “Variable line-space gratings: new designs for use in grazing incidence spectrometers,” Appl. Opt. 22, 3921–3930 (1983).
    [CrossRef] [PubMed]

2002 (1)

A. B. Meinel, M. P. Meinel, “Large membrane space optics: imagery and aberrations of lachromatized diffractive and holographic optical elements of high diffraction order,” Opt. Eng. 41, 1995–2007 (2002).
[CrossRef]

1999 (2)

1998 (1)

1995 (1)

1989 (2)

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

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

1988 (1)

1983 (1)

1979 (1)

G. H. Derrick, R. C. McPhedian, D. Maystre, M. Neviere, “Crossed gratings: a theory and its applications,” Appl. Opt. 18, 39–52 (1979).

1976 (1)

1973 (1)

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

Bennett, S.

Bowyer, C. S.

Ceglio, N. M.

N. M. Ceglio, A. M. Hawryluk, D. P. Gaines, R. A. London, L. G. Seppala, “Broadband diffractive lens,” Internal unnumbered report (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

Chavel, P.

Derrick, G. H.

G. H. Derrick, R. C. McPhedian, D. Maystre, M. Neviere, “Crossed gratings: a theory and its applications,” Appl. Opt. 18, 39–52 (1979).

Erdai, G.

Faklis, D.

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

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

D. Faklis, G. M. Morris, “Spectral properties of multi-order diffractive lenses,” Appl. Opt. 27, 2960–2971 (1988).

Gaines, D. P.

N. M. Ceglio, A. M. Hawryluk, D. P. Gaines, R. A. London, L. G. Seppala, “Broadband diffractive lens,” Internal unnumbered report (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

Hawryluk, A. M.

N. M. Ceglio, A. M. Hawryluk, D. P. Gaines, R. A. London, L. G. Seppala, “Broadband diffractive lens,” Internal unnumbered report (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

Hettrick, M. C.

Hufnagel, R. E.

R. E. Hufnagel, “Achromatic holographic optical systems,” U.S. patent4,550,973 (5November1985).

Hyde, R. A.

Lampton, M.

M. Lampton, BEAM 4-3.01 (Stellar Software, Berkeley, Calif., 1998).

London, R. A.

N. M. Ceglio, A. M. Hawryluk, D. P. Gaines, R. A. London, L. G. Seppala, “Broadband diffractive lens,” Internal unnumbered report (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

Maystre, D.

G. H. Derrick, R. C. McPhedian, D. Maystre, M. Neviere, “Crossed gratings: a theory and its applications,” Appl. Opt. 18, 39–52 (1979).

McPhedian, R. C.

G. H. Derrick, R. C. McPhedian, D. Maystre, M. Neviere, “Crossed gratings: a theory and its applications,” Appl. Opt. 18, 39–52 (1979).

Meinel, A. B.

A. B. Meinel, M. P. Meinel, “Large membrane space optics: imagery and aberrations of lachromatized diffractive and holographic optical elements of high diffraction order,” Opt. Eng. 41, 1995–2007 (2002).
[CrossRef]

Meinel, M. P.

A. B. Meinel, M. P. Meinel, “Large membrane space optics: imagery and aberrations of lachromatized diffractive and holographic optical elements of high diffraction order,” Opt. Eng. 41, 1995–2007 (2002).
[CrossRef]

Morris, G. M.

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

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

D. Faklis, G. M. Morris, “Spectral properties of multi-order diffractive lenses,” Appl. Opt. 27, 2960–2971 (1988).

Neviere, M.

G. H. Derrick, R. C. McPhedian, D. Maystre, M. Neviere, “Crossed gratings: a theory and its applications,” Appl. Opt. 18, 39–52 (1979).

O’Shea, D. C.

Rockward, W. S.

Sauer, H.

Seppala, L. G.

N. M. Ceglio, A. M. Hawryluk, D. P. Gaines, R. A. London, L. G. Seppala, “Broadband diffractive lens,” Internal unnumbered report (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

Sinzinger, S.

Testorf, M.

Welford, W. T.

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

Appl. Opt. (8)

Opt. Commun. (1)

W. T. Welford, “Aplanatic hologram lenses on spherical surfaces,” Opt. Commun. 9, 268–269 (1973).
[CrossRef]

Opt. Eng. (3)

A. B. Meinel, M. P. Meinel, “Large membrane space optics: imagery and aberrations of lachromatized diffractive and holographic optical elements of high diffraction order,” Opt. Eng. 41, 1995–2007 (2002).
[CrossRef]

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

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

Other (3)

R. E. Hufnagel, “Achromatic holographic optical systems,” U.S. patent4,550,973 (5November1985).

N. M. Ceglio, A. M. Hawryluk, D. P. Gaines, R. A. London, L. G. Seppala, “Broadband diffractive lens,” Internal unnumbered report (Lawrence Livermore National Laboratory, Livermore, Calif., 1991).

M. Lampton, BEAM 4-3.01 (Stellar Software, Berkeley, Calif., 1998).

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Figures (29)

Fig. 1
Fig. 1

Limit of the chromatic fan is independent of diffraction order.

Fig. 2
Fig. 2

Configuration schematics for the five configurations.

Fig. 3
Fig. 3

Two basic configurations obtained with a highly curved DOE #2 thereby eliminating the reimaging mirror.

Fig. 4
Fig. 4

Arrangement for injecting the spectral fan from DOE #1 into the achromatizing subsystem through a central aperture in DOE #2, configuration B.

Fig. 5
Fig. 5

Imagery is essentially identical for different values of N and their associated central wavelengths.

Fig. 6
Fig. 6

Variation of the relative width of the blaze as a function of central wavelength and the associated diffraction order.

Fig. 7
Fig. 7

Spot diagram and full-aperture ray fan for the 100-m F/100 coronagraphic telescope before achromatization optimization was completed. For N = 100 and for the 0.6-µm triad.

Fig. 8
Fig. 8

Spot diagram and full-aperture ray fan for the 100-m F/100 coronagraphic telescope after final optimization. For N = 100 and for the 0.6-µm triad.

Fig. 9
Fig. 9

Ray spot images (left) and full-aperture ray fan (right) for configurations obtained with transmissive DOEs and a lens pupil imager, configuration A. For N = 100 and for the 0.6-µm triad.

Fig. 10
Fig. 10

Ray spot images (left) and full-aperture ray fan (right) for configurations obtained with transmissive DOEs and a reflective pupil imager, configuration B. For N = 100 and for the 0.6-µm triad.

Fig. 11
Fig. 11

Comparison of the ray spot images for a lens pupil imager (left) and a reflective pupil imager (right) showing equal image acuity. For N = 100 and for the 0.6-µm triad.

Fig. 12
Fig. 12

Lens pupil imager, reflective DOE #2, configuration C. For N = 100 and for the 0.6-µm triad.

Fig. 13
Fig. 13

Imagery for the configuration obtained with a reflective DOE #2 (left) is slightly better than for a transmissive DOE #2 (right). For N = 100 and for the 0.6 µm triad.

Fig. 14
Fig. 14

Reflective pupil imager, reflective DOE #2 F/25 to F/20. For N = 100 and for the 0.6-µm triad.

Fig. 15
Fig. 15

Comparison of the imagery for configurations obtained with a mirror pupil imager with transmissive DOE #2 (left) and a mirror pupil imager with reflective DOE #2 (right). For N = 100 and for the 0.6-µm triad.

Fig. 16
Fig. 16

Imagery for configuration F obtained with a curved reflective DOE #2 in lieu of a reflective reimager. For N = 100 and for the 0.6-µm triad.

Fig. 17
Fig. 17

View of an F/12.5 Cass compressed by the perspective angle of 80° illustrating the small diameter of DOE #2.

Fig. 18
Fig. 18

Full-aperture ray spot image for two Cassegrain configurations for N = 100 and for the 0.6-µm triad.

Fig. 19
Fig. 19

Change of image size with configuration parameters for several examples in which crossed-linear DOEs are used with a reflective pupil imager. For N = 100 and for the 0.6-µm triad.

Fig. 20
Fig. 20

Comparison of the image without field flattener (left) and after insertion of a field flattener between the pupil imager and the DOE #2 to reduce pupil aberrations (right). For N = 100 and for the 0.6-µm triad.

Fig. 21
Fig. 21

Distribution of rms values for different combinations of DOE #1 focal ratios and with lens and mirror pupil imagers as a function of the f-number out of DOE #2.

Fig. 22
Fig. 22

Off-axis images for DOE F/100 to F/74 optimized for 0.0003 rad on a flat field of view. For N = 100 and for the 0.6-µm triad.

Fig. 23
Fig. 23

Off-axis images for DOE F/50 to F/37 optimized for 0.0003 rad on a flat field of view. For N = 100 and for the 0.6-µm triad.

Fig. 24
Fig. 24

Off-axis images for DOE F/25 to F/17 optimized for 0.0003 rad on a flat field of view. For N = 100 and for the 0.6-µm triad.

Fig. 25
Fig. 25

Off-axis images for DOE F/12.5 to F/7.5 optimized for 0.0003 rad on a flat field of view. For N = 100 and for the 0.6-µm triad.

Fig. 26
Fig. 26

Off-axis images for DOE F/6.25 to F/3.7 optimized for 0.0002 rad on a flat field of view. For N = 100 and for the 0.6-µm triad.

Fig. 27
Fig. 27

Variation of image size with field angle for configuration DOE F/50 to F/27 optimized for 0.0003 rad on a flat field. For N = 100 and for the 0.6-µm triad.

Fig. 28
Fig. 28

Image for configuration DOE F/50 to F/27 reduced significantly when optimized on a curved focal surface. For N = 100 and for the 0.6-µm triad.

Fig. 29
Fig. 29

Layout to scale for the DOE F/6.25 to F/3.7 configuration and diffraction order N = 100 and for configuration DOE F/50 to F/27.

Tables (3)

Tables Icon

Table 1 Example Wavelength Sets for 0, ±0.5, and 1.0 Relative Blaze Intensities for 0.6 µm at N = 100

Tables Icon

Table 2 Image Performance for a Parametric Series of DOE Configurations at Diffraction Order N = 100 and 0.6-µm Triad

Tables Icon

Table 3 Image Performance for a Parametric Series of XX DOE Configurations at Diffraction Order N = 100 and 0.6-µm Triad

Equations (3)

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FWHM=1.22 λF.
Dmax=DFWHM/Δx
Dmax=0.59λ/D α arc sec.

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