Abstract

The refractive index of the amorphous carbon layers inside multilayer soft x-ray mirrors is derived in the λ = 42–58-Å wavelength range by measuring the shift in the Bragg angle caused by refraction. Reflectivity curves are measured with a reflectometer behind a zone plate monochromator at the National Synchrotron Light Source. The monochromator consists only of a freestanding zone plate of gold and an exit slit and is free of any of the contamination problems often found in monochromators that contain mirrors.

© 1990 Optical Society of America

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References

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  1. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
    [CrossRef]
  2. D. L. Windt et al., “Optical Constants for Thin Films of C, Diamond, Al, Si, and CVD SiC from 24 Å to 1216 Å,” Appl. Opt. 27, 279–295 (1988).
    [CrossRef] [PubMed]
  3. A. Ya. Grudskii, I. A. Brytov, “Optical Constants of Tungsten and Carbon Films Deposited in the Ultrasoft X-Ray Region,” Opt. Spectrosc. (U.S.S.R.) 59, 760–762 (1985).
  4. E. D. Palik, Ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).
  5. D. W. Lynch, “Optical Constants,” in Handbook on Synchrotron Radiation, Vol. 2, G. V. Marr, Ed. (North-Holland, Amsterdam, 1987), pp. 723–783.
  6. E. Spiller, “Reflecting Multilayer Coatings for the Far UV Region,” Appl. Opt. 15, 2333–2338 (1976).
    [CrossRef] [PubMed]
  7. R.-P. Haelbich, A. Segmuller, E. Spiller, “Smooth Multilayer Films Suitable for X-Ray Mirrors,” Appl. Phys. Lett. 34, 184–186 (1979).
    [CrossRef]
  8. D. Rudolph, B. Nieman, G. Schmahl, “Status of the Sputtered Sliced Zone Plates for X-Ray Microscopy, in High Resolution X-Ray Optics, E. Spiller, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.316, 103–105 (1981).
    [CrossRef]
  9. R. M. Bionta, “Transmission Gratings that Diffract 8 keV X Rays,” Appl. Phys. Lett. 51, 725–727, (1987).
    [CrossRef]
  10. W. Stenström, Dissertation, U. Lund, Sweden (1919) as quoted by A. H. Compton, S. K. Allison, X-ray in Theory and Experiment (Van Nostrand Reinhold, New York, 1935); R. W. James, The Optical Principles of Diffraction of X Rays (Cornell U. P., Ithaca, NY, 1965).
  11. T. W. Barbee, “Sputtered Layered Synthetic Microstructure Dispersion Elements,” AIP Conf. Proc. 75, 131–145 (1981); O. J. Petersen, J. M. Thorne, L. V. Knight, T. W. Barbee, “Reflectivity and Roughness of Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 27–32 (1984); W. K. Warburton, K. F. Ludwig, T. W. Barbee, “Comparison Between Ti Anomalous X-Ray Scattering Factors Obtained from Layered Synthetic Microstructures and the Dispersion Relationship,” J. Opt. Soc. Am. B 2, 565–567 (1985).
    [CrossRef]
  12. H. van Brug, M. P. Bruijn, R. van der Pol, M. J. van der Wiel, “Ni-C Multilayer Reflectivity and Photoelectron Yield in the Ni L-Edge Region,” Appl. Phys. Lett. 49, 914–916 (1986).
    [CrossRef]
  13. E. Spiller, “A Zone Plate Monochromator for Synchrotron Radiation,” in Technical Digest, Workshop on X-Ray Instrumentation for Synchrotron Radiation Research, H. Winick, G. Brown, Eds., Stanford SSRL Report 78/04 (1978), pp. VI, 44–49.
  14. A. E. Rosenbluth, P. Lee, “Bragg Condition in Absorbing Multilayers,” Appl. Phys. Lett. 40, 466–468 (1982).
    [CrossRef]
  15. E. Spiller, “Experience with the in situ Monitor System for the Fabrication of X-Ray Mirrors, Proc. Soc. Photo-Opt. Instrum. Eng. 563, 367–375 (1985).
  16. E. Spiller, A. A. Rosenbluth, “Determination of Thickness Errors and Boundary Roughness from the Measured Performance of a Multilayer Coating,” Proc. Soc. Photo-Opt. Instrum. Eng. 563, 221–236 (1985); Opt. Eng. 25, 954–963 (1986).
  17. E. Spiller, “Characterization of Multilayer Coatings by X-Ray Reflection,” Revue Phys. Appl. 23, 1687–1700 (1988).
    [CrossRef]
  18. Y. Vladimirski, E. Kallne, E. Spiller, “The Fabrication of Free-Standing Zone Plates and Transmission Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 25–37 (1984).
  19. Rapidsyn, 3233 Roymar Road, Oceanside, CA 92054, stepper motor 23C-6102C and microstep drive DPM-10.
  20. T. W. Barbee, “The Use of Multilayer Diffraction Gratings in the Determination of X-ray, Soft X-ray, and VUV Elemental Scattering Cross-sections,” Proc. Soc. Photo-Opt. Instrum. Eng. 911, 169–176, (1988).

1988 (3)

E. Spiller, “Characterization of Multilayer Coatings by X-Ray Reflection,” Revue Phys. Appl. 23, 1687–1700 (1988).
[CrossRef]

T. W. Barbee, “The Use of Multilayer Diffraction Gratings in the Determination of X-ray, Soft X-ray, and VUV Elemental Scattering Cross-sections,” Proc. Soc. Photo-Opt. Instrum. Eng. 911, 169–176, (1988).

D. L. Windt et al., “Optical Constants for Thin Films of C, Diamond, Al, Si, and CVD SiC from 24 Å to 1216 Å,” Appl. Opt. 27, 279–295 (1988).
[CrossRef] [PubMed]

1987 (1)

R. M. Bionta, “Transmission Gratings that Diffract 8 keV X Rays,” Appl. Phys. Lett. 51, 725–727, (1987).
[CrossRef]

1986 (1)

H. van Brug, M. P. Bruijn, R. van der Pol, M. J. van der Wiel, “Ni-C Multilayer Reflectivity and Photoelectron Yield in the Ni L-Edge Region,” Appl. Phys. Lett. 49, 914–916 (1986).
[CrossRef]

1985 (3)

E. Spiller, “Experience with the in situ Monitor System for the Fabrication of X-Ray Mirrors, Proc. Soc. Photo-Opt. Instrum. Eng. 563, 367–375 (1985).

E. Spiller, A. A. Rosenbluth, “Determination of Thickness Errors and Boundary Roughness from the Measured Performance of a Multilayer Coating,” Proc. Soc. Photo-Opt. Instrum. Eng. 563, 221–236 (1985); Opt. Eng. 25, 954–963 (1986).

A. Ya. Grudskii, I. A. Brytov, “Optical Constants of Tungsten and Carbon Films Deposited in the Ultrasoft X-Ray Region,” Opt. Spectrosc. (U.S.S.R.) 59, 760–762 (1985).

1984 (1)

Y. Vladimirski, E. Kallne, E. Spiller, “The Fabrication of Free-Standing Zone Plates and Transmission Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 25–37 (1984).

1982 (1)

A. E. Rosenbluth, P. Lee, “Bragg Condition in Absorbing Multilayers,” Appl. Phys. Lett. 40, 466–468 (1982).
[CrossRef]

1981 (2)

T. W. Barbee, “Sputtered Layered Synthetic Microstructure Dispersion Elements,” AIP Conf. Proc. 75, 131–145 (1981); O. J. Petersen, J. M. Thorne, L. V. Knight, T. W. Barbee, “Reflectivity and Roughness of Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 27–32 (1984); W. K. Warburton, K. F. Ludwig, T. W. Barbee, “Comparison Between Ti Anomalous X-Ray Scattering Factors Obtained from Layered Synthetic Microstructures and the Dispersion Relationship,” J. Opt. Soc. Am. B 2, 565–567 (1985).
[CrossRef]

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

1979 (1)

R.-P. Haelbich, A. Segmuller, E. Spiller, “Smooth Multilayer Films Suitable for X-Ray Mirrors,” Appl. Phys. Lett. 34, 184–186 (1979).
[CrossRef]

1976 (1)

Barbee, T. W.

T. W. Barbee, “The Use of Multilayer Diffraction Gratings in the Determination of X-ray, Soft X-ray, and VUV Elemental Scattering Cross-sections,” Proc. Soc. Photo-Opt. Instrum. Eng. 911, 169–176, (1988).

T. W. Barbee, “Sputtered Layered Synthetic Microstructure Dispersion Elements,” AIP Conf. Proc. 75, 131–145 (1981); O. J. Petersen, J. M. Thorne, L. V. Knight, T. W. Barbee, “Reflectivity and Roughness of Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 27–32 (1984); W. K. Warburton, K. F. Ludwig, T. W. Barbee, “Comparison Between Ti Anomalous X-Ray Scattering Factors Obtained from Layered Synthetic Microstructures and the Dispersion Relationship,” J. Opt. Soc. Am. B 2, 565–567 (1985).
[CrossRef]

Bionta, R. M.

R. M. Bionta, “Transmission Gratings that Diffract 8 keV X Rays,” Appl. Phys. Lett. 51, 725–727, (1987).
[CrossRef]

Bruijn, M. P.

H. van Brug, M. P. Bruijn, R. van der Pol, M. J. van der Wiel, “Ni-C Multilayer Reflectivity and Photoelectron Yield in the Ni L-Edge Region,” Appl. Phys. Lett. 49, 914–916 (1986).
[CrossRef]

Brytov, I. A.

A. Ya. Grudskii, I. A. Brytov, “Optical Constants of Tungsten and Carbon Films Deposited in the Ultrasoft X-Ray Region,” Opt. Spectrosc. (U.S.S.R.) 59, 760–762 (1985).

Fujikawa, B. K.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Grudskii, A. Ya.

A. Ya. Grudskii, I. A. Brytov, “Optical Constants of Tungsten and Carbon Films Deposited in the Ultrasoft X-Ray Region,” Opt. Spectrosc. (U.S.S.R.) 59, 760–762 (1985).

Haelbich, R.-P.

R.-P. Haelbich, A. Segmuller, E. Spiller, “Smooth Multilayer Films Suitable for X-Ray Mirrors,” Appl. Phys. Lett. 34, 184–186 (1979).
[CrossRef]

Henke, B. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Kallne, E.

Y. Vladimirski, E. Kallne, E. Spiller, “The Fabrication of Free-Standing Zone Plates and Transmission Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 25–37 (1984).

Lee, P.

A. E. Rosenbluth, P. Lee, “Bragg Condition in Absorbing Multilayers,” Appl. Phys. Lett. 40, 466–468 (1982).
[CrossRef]

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Lynch, D. W.

D. W. Lynch, “Optical Constants,” in Handbook on Synchrotron Radiation, Vol. 2, G. V. Marr, Ed. (North-Holland, Amsterdam, 1987), pp. 723–783.

Nieman, B.

D. Rudolph, B. Nieman, G. Schmahl, “Status of the Sputtered Sliced Zone Plates for X-Ray Microscopy, in High Resolution X-Ray Optics, E. Spiller, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.316, 103–105 (1981).
[CrossRef]

Rosenbluth, A. A.

E. Spiller, A. A. Rosenbluth, “Determination of Thickness Errors and Boundary Roughness from the Measured Performance of a Multilayer Coating,” Proc. Soc. Photo-Opt. Instrum. Eng. 563, 221–236 (1985); Opt. Eng. 25, 954–963 (1986).

Rosenbluth, A. E.

A. E. Rosenbluth, P. Lee, “Bragg Condition in Absorbing Multilayers,” Appl. Phys. Lett. 40, 466–468 (1982).
[CrossRef]

Rudolph, D.

D. Rudolph, B. Nieman, G. Schmahl, “Status of the Sputtered Sliced Zone Plates for X-Ray Microscopy, in High Resolution X-Ray Optics, E. Spiller, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.316, 103–105 (1981).
[CrossRef]

Schmahl, G.

D. Rudolph, B. Nieman, G. Schmahl, “Status of the Sputtered Sliced Zone Plates for X-Ray Microscopy, in High Resolution X-Ray Optics, E. Spiller, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.316, 103–105 (1981).
[CrossRef]

Segmuller, A.

R.-P. Haelbich, A. Segmuller, E. Spiller, “Smooth Multilayer Films Suitable for X-Ray Mirrors,” Appl. Phys. Lett. 34, 184–186 (1979).
[CrossRef]

Shimabukuro, R. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Spiller, E.

E. Spiller, “Characterization of Multilayer Coatings by X-Ray Reflection,” Revue Phys. Appl. 23, 1687–1700 (1988).
[CrossRef]

E. Spiller, “Experience with the in situ Monitor System for the Fabrication of X-Ray Mirrors, Proc. Soc. Photo-Opt. Instrum. Eng. 563, 367–375 (1985).

E. Spiller, A. A. Rosenbluth, “Determination of Thickness Errors and Boundary Roughness from the Measured Performance of a Multilayer Coating,” Proc. Soc. Photo-Opt. Instrum. Eng. 563, 221–236 (1985); Opt. Eng. 25, 954–963 (1986).

Y. Vladimirski, E. Kallne, E. Spiller, “The Fabrication of Free-Standing Zone Plates and Transmission Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 25–37 (1984).

R.-P. Haelbich, A. Segmuller, E. Spiller, “Smooth Multilayer Films Suitable for X-Ray Mirrors,” Appl. Phys. Lett. 34, 184–186 (1979).
[CrossRef]

E. Spiller, “Reflecting Multilayer Coatings for the Far UV Region,” Appl. Opt. 15, 2333–2338 (1976).
[CrossRef] [PubMed]

E. Spiller, “A Zone Plate Monochromator for Synchrotron Radiation,” in Technical Digest, Workshop on X-Ray Instrumentation for Synchrotron Radiation Research, H. Winick, G. Brown, Eds., Stanford SSRL Report 78/04 (1978), pp. VI, 44–49.

Stenström, W.

W. Stenström, Dissertation, U. Lund, Sweden (1919) as quoted by A. H. Compton, S. K. Allison, X-ray in Theory and Experiment (Van Nostrand Reinhold, New York, 1935); R. W. James, The Optical Principles of Diffraction of X Rays (Cornell U. P., Ithaca, NY, 1965).

Tanaka, T. J.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

van Brug, H.

H. van Brug, M. P. Bruijn, R. van der Pol, M. J. van der Wiel, “Ni-C Multilayer Reflectivity and Photoelectron Yield in the Ni L-Edge Region,” Appl. Phys. Lett. 49, 914–916 (1986).
[CrossRef]

van der Pol, R.

H. van Brug, M. P. Bruijn, R. van der Pol, M. J. van der Wiel, “Ni-C Multilayer Reflectivity and Photoelectron Yield in the Ni L-Edge Region,” Appl. Phys. Lett. 49, 914–916 (1986).
[CrossRef]

van der Wiel, M. J.

H. van Brug, M. P. Bruijn, R. van der Pol, M. J. van der Wiel, “Ni-C Multilayer Reflectivity and Photoelectron Yield in the Ni L-Edge Region,” Appl. Phys. Lett. 49, 914–916 (1986).
[CrossRef]

Vladimirski, Y.

Y. Vladimirski, E. Kallne, E. Spiller, “The Fabrication of Free-Standing Zone Plates and Transmission Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 25–37 (1984).

Windt, D. L.

AIP Conf. Proc. (2)

T. W. Barbee, “Sputtered Layered Synthetic Microstructure Dispersion Elements,” AIP Conf. Proc. 75, 131–145 (1981); O. J. Petersen, J. M. Thorne, L. V. Knight, T. W. Barbee, “Reflectivity and Roughness of Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 27–32 (1984); W. K. Warburton, K. F. Ludwig, T. W. Barbee, “Comparison Between Ti Anomalous X-Ray Scattering Factors Obtained from Layered Synthetic Microstructures and the Dispersion Relationship,” J. Opt. Soc. Am. B 2, 565–567 (1985).
[CrossRef]

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “The Atomic Scattering Factor, f1 + if2, for 94 Elements and for the 100 to 2000 eV Photon Energy Range,” AIP Conf. Proc. 75, 340–388, (1981); At. Data Nucl. Data Tables 27, 1–144 (1982).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

H. van Brug, M. P. Bruijn, R. van der Pol, M. J. van der Wiel, “Ni-C Multilayer Reflectivity and Photoelectron Yield in the Ni L-Edge Region,” Appl. Phys. Lett. 49, 914–916 (1986).
[CrossRef]

R.-P. Haelbich, A. Segmuller, E. Spiller, “Smooth Multilayer Films Suitable for X-Ray Mirrors,” Appl. Phys. Lett. 34, 184–186 (1979).
[CrossRef]

R. M. Bionta, “Transmission Gratings that Diffract 8 keV X Rays,” Appl. Phys. Lett. 51, 725–727, (1987).
[CrossRef]

A. E. Rosenbluth, P. Lee, “Bragg Condition in Absorbing Multilayers,” Appl. Phys. Lett. 40, 466–468 (1982).
[CrossRef]

Opt. Spectrosc. (U.S.S.R.) (1)

A. Ya. Grudskii, I. A. Brytov, “Optical Constants of Tungsten and Carbon Films Deposited in the Ultrasoft X-Ray Region,” Opt. Spectrosc. (U.S.S.R.) 59, 760–762 (1985).

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

Y. Vladimirski, E. Kallne, E. Spiller, “The Fabrication of Free-Standing Zone Plates and Transmission Gratings,” Proc. Soc. Photo-Opt. Instrum. Eng. 448, 25–37 (1984).

E. Spiller, “Experience with the in situ Monitor System for the Fabrication of X-Ray Mirrors, Proc. Soc. Photo-Opt. Instrum. Eng. 563, 367–375 (1985).

E. Spiller, A. A. Rosenbluth, “Determination of Thickness Errors and Boundary Roughness from the Measured Performance of a Multilayer Coating,” Proc. Soc. Photo-Opt. Instrum. Eng. 563, 221–236 (1985); Opt. Eng. 25, 954–963 (1986).

T. W. Barbee, “The Use of Multilayer Diffraction Gratings in the Determination of X-ray, Soft X-ray, and VUV Elemental Scattering Cross-sections,” Proc. Soc. Photo-Opt. Instrum. Eng. 911, 169–176, (1988).

Revue Phys. Appl. (1)

E. Spiller, “Characterization of Multilayer Coatings by X-Ray Reflection,” Revue Phys. Appl. 23, 1687–1700 (1988).
[CrossRef]

Other (6)

W. Stenström, Dissertation, U. Lund, Sweden (1919) as quoted by A. H. Compton, S. K. Allison, X-ray in Theory and Experiment (Van Nostrand Reinhold, New York, 1935); R. W. James, The Optical Principles of Diffraction of X Rays (Cornell U. P., Ithaca, NY, 1965).

D. Rudolph, B. Nieman, G. Schmahl, “Status of the Sputtered Sliced Zone Plates for X-Ray Microscopy, in High Resolution X-Ray Optics, E. Spiller, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.316, 103–105 (1981).
[CrossRef]

Rapidsyn, 3233 Roymar Road, Oceanside, CA 92054, stepper motor 23C-6102C and microstep drive DPM-10.

E. Spiller, “A Zone Plate Monochromator for Synchrotron Radiation,” in Technical Digest, Workshop on X-Ray Instrumentation for Synchrotron Radiation Research, H. Winick, G. Brown, Eds., Stanford SSRL Report 78/04 (1978), pp. VI, 44–49.

E. D. Palik, Ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).

D. W. Lynch, “Optical Constants,” in Handbook on Synchrotron Radiation, Vol. 2, G. V. Marr, Ed. (North-Holland, Amsterdam, 1987), pp. 723–783.

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Figures (9)

Fig. 1
Fig. 1

Calculated reflectivity vs grazing angle R(θ) curve for a sixty-layer Co–C coating with p = 58.8 Å for λ = 49.1 Å for three values of the boundary width σ. The dashed vertical line represents θ0, the index shifted Bragg angle as calculated from Eq. (6).

Fig. 2
Fig. 2

Correction θcorr = θ0θmax between the index corrected Bragg angle θ0 as obtained from Eq. (6) and θmax as obtained from the full theory for the three mirrors of Table I for a σ = 7.5- Å value. Points are calculated with the optical constants of Ref. 1, full curves are interpolation used in the data analysis. The main contribution to the correction is due to absorption.

Fig. 3
Fig. 3

Geometry of the zone plate monochromator at the National Synchrotron Light Source.

Fig. 4
Fig. 4

Measured reflectivities R(θ) (points) for the sixty-layer Co–C mirror with a 58.8-Å period for two wavelengths and calculated reflectivity curves obtained with the parameters in Table I and those in the figure (solid curves). The refractive index of carbon is used as a fitting parameter to obtain the same value of θmax for the measured as for the calculated curve.

Fig. 5
Fig. 5

Measured reflectivities R(θ) (points) for the 140-layer Co–C mirror with a 32.1-Å period for two wavelengths and calculated reflectivity curves obtained with the parameters in Table I and those in the figure (solid curves). The index of carbon is used as a fitting parameter to obtain the same θmax value for the measured and calculated curve. The main cause for the larger width of the experimental curve is the limited resolution of the monochromator.

Fig. 6
Fig. 6

Measured values of the grazing angle for maximum reflectivity θmax vs λ as obtained from a reflectivity curve similar to those in Figs. 4 and 5 for the three mirrors in Table I.

Fig. 7
Fig. 7

Refractive index δ = 1 − n obtained from the data points in Fig. 6 (open symbols). The solid circles are the data from Ref. 1 and the smooth solid curve represents Eq. (8).

Fig. 8
Fig. 8

Measured peak reflectivities vs wavelength as obtained for the sixty-layer mirror or period 58.8 Å (points) and calculated values using optical constants of Ref. 1 and the parameters of Table I. The large variations are due to the fact that the incident beam intensity was not measured for each data point.

Fig. 9
Fig. 9

Measured reflectivity vs wavelength for the sixty-layer Co–C mirror for three angles of incidence for wavelengths around the carbon edge. The short wavelength drop in the reflectivity curves for θ = 21.98° and 21.78° is produced by the increase in absorption at the edge.

Tables (1)

Tables Icon

Table I Parameters of the Co–C Multilayer Mirrors

Equations (8)

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

2 φ = 4 π λ n p cos α = 4 π λ n p sin θ ,
m λ = 2 p n sin θ .
m λ = 2 p sin θ 0 1 - 2 δ eff sin 2 θ 0 ·
δ eff = d 1 δ 1 + d 2 δ 2 d 1 + d 2 .
2 δ eff = sin 2 θ 0 - ( m λ 2 p ) 2 ,
sin θ 0 = m λ 4 p ( 1 + 1 + 16 p 2 δ eff m 2 λ 2 ) .
δ C o = 0.01138 + 0.000561 λ .
δ = 0.0067 - 1 ( λ - λ 1 ) ( λ - λ 2 ) + 0.009 - ( λ 3 - λ ) / 4 ,

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