Abstract

We have measured the efficiency over the range 125–225 Å of a bare ion-etched plane laminar holographic grating made of fused silica and with 1000 grooves/mm. The measured efficiency of each order oscillates with wavelength because of constructive and destructive interference between radiation diffracted from the lands and the grooves. We measured the grating groove profile with an atomic force microscope, and the resulting groove depth of 434 ± 6 Å agrees well with the values determined independently from the oscillatory behavior of the efficiency measurements. Grating efficiency in the +1 order peaked at values of 0.027%, 0.011%, and 0.005% at wavelengths of 191, 157, and 132 Å, respectively; and the derived groove efficiencies are 27%, 25%, and 27%. The irregular shape at the land–groove edges dominates the large grating roughness of 23–45-Å rms, but even regions far from the edges have a roughness of 10–18-Å rms. The average groove profile was used to model the grating efficiency, and the resulting wavelengths predicted for different order maxima and minima agree well with measured wavelengths, although the calculated efficiencies are greater than the measured results by 10–20%.

© 2001 Optical Society of America

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  1. B. Vidal, P. Vincent, P. Dhez, M. Nevière, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 142–149 (1985).
    [CrossRef]
  2. K.-H. Hellwege, “Über rasterförmige Reflexionsgitter,” Z. Phys. 106, 588–596 (1937).
    [CrossRef]
  3. K.-H. Hellwege, “Über rasterförmige Reflexionsgitter, Nachtrag,” Z. Phys. 111, 495–497 (1939).
    [CrossRef]
  4. R. G. Cruddace, T. W. Barbee, J. C. Rife, W. R. Hunter, “Measurements of the normal-incidence x-ray reflectance of a molybdenum-silicon multilayer deposited on a 2000-1/mm grating,” Phys. Scr. 41, 396–399 (1990).
    [CrossRef]
  5. M. P. Kowalski, T. W. Barbee, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Efficiency and long-term stability of a multilayer-coated ion-etched holographic grating in the 125–133-Å wavelength region,” Appl. Opt. 34, 7338–7346 (1995).
    [CrossRef] [PubMed]
  6. J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Eby, K. G. Stolt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya–Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
    [CrossRef] [PubMed]
  7. M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0-nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
    [CrossRef] [PubMed]
  8. J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
    [CrossRef]
  9. M. P. Kowalski, T. W. Barbee, K. F. Heidemann, H. Gursky, J. C. Rife, W. R. Hunter, G. G. Fritz, R. G. Cruddace, “Efficiency calibration of the first multilayer-coated holographic ion-etched flight grating for a sounding rocket high-resolution spectrometer,” Appl. Opt. 38, 6487–6493 (1999).
    [CrossRef]
  10. M. Kowalski, “Space Science Division’s J-PEX instrument to provide new data on the evolution of white dwarf stars,” NRL Labstracts (Naval Research Laboratory, Washington, D.C., 2001).
  11. G. Quincke, Pogg. Ann. Phys. Chem. 132, 364 (1867).
  12. G. Quincke, Pogg, Ann. Phys. Chem.146, 1 (1872).
  13. C. H. Cartwright, “Laminar reflection gratings for infrared investigation,” J. Opt. Soc. Am. 21, 785 (1931).
    [CrossRef]
  14. C. Candler, Modern Interferometers (Hilger, London, 1951).
  15. A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
    [CrossRef]
  16. W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
    [CrossRef]
  17. M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Uncertainties in reflectance measurements made on the NRL beam line X24C,” (Naval Research Laboratory, Washington, D.C., 1995).
  18. W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods Phys. Res. A 246, 465–468 (1986).
    [CrossRef]
  19. M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
    [CrossRef]
  20. L. I. Goray, “Numerical analysis for relief gratings working in the soft x-ray and XUV region by the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover, M. W. Tate, eds., Proc. SPIE2278, 168–172 (1994).
    [CrossRef]
  21. L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2215, 240–245 (1995).
    [CrossRef]
  22. J. F. Seely, C. Montcalm, S. Baker, S. Bajt, “High-efficiency MoRu–Be multilayer-coated gratings operating near-normal incidence in the 11.1–12.0-nm wavelength range,” Appl. Opt. 40, 5565–5574 (2001).
    [CrossRef]

2001 (1)

1999 (1)

1997 (3)

1995 (2)

1990 (1)

R. G. Cruddace, T. W. Barbee, J. C. Rife, W. R. Hunter, “Measurements of the normal-incidence x-ray reflectance of a molybdenum-silicon multilayer deposited on a 2000-1/mm grating,” Phys. Scr. 41, 396–399 (1990).
[CrossRef]

1986 (1)

W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods Phys. Res. A 246, 465–468 (1986).
[CrossRef]

1982 (1)

W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
[CrossRef]

1975 (1)

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

1939 (1)

K.-H. Hellwege, “Über rasterförmige Reflexionsgitter, Nachtrag,” Z. Phys. 111, 495–497 (1939).
[CrossRef]

1937 (1)

K.-H. Hellwege, “Über rasterförmige Reflexionsgitter,” Z. Phys. 106, 588–596 (1937).
[CrossRef]

1931 (1)

1867 (1)

G. Quincke, Pogg. Ann. Phys. Chem. 132, 364 (1867).

Bajt, S.

Baker, S.

Barbee, T. W.

Bennett, J. M.

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

Candler, C.

C. Candler, Modern Interferometers (Hilger, London, 1951).

Cartwright, C. H.

Chernov, B. C.

L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2215, 240–245 (1995).
[CrossRef]

Cruddace, R. G.

M. P. Kowalski, T. W. Barbee, K. F. Heidemann, H. Gursky, J. C. Rife, W. R. Hunter, G. G. Fritz, R. G. Cruddace, “Efficiency calibration of the first multilayer-coated holographic ion-etched flight grating for a sounding rocket high-resolution spectrometer,” Appl. Opt. 38, 6487–6493 (1999).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0-nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
[CrossRef]

J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Eby, K. G. Stolt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya–Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
[CrossRef] [PubMed]

M. P. Kowalski, T. W. Barbee, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Efficiency and long-term stability of a multilayer-coated ion-etched holographic grating in the 125–133-Å wavelength region,” Appl. Opt. 34, 7338–7346 (1995).
[CrossRef] [PubMed]

R. G. Cruddace, T. W. Barbee, J. C. Rife, W. R. Hunter, “Measurements of the normal-incidence x-ray reflectance of a molybdenum-silicon multilayer deposited on a 2000-1/mm grating,” Phys. Scr. 41, 396–399 (1990).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Uncertainties in reflectance measurements made on the NRL beam line X24C,” (Naval Research Laboratory, Washington, D.C., 1995).

Dhez, P.

B. Vidal, P. Vincent, P. Dhez, M. Nevière, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 142–149 (1985).
[CrossRef]

Eby, R.

Franks, A.

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

Fritz, G. G.

Goray, L. I.

M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
[CrossRef]

L. I. Goray, “Numerical analysis for relief gratings working in the soft x-ray and XUV region by the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover, M. W. Tate, eds., Proc. SPIE2278, 168–172 (1994).
[CrossRef]

L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2215, 240–245 (1995).
[CrossRef]

Gursky, H.

Heidemann, K. F.

Heinzmann, U.

Hellwege, K.-H.

K.-H. Hellwege, “Über rasterförmige Reflexionsgitter, Nachtrag,” Z. Phys. 111, 495–497 (1939).
[CrossRef]

K.-H. Hellwege, “Über rasterförmige Reflexionsgitter,” Z. Phys. 106, 588–596 (1937).
[CrossRef]

Hunt, D. J.

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

Hunter, W. R.

M. P. Kowalski, T. W. Barbee, K. F. Heidemann, H. Gursky, J. C. Rife, W. R. Hunter, G. G. Fritz, R. G. Cruddace, “Efficiency calibration of the first multilayer-coated holographic ion-etched flight grating for a sounding rocket high-resolution spectrometer,” Appl. Opt. 38, 6487–6493 (1999).
[CrossRef]

J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0-nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
[CrossRef]

M. P. Kowalski, T. W. Barbee, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Efficiency and long-term stability of a multilayer-coated ion-etched holographic grating in the 125–133-Å wavelength region,” Appl. Opt. 34, 7338–7346 (1995).
[CrossRef] [PubMed]

J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Eby, K. G. Stolt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya–Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
[CrossRef] [PubMed]

R. G. Cruddace, T. W. Barbee, J. C. Rife, W. R. Hunter, “Measurements of the normal-incidence x-ray reflectance of a molybdenum-silicon multilayer deposited on a 2000-1/mm grating,” Phys. Scr. 41, 396–399 (1990).
[CrossRef]

W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods Phys. Res. A 246, 465–468 (1986).
[CrossRef]

W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Uncertainties in reflectance measurements made on the NRL beam line X24C,” (Naval Research Laboratory, Washington, D.C., 1995).

Kabler, M. N.

W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
[CrossRef]

Kirkland, J. P.

W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
[CrossRef]

Kleineberg, U.

Kowalski, M.

M. Kowalski, “Space Science Division’s J-PEX instrument to provide new data on the evolution of white dwarf stars,” NRL Labstracts (Naval Research Laboratory, Washington, D.C., 2001).

Kowalski, M. P.

M. P. Kowalski, T. W. Barbee, K. F. Heidemann, H. Gursky, J. C. Rife, W. R. Hunter, G. G. Fritz, R. G. Cruddace, “Efficiency calibration of the first multilayer-coated holographic ion-etched flight grating for a sounding rocket high-resolution spectrometer,” Appl. Opt. 38, 6487–6493 (1999).
[CrossRef]

J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
[CrossRef]

M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0-nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

M. P. Kowalski, T. W. Barbee, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Efficiency and long-term stability of a multilayer-coated ion-etched holographic grating in the 125–133-Å wavelength region,” Appl. Opt. 34, 7338–7346 (1995).
[CrossRef] [PubMed]

J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Eby, K. G. Stolt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya–Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
[CrossRef] [PubMed]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Uncertainties in reflectance measurements made on the NRL beam line X24C,” (Naval Research Laboratory, Washington, D.C., 1995).

Lindsey, K.

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

Menke, D.

Montcalm, C.

Nevière, M.

B. Vidal, P. Vincent, P. Dhez, M. Nevière, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 142–149 (1985).
[CrossRef]

Osterried, K.

Quincke, G.

G. Quincke, Pogg. Ann. Phys. Chem. 132, 364 (1867).

Rife, J. C.

M. P. Kowalski, T. W. Barbee, K. F. Heidemann, H. Gursky, J. C. Rife, W. R. Hunter, G. G. Fritz, R. G. Cruddace, “Efficiency calibration of the first multilayer-coated holographic ion-etched flight grating for a sounding rocket high-resolution spectrometer,” Appl. Opt. 38, 6487–6493 (1999).
[CrossRef]

J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0-nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
[CrossRef]

M. P. Kowalski, T. W. Barbee, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Efficiency and long-term stability of a multilayer-coated ion-etched holographic grating in the 125–133-Å wavelength region,” Appl. Opt. 34, 7338–7346 (1995).
[CrossRef] [PubMed]

J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Eby, K. G. Stolt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya–Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
[CrossRef] [PubMed]

R. G. Cruddace, T. W. Barbee, J. C. Rife, W. R. Hunter, “Measurements of the normal-incidence x-ray reflectance of a molybdenum-silicon multilayer deposited on a 2000-1/mm grating,” Phys. Scr. 41, 396–399 (1990).
[CrossRef]

W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods Phys. Res. A 246, 465–468 (1986).
[CrossRef]

W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Uncertainties in reflectance measurements made on the NRL beam line X24C,” (Naval Research Laboratory, Washington, D.C., 1995).

Seely, J. F.

J. F. Seely, C. Montcalm, S. Baker, S. Bajt, “High-efficiency MoRu–Be multilayer-coated gratings operating near-normal incidence in the 11.1–12.0-nm wavelength range,” Appl. Opt. 40, 5565–5574 (2001).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0-nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
[CrossRef]

M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
[CrossRef]

J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Eby, K. G. Stolt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya–Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
[CrossRef] [PubMed]

M. P. Kowalski, T. W. Barbee, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Efficiency and long-term stability of a multilayer-coated ion-etched holographic grating in the 125–133-Å wavelength region,” Appl. Opt. 34, 7338–7346 (1995).
[CrossRef] [PubMed]

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Uncertainties in reflectance measurements made on the NRL beam line X24C,” (Naval Research Laboratory, Washington, D.C., 1995).

Speer, R. J.

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

Stolt, K. G.

Turner, D.

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

Vidal, B.

B. Vidal, P. Vincent, P. Dhez, M. Nevière, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 142–149 (1985).
[CrossRef]

Vincent, P.

B. Vidal, P. Vincent, P. Dhez, M. Nevière, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 142–149 (1985).
[CrossRef]

Williams, R. T.

W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
[CrossRef]

Appl. Opt. (6)

M. P. Kowalski, T. W. Barbee, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Efficiency and long-term stability of a multilayer-coated ion-etched holographic grating in the 125–133-Å wavelength region,” Appl. Opt. 34, 7338–7346 (1995).
[CrossRef] [PubMed]

J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Eby, K. G. Stolt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya–Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
[CrossRef] [PubMed]

J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å wavelength region,” Appl. Opt. 36, 8206–8213 (1997).
[CrossRef]

M. P. Kowalski, T. W. Barbee, K. F. Heidemann, H. Gursky, J. C. Rife, W. R. Hunter, G. G. Fritz, R. G. Cruddace, “Efficiency calibration of the first multilayer-coated holographic ion-etched flight grating for a sounding rocket high-resolution spectrometer,” Appl. Opt. 38, 6487–6493 (1999).
[CrossRef]

M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
[CrossRef]

J. F. Seely, C. Montcalm, S. Baker, S. Bajt, “High-efficiency MoRu–Be multilayer-coated gratings operating near-normal incidence in the 11.1–12.0-nm wavelength range,” Appl. Opt. 40, 5565–5574 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

Nucl. Instrum. Methods Phys. Res. (1)

W. R. Hunter, R. T. Williams, J. C. Rife, J. P. Kirkland, M. N. Kabler, “A grating/crystal monochromator for the spectral range 5 eV to 5 keV,” Nucl. Instrum. Methods Phys. Res. 195, 141–153 (1982).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

W. R. Hunter, J. C. Rife, “An ultrahigh vacuum reflectometer/goniometer for use with synchrotron radiation,” Nucl. Instrum. Methods Phys. Res. A 246, 465–468 (1986).
[CrossRef]

Opt. Lett. (1)

Philos. Trans. R. Soc. London (1)

A. Franks, K. Lindsey, J. M. Bennett, R. J. Speer, D. Turner, D. J. Hunt, “The theory, manufacture, structure and performance of N.P.L. x-ray gratings,” Philos. Trans. R. Soc. London 277, 503–543 (1975).
[CrossRef]

Phys. Scr. (1)

R. G. Cruddace, T. W. Barbee, J. C. Rife, W. R. Hunter, “Measurements of the normal-incidence x-ray reflectance of a molybdenum-silicon multilayer deposited on a 2000-1/mm grating,” Phys. Scr. 41, 396–399 (1990).
[CrossRef]

Pogg. Ann. Phys. Chem. (1)

G. Quincke, Pogg. Ann. Phys. Chem. 132, 364 (1867).

Z. Phys. (2)

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[CrossRef]

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Other (7)

B. Vidal, P. Vincent, P. Dhez, M. Nevière, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE563, 142–149 (1985).
[CrossRef]

M. Kowalski, “Space Science Division’s J-PEX instrument to provide new data on the evolution of white dwarf stars,” NRL Labstracts (Naval Research Laboratory, Washington, D.C., 2001).

G. Quincke, Pogg, Ann. Phys. Chem.146, 1 (1872).

C. Candler, Modern Interferometers (Hilger, London, 1951).

M. P. Kowalski, R. G. Cruddace, J. F. Seely, J. C. Rife, W. R. Hunter, “Uncertainties in reflectance measurements made on the NRL beam line X24C,” (Naval Research Laboratory, Washington, D.C., 1995).

L. I. Goray, “Numerical analysis for relief gratings working in the soft x-ray and XUV region by the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover, M. W. Tate, eds., Proc. SPIE2278, 168–172 (1994).
[CrossRef]

L. I. Goray, B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. C. Walker, eds., Proc. SPIE2215, 240–245 (1995).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Shaded AFM image of one period of the grating. The vertical scale is exaggerated to reveal the texture.

Fig. 2
Fig. 2

PSD of the whole grating image of Fig. 1 in the (a) X direction (perpendicular to the grooves) and (b) the Y direction (parallel to the grooves). The markers indicate the frequency ranges over which the PSD was integrated to produce a value of roughness (Table 1).

Fig. 3
Fig. 3

X PSD of (a) a region on the grating land and (b) flat 371. Markers are as in Fig. 2.

Fig. 4
Fig. 4

Grating groove profile. The shaded area is the superposition of all 300 rows of data in the grating image. The solid curve is the average over all rows, and the two dashed curves are the standard deviation.

Fig. 5
Fig. 5

Diagram showing the geometry used to calculate path differences for a laminar grating.

Fig. 6
Fig. 6

Calculation of the efficiency of a perfectly reflecting ideal laminar grating in the 0th, 1st, and 3rd orders as a function of wavelength and groove depth. The grating has a groove depth of 400 Å, a groove density of 1000 grooves/mm, and is illuminated at 0° angle of incidence.

Fig. 7
Fig. 7

Calculated efficiency of a perfectly reflecting ideal laminar grating as a function of diffraction angle.

Fig. 8
Fig. 8

Typical measurement of efficiency of the grating, made at 182.33 Å (68 eV) as a function of diffraction angle after correction for background noise and angular error in the reflectometer. The plus signs indicate the location of the different orders.

Fig. 9
Fig. 9

Measured efficiency of the grating as a function of wavelength. For the grating, the 0-order results are circles, the -1-order results are filled squares, and the +1-order results are open squares. The solid curves are the calculated reflectances for parallel-polarized radiation (R p ) from fused-silica surfaces with 0- and 15-Å rms roughness.

Fig. 10
Fig. 10

Comparison of the measured grating efficiency (data points) and the calculated efficiency. The data point symbols are the same as in Fig. 9. The solid curves are results of calculations for the 0th and ±1st orders.

Fig. 11
Fig. 11

Measured 0th, 1st, 2nd, and 3rd orders from the grating. The ordinate is presented on a log scale to emphasize detail at low efficiency. Open symbols are inside (plus) orders. Filled symbols are outside (minus) orders. Circles are the 0th order, squares are the 1st order, triangles are the 2nd order, diamonds are the 3rd order.

Tables (2)

Tables Icon

Table 1 AFM Results for Grating and Witness Flats

Tables Icon

Table 2 Groove Depth Calculation from Efficiency Maxima

Equations (7)

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

FD=sin2Naksin ϕ-sin ϕ0/sin2 aksin ϕ-sin ϕ0,
FS=sin2ksin ϕ-sin ϕ0a/2/k2sin ϕ-sin ϕ02a/22.
FI=cos2π/λΔS,
ΔS=asin ϕ-sin ϕ0+dcos ϕ+cos ϕ0
J=AZncos2π/λΔS,
ΔS=cos2π/2λ2dcos ϕ+cos ϕ0+nλ.
ΔS=cos2π/2λnλ+2d cos ϕ+2dcos2 ϕ+2nλ/asin ϕ-nλ/a20.5.

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