Abstract

The ultraviolet groove efficiency for a holographically ruled diffraction grating with a trapezoidal profile has been measured. The efficiencies for the ±1 and the zero orders are in good agreement with those derived from scalar theory. The ±1 orders have equal efficiency as a function of wavelength. The peak of the sum of fitted groove efficiency functions is 76%, a level that is competitive with the groove efficiency of a mechanically blazed grating. We suggest that a normal-incidence grating mount with detectors at both orders will offer a system with twice the efficiency and provide a built-in redundancy. We discuss design considerations for reducing astigmatism equally in both orders in such dual-order mountings.

© 2001 Optical Society of America

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References

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  1. E. G. Loewen, M. Nevière, “Simple selection rules for VUV and XUV diffraction gratings,” Appl. Opt. 17, 1087–1092 (1978).
    [CrossRef] [PubMed]
  2. R. W. Wood, “The echelette grating for the infrared,” Phil. Mag. 20, 770–778 (1910).
    [CrossRef]
  3. R. W. Wood, Physical Optics, 3rd ed. (Optical Society of America, Washington, D.C., 1988), p. 264.
  4. S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.
  5. G. R. Harrison, “The diffraction grating—an opinionated appraisal,” Appl. Opt. 12, 2039–2049 (1973).
    [CrossRef] [PubMed]
  6. D. Dravins, “High-dispersion astronomical spectroscopy with holographic and ruled diffraction gratings,” Appl. Opt. 17, 404–414 (1978).
    [CrossRef] [PubMed]
  7. G. H. Mount, W. G. Fastie, “Comprehensive analysis of gratings for ultraviolet space instrumentation,” Appl. Opt. 17, 3108–3116 (1978).
    [CrossRef] [PubMed]
  8. G. J. Dunning, M. L. Minden, “Scattering from high efficiency diffraction gratings,” Appl. Opt. 19, 2419–2425 (1980).
    [CrossRef] [PubMed]
  9. J. Kielkopf, “Echelle and holographic gratings compared for scattering and spectral resolution,” Appl. Opt. 20, 3327–3331 (1981).
    [CrossRef] [PubMed]
  10. R. G. Tull, “A comparison of holographic and echelle gratings in astronomical spectrometry,” in Instrumentation for Ground-Based Optical Astronomy, Present and Future, The Ninth Santa Cruz Summer Workshop in Astronomy and Astrophysics, L. B. Robinson, ed. (Springer-Verlag, New York, 1988), pp. 104–117.
  11. J. Flamand, F. Bonnemason, A. Thevenon, J. M. Lerner, “Blazing of holographic gratings using ion-etching,” in Raman Scattering, Luminescence, and Spectroscopic Instrumentation in Technology, F. Adar, J. E. Griffiths, J. M. Lerner, eds., Proc. SPIE1055, 288–294 (1989).
    [CrossRef]
  12. J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).
  13. P. F. Romanenko, M. V. Sopinski, I. Z. Indutnyi, “Blazed holographic diffraction grating fabrication using As2Se3 inorganic photoresist,” in OPTIKA ’98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 457–460 (1998).
  14. E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
    [CrossRef] [PubMed]
  15. R. W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phil. Mag. 4, 396–402 (1902).
    [CrossRef]
  16. D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics XXI, E. Wolf, ed. (Elsevier, New York, 1984), Vol. 21, Chap. 1, pp. 1–67.
    [CrossRef]
  17. W. G. Fastie, D. E. Kerr, “Spectroradiometric calibration techniques in the far ultraviolet: stable emission source for the Lyman bands of molecular hydrogen,” Appl. Opt. 14, 2133–2142 (1975).
    [CrossRef] [PubMed]
  18. A. Wirgin, “Scattering from sinusoidal gratings: an evaluation of the Kirchhoff approximation,” J. Opt. Soc. Am. 73, 1028–1041 (1983).
    [CrossRef]
  19. H. Haber, “The torus grating,” J. Opt. Soc. Am. 40, 153–165 (1950).
    [CrossRef]
  20. T. Namioka, “Theory of the ellipsoidal concave grating. I,” J. Opt. Soc. Am. 51, 4–12 (1961).
    [CrossRef]
  21. R. Grange, “Aberration-reduced holographic spherical gratings for Rowland circle spectrographs,” Appl. Opt. 31, 3744–3749 (1992).
    [CrossRef] [PubMed]
  22. H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1036 (1974).
    [CrossRef]
  23. There is another astigmatism correction solution a = c = R cos α cos β and b = R(cos α cos β)1/2 that has the added advantage of yielding a smaller spherical aberration25 term but the disadvantage of being somewhat less intuitive, since none of the semiaxes are equal to the Rowland circle diameter.
  24. J.-L. Reynaud, “Test results of the 5800g/mm ROALEX holographic grating from Jobin–Yvon,” memo from Laboratorie d’Astronomie Spatiale du CNRS (Centre National de Recherche Scientifique, Marseille, France, 1994).
  25. P. Davila, D. Content, C. Trout, “Aberration-corrected aspheric gratings for far-ultraviolet spectrographs: holographic approach,” Appl. Opt. 31, 949–954 (1992).
    [CrossRef] [PubMed]

1992 (2)

1983 (1)

1981 (1)

1980 (1)

1978 (3)

1977 (1)

1975 (1)

1974 (1)

1973 (1)

1961 (1)

1950 (1)

1910 (1)

R. W. Wood, “The echelette grating for the infrared,” Phil. Mag. 20, 770–778 (1910).
[CrossRef]

1902 (1)

R. W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phil. Mag. 4, 396–402 (1902).
[CrossRef]

Barbee, T. W.

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

Bonnemason, F.

J. Flamand, F. Bonnemason, A. Thevenon, J. M. Lerner, “Blazing of holographic gratings using ion-etching,” in Raman Scattering, Luminescence, and Spectroscopic Instrumentation in Technology, F. Adar, J. E. Griffiths, J. M. Lerner, eds., Proc. SPIE1055, 288–294 (1989).
[CrossRef]

Burgh, E. B.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Content, D.

Cruddace, R. G.

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

Davila, P.

Dravins, D.

Dunning, G. J.

Fastie, W. G.

Feldman, P. D.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Flamand, J.

J. Flamand, F. Bonnemason, A. Thevenon, J. M. Lerner, “Blazing of holographic gratings using ion-etching,” in Raman Scattering, Luminescence, and Spectroscopic Instrumentation in Technology, F. Adar, J. E. Griffiths, J. M. Lerner, eds., Proc. SPIE1055, 288–294 (1989).
[CrossRef]

Grange, R.

Haber, H.

Harrison, G. R.

Holland, G. E.

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

Hunter, W. R.

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

Indutnyi, I. Z.

P. F. Romanenko, M. V. Sopinski, I. Z. Indutnyi, “Blazed holographic diffraction grating fabrication using As2Se3 inorganic photoresist,” in OPTIKA ’98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 457–460 (1998).

Kerr, D. E.

Kielkopf, J.

Kowalski, M. P.

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

Lerner, J. M.

J. Flamand, F. Bonnemason, A. Thevenon, J. M. Lerner, “Blazing of holographic gratings using ion-etching,” in Raman Scattering, Luminescence, and Spectroscopic Instrumentation in Technology, F. Adar, J. E. Griffiths, J. M. Lerner, eds., Proc. SPIE1055, 288–294 (1989).
[CrossRef]

Loewen, E. G.

Maystre, D.

E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
[CrossRef] [PubMed]

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics XXI, E. Wolf, ed. (Elsevier, New York, 1984), Vol. 21, Chap. 1, pp. 1–67.
[CrossRef]

McCandliss, S. R.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

McPhate, J. B.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Minden, M. L.

Mount, G. H.

Namioka, T.

Nevière, M.

Nikzad, S.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Noda, H.

Pankratz, C.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Pelton, R.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Reynaud, J.-L.

J.-L. Reynaud, “Test results of the 5800g/mm ROALEX holographic grating from Jobin–Yvon,” memo from Laboratorie d’Astronomie Spatiale du CNRS (Centre National de Recherche Scientifique, Marseille, France, 1994).

Rife, J. C.

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

Romanenko, P. F.

P. F. Romanenko, M. V. Sopinski, I. Z. Indutnyi, “Blazed holographic diffraction grating fabrication using As2Se3 inorganic photoresist,” in OPTIKA ’98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 457–460 (1998).

Seely, J. F.

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

Seya, M.

Siegmund, O.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Sopinski, M. V.

P. F. Romanenko, M. V. Sopinski, I. Z. Indutnyi, “Blazed holographic diffraction grating fabrication using As2Se3 inorganic photoresist,” in OPTIKA ’98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 457–460 (1998).

Thevenon, A.

J. Flamand, F. Bonnemason, A. Thevenon, J. M. Lerner, “Blazing of holographic gratings using ion-etching,” in Raman Scattering, Luminescence, and Spectroscopic Instrumentation in Technology, F. Adar, J. E. Griffiths, J. M. Lerner, eds., Proc. SPIE1055, 288–294 (1989).
[CrossRef]

Trout, C.

Tull, R. G.

R. G. Tull, “A comparison of holographic and echelle gratings in astronomical spectrometry,” in Instrumentation for Ground-Based Optical Astronomy, Present and Future, The Ninth Santa Cruz Summer Workshop in Astronomy and Astrophysics, L. B. Robinson, ed. (Springer-Verlag, New York, 1988), pp. 104–117.

Vallerga, J.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

Wirgin, A.

Wood, R. W.

R. W. Wood, “The echelette grating for the infrared,” Phil. Mag. 20, 770–778 (1910).
[CrossRef]

R. W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phil. Mag. 4, 396–402 (1902).
[CrossRef]

R. W. Wood, Physical Optics, 3rd ed. (Optical Society of America, Washington, D.C., 1988), p. 264.

Appl. Opt. (10)

G. R. Harrison, “The diffraction grating—an opinionated appraisal,” Appl. Opt. 12, 2039–2049 (1973).
[CrossRef] [PubMed]

W. G. Fastie, D. E. Kerr, “Spectroradiometric calibration techniques in the far ultraviolet: stable emission source for the Lyman bands of molecular hydrogen,” Appl. Opt. 14, 2133–2142 (1975).
[CrossRef] [PubMed]

E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
[CrossRef] [PubMed]

D. Dravins, “High-dispersion astronomical spectroscopy with holographic and ruled diffraction gratings,” Appl. Opt. 17, 404–414 (1978).
[CrossRef] [PubMed]

E. G. Loewen, M. Nevière, “Simple selection rules for VUV and XUV diffraction gratings,” Appl. Opt. 17, 1087–1092 (1978).
[CrossRef] [PubMed]

G. H. Mount, W. G. Fastie, “Comprehensive analysis of gratings for ultraviolet space instrumentation,” Appl. Opt. 17, 3108–3116 (1978).
[CrossRef] [PubMed]

G. J. Dunning, M. L. Minden, “Scattering from high efficiency diffraction gratings,” Appl. Opt. 19, 2419–2425 (1980).
[CrossRef] [PubMed]

J. Kielkopf, “Echelle and holographic gratings compared for scattering and spectral resolution,” Appl. Opt. 20, 3327–3331 (1981).
[CrossRef] [PubMed]

P. Davila, D. Content, C. Trout, “Aberration-corrected aspheric gratings for far-ultraviolet spectrographs: holographic approach,” Appl. Opt. 31, 949–954 (1992).
[CrossRef] [PubMed]

R. Grange, “Aberration-reduced holographic spherical gratings for Rowland circle spectrographs,” Appl. Opt. 31, 3744–3749 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (4)

Phil. Mag. (2)

R. W. Wood, “The echelette grating for the infrared,” Phil. Mag. 20, 770–778 (1910).
[CrossRef]

R. W. Wood, “On the remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phil. Mag. 4, 396–402 (1902).
[CrossRef]

Other (9)

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics XXI, E. Wolf, ed. (Elsevier, New York, 1984), Vol. 21, Chap. 1, pp. 1–67.
[CrossRef]

There is another astigmatism correction solution a = c = R cos α cos β and b = R(cos α cos β)1/2 that has the added advantage of yielding a smaller spherical aberration25 term but the disadvantage of being somewhat less intuitive, since none of the semiaxes are equal to the Rowland circle diameter.

J.-L. Reynaud, “Test results of the 5800g/mm ROALEX holographic grating from Jobin–Yvon,” memo from Laboratorie d’Astronomie Spatiale du CNRS (Centre National de Recherche Scientifique, Marseille, France, 1994).

R. W. Wood, Physical Optics, 3rd ed. (Optical Society of America, Washington, D.C., 1988), p. 264.

S. R. McCandliss, P. D. Feldman, J. B. McPhate, E. B. Burgh, C. Pankratz, R. Pelton, S. Nikzad, O. Siegmund, J. Vallerga, “Current and planned FUV technology development at the Johns Hopkins University,” in Ultraviolet-Optical Space Astronomy Beyond HST, A. Morse, J. M. Shull, A. L. Kinney, eds., Astronomical Society of the Pacific Conference Series 164 (Astronomical Society of the Pacific, San Francisco, 1999), pp. 437–445.

R. G. Tull, “A comparison of holographic and echelle gratings in astronomical spectrometry,” in Instrumentation for Ground-Based Optical Astronomy, Present and Future, The Ninth Santa Cruz Summer Workshop in Astronomy and Astrophysics, L. B. Robinson, ed. (Springer-Verlag, New York, 1988), pp. 104–117.

J. Flamand, F. Bonnemason, A. Thevenon, J. M. Lerner, “Blazing of holographic gratings using ion-etching,” in Raman Scattering, Luminescence, and Spectroscopic Instrumentation in Technology, F. Adar, J. E. Griffiths, J. M. Lerner, eds., Proc. SPIE1055, 288–294 (1989).
[CrossRef]

J. F. Seely, M. P. Kowalski, R. G. Cruddace, J. C. Rife, T. W. Barbee, W. R. Hunter, G. E. Holland, “High-efficiency holographic ion-etched gratings with multilayer coatings and operating on-blaze at normal incidence in the 125 to 300 Å range,” in Multilayer and Grazing Incidence X-Ray/EUV Optics III, R B. Hoover, A B. Walker, eds., Proc. SPIE2805, 148–155 (1996).

P. F. Romanenko, M. V. Sopinski, I. Z. Indutnyi, “Blazed holographic diffraction grating fabrication using As2Se3 inorganic photoresist,” in OPTIKA ’98: 5th Congress on Modern Optics, G. Akos, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE3573, 457–460 (1998).

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Figures (5)

Fig. 1
Fig. 1

Configuration used for measuring the absolute efficiency of the grating in the ±1and the zero orders. The diffracted angles (β±1) are measured from the grating normal.

Fig. 2
Fig. 2

Absolute reflectivity of the grating in the ±1 (triangles and squares, respectively) and the zero (diamonds) orders.

Fig. 3
Fig. 3

Reflectivity of the Pt witness sample.

Fig. 4
Fig. 4

Groove profile as parameterized in the text.

Fig. 5
Fig. 5

Groove efficiencies as a function of wavelength of the ±1 and the zero orders, with the best-fit groove efficiencies overplotted with symbols as in Fig. 2.

Tables (1)

Tables Icon

Table 1 Best-Fit Groove Profile Parameters

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

En=BnB¯n cos βn/cos α,
sin βn=nλ/d+sin α.
nEn=1.
Bn=-1d1+cosα+βncos βncos α+cos βn×0dexp-inKdx-iKλcos α+cos βnFxdx,
F02α, β, rα, rβ, γ, δ, rγ, rδ=M02α, β, rα, rβ+mλ/λ0H02γ, δ, rγ, rδ=0.
F20α, β, rα, rβ, γ, δ, rγ, rδ=M20α, β, rα, rβ+mλ/λ0H20γ, δ, rγ, rδ=0
M02α, β, rα, rβ=1/rα+1/rβ-2a02cos α+cos β=0,
M20α, β,rα, rβ=cos2 α/rα+cos2 β/rβ-2a20cos α+cos β=0.

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