Abstract

We have measured zero- and first-order efficiencies of plane diffraction grazings over the 100–300-Å band using the NRL beamline facility at the National Synchrotron Light Source. Measurements were taken at grating angles of 5°, 10°, and 15° and the incident radiation was polarized primarily in the transverse magnetic mode. Four (three laminar, one blazed) of the gratings were ion etched in high quality quartz blanks, overcoated with 200 Å of gold. A fifth (blazed) grating was ruled in gold. The line densities are 1000, 2000, and 3600 grooves/mm for those with laminar profiles. Both blazed gratings have a blaze angle of 8° and line densities of 3600 grooves/mm. Measured first-order efficiencies up to 15% were obtained for the laminar gratings and up to 8% was obtained for the ion-etched blazed grating. Much lower efficiencies (≤2%) were measured for the ruled grating. A computer program was written to calculate grating efficiencies using a full electromagnetic model. Measured efficiencies of the ion-etched gratings agree well with predicted values, but the measured first-order efficiency of the ruled grating is much lower than predicted.

© 1989 Optical Society of America

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References

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  1. K. S. Wood et al., “The HEAO A-l X-Ray Source Catalog,” Astrophys. J. Suppl. 56, 507 (1984).
    [CrossRef]
  2. H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optik en für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
    [CrossRef]
  3. H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
    [CrossRef]
  4. J. L. Culhane, W. Cash, R. C. Catura, “New Applications of X-Ray Optical Techniques,” Nucl. Instrum. Methods 221, 251 (1984).
    [CrossRef]
  5. M. C. Hettrick, S. Bowyer, “Variable Line-Space Gratings: New Designs for Use in Grazing Incidence Spectrometers,” Appl. Opt. 22, 3921 (1983).
    [CrossRef] [PubMed]
  6. W. C. Cash, “X-Ray Spectrographs Using Radial Groove Gratings,” Appl. Opt. 22, 3971 (1983).
    [CrossRef] [PubMed]
  7. W. E. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).
  8. M. C. E. Huber, G. Tondello, “Stigmatic Performance of an XUV Spectrograph with a Single Toroidal Grating,” Appl. Opt. 18, 3948 (1979).
    [CrossRef] [PubMed]
  9. A. M. Malvezzi, L. Garifo, G. Tondello, “Grazing-Incidence High-Resolution Stigmatic Spectrograph with Two Optical Elements,” Appl. Opt. 20, 2560 (1981).
    [CrossRef] [PubMed]
  10. J. F. Meekins, H. Gursky, R. G. Cruddace, “Optimization of the Rowland Circle Grating for High-Resolution Astrophysical Spectrometers Working at Soft X-Ray and EUV Wavelengths,” Appl. Opt. 24, 2987 (1985).
    [CrossRef] [PubMed]
  11. 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 195, 141 (1982).
    [CrossRef]
  12. W. R. Hunter, J. C. Rife, “Higher-Order Suppression in an On-Blaze Plane-Grating Monochromator,” Appl. Opt. 23, 293 (1984).
    [CrossRef] [PubMed]
  13. W. R. Hunter, J. C. Rife, “An Ultrahigh Vacuum Reflectometer/Goniometer for Use with Synchrotron Radiation,” Nucl. Instrum. Methods A 246, 465 (1986).
    [CrossRef]
  14. W. R. Hunter, Sachs/Freeman Associates, Inc.; private communication (1985).
  15. Hyperfine Corp.; private communication (1987).
  16. P. Vincent, “Differential Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, New York, 1980), p. 101.
    [CrossRef]
  17. M. Neviere, “The Homogeneous Problem,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, New York, 1980), p. 123.
    [CrossRef]
  18. P. J. Davis, I. Polonsky, “Numerical Interpolation, Differentiation, and Integration,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz, I. A. Stegun, Eds., National Bureau of Standards Applied Mathematics Series 55 (1964, revised 1966), p. 875.

1986 (1)

W. R. Hunter, J. C. Rife, “An Ultrahigh Vacuum Reflectometer/Goniometer for Use with Synchrotron Radiation,” Nucl. Instrum. Methods A 246, 465 (1986).
[CrossRef]

1985 (1)

1984 (3)

W. R. Hunter, J. C. Rife, “Higher-Order Suppression in an On-Blaze Plane-Grating Monochromator,” Appl. Opt. 23, 293 (1984).
[CrossRef] [PubMed]

K. S. Wood et al., “The HEAO A-l X-Ray Source Catalog,” Astrophys. J. Suppl. 56, 507 (1984).
[CrossRef]

J. L. Culhane, W. Cash, R. C. Catura, “New Applications of X-Ray Optical Techniques,” Nucl. Instrum. Methods 221, 251 (1984).
[CrossRef]

1983 (2)

1982 (2)

W. E. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).

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 195, 141 (1982).
[CrossRef]

1981 (1)

1979 (1)

1964 (1)

P. J. Davis, I. Polonsky, “Numerical Interpolation, Differentiation, and Integration,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz, I. A. Stegun, Eds., National Bureau of Standards Applied Mathematics Series 55 (1964, revised 1966), p. 875.

1952 (2)

H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optik en für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
[CrossRef]

Bowyer, S.

Cash, W.

J. L. Culhane, W. Cash, R. C. Catura, “New Applications of X-Ray Optical Techniques,” Nucl. Instrum. Methods 221, 251 (1984).
[CrossRef]

W. E. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).

Cash, W. C.

Catura, R. C.

J. L. Culhane, W. Cash, R. C. Catura, “New Applications of X-Ray Optical Techniques,” Nucl. Instrum. Methods 221, 251 (1984).
[CrossRef]

Cruddace, R. G.

Culhane, J. L.

J. L. Culhane, W. Cash, R. C. Catura, “New Applications of X-Ray Optical Techniques,” Nucl. Instrum. Methods 221, 251 (1984).
[CrossRef]

Davis, P. J.

P. J. Davis, I. Polonsky, “Numerical Interpolation, Differentiation, and Integration,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz, I. A. Stegun, Eds., National Bureau of Standards Applied Mathematics Series 55 (1964, revised 1966), p. 875.

Garifo, L.

Gursky, H.

Hettrick, M. C.

Huber, M. C. E.

Hunter, W. R.

W. R. Hunter, J. C. Rife, “An Ultrahigh Vacuum Reflectometer/Goniometer for Use with Synchrotron Radiation,” Nucl. Instrum. Methods A 246, 465 (1986).
[CrossRef]

W. R. Hunter, J. C. Rife, “Higher-Order Suppression in an On-Blaze Plane-Grating Monochromator,” Appl. Opt. 23, 293 (1984).
[CrossRef] [PubMed]

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 195, 141 (1982).
[CrossRef]

W. R. Hunter, Sachs/Freeman Associates, Inc.; private communication (1985).

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 195, 141 (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 195, 141 (1982).
[CrossRef]

Malvezzi, A. M.

McClintock, W. E.

W. E. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).

Meekins, J. F.

Neviere, M.

M. Neviere, “The Homogeneous Problem,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, New York, 1980), p. 123.
[CrossRef]

Polonsky, I.

P. J. Davis, I. Polonsky, “Numerical Interpolation, Differentiation, and Integration,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz, I. A. Stegun, Eds., National Bureau of Standards Applied Mathematics Series 55 (1964, revised 1966), p. 875.

Rife, J. C.

W. R. Hunter, J. C. Rife, “An Ultrahigh Vacuum Reflectometer/Goniometer for Use with Synchrotron Radiation,” Nucl. Instrum. Methods A 246, 465 (1986).
[CrossRef]

W. R. Hunter, J. C. Rife, “Higher-Order Suppression in an On-Blaze Plane-Grating Monochromator,” Appl. Opt. 23, 293 (1984).
[CrossRef] [PubMed]

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 195, 141 (1982).
[CrossRef]

Tondello, G.

Vincent, P.

P. Vincent, “Differential Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, New York, 1980), p. 101.
[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 195, 141 (1982).
[CrossRef]

Wolter, H.

H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optik en für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
[CrossRef]

Wood, K. S.

K. S. Wood et al., “The HEAO A-l X-Ray Source Catalog,” Astrophys. J. Suppl. 56, 507 (1984).
[CrossRef]

Ann. Phys. (2)

H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optik en für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
[CrossRef]

Appl. Opt. (6)

Astrophys. J. Suppl. (1)

K. S. Wood et al., “The HEAO A-l X-Ray Source Catalog,” Astrophys. J. Suppl. 56, 507 (1984).
[CrossRef]

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1)

P. J. Davis, I. Polonsky, “Numerical Interpolation, Differentiation, and Integration,” in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz, I. A. Stegun, Eds., National Bureau of Standards Applied Mathematics Series 55 (1964, revised 1966), p. 875.

Nucl. Instrum. Methods (2)

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 195, 141 (1982).
[CrossRef]

J. L. Culhane, W. Cash, R. C. Catura, “New Applications of X-Ray Optical Techniques,” Nucl. Instrum. Methods 221, 251 (1984).
[CrossRef]

Nucl. Instrum. Methods A (1)

W. R. Hunter, J. C. Rife, “An Ultrahigh Vacuum Reflectometer/Goniometer for Use with Synchrotron Radiation,” Nucl. Instrum. Methods A 246, 465 (1986).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. E. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).

Other (4)

W. R. Hunter, Sachs/Freeman Associates, Inc.; private communication (1985).

Hyperfine Corp.; private communication (1987).

P. Vincent, “Differential Methods,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, New York, 1980), p. 101.
[CrossRef]

M. Neviere, “The Homogeneous Problem,” in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer-Verlag, New York, 1980), p. 123.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Zero-order efficiency of the 1000-grooves/mm laminar, ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 2
Fig. 2

First- (n = −1) order efficiency of the 1000-grooves/mm laminar ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 3
Fig. 3

Zero-order efficiency of the 2000-grooves/mm laminar ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 4
Fig. 4

First- (n = −1) order efficiency of the 2000-grooves/mm laminar ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 5
Fig. 5

Zero-order efficiency of the 3600-grooves/mm laminar ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 6
Fig. 6

First- (n = −1) order efficiency of the 3600-grooves/mm laminar ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 7
Fig. 7

Zero-order efficiency of the 3600-grooves/mm blazed ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidences. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 8
Fig. 8

First- (n= −1) order efficiency of the 3600-grooves/mm blazed ion-etched grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 9
Fig. 9

Zero-order efficiency of the 3600-grooves/mm blazed ruled grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation.

Fig. 10
Fig. 10

First- (n = −1) order efficiency of the 3600-grooves/mm blazed ruled grating for (a) 5°, (b) 10°, and (c) 15° angles of incidence. The dashed and solid curves are the efficiencies calculated for unpolarized (RAN) and TM mode incident radiation. Because the low efficiencies in (c) are subject to unknown systematic errors, error estimation for them is difficult and it is doubtful that the small error bars shown are true indications of the actual measurement errors.

Fig. 11
Fig. 11

Groove profile used for the 2000-grooves/mm laminar ion-etched grating efficiency calculations. The profile of the 200-Å gold overcoat was assumed to faithfully follow the Talystep measurements of the ion-etched quartz substrate. Also shown is a Talystep trace of the surface of the superpolished blank before etching.

Fig. 12
Fig. 12

Assumed grating profile of the 3600-grooves/mm blazed ruled grating.

Fig. 13
Fig. 13

Schematic of the grating orientation. The z axis is perpendicular to the grating surface. The grooves are aligned parallel to the y axis.

Fig. 14
Fig. 14

Schematic of the grating groove profile and the permittivity, showing the discontinuities at the boundaries of dissimilar materials.

Equations (24)

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E = E  exp( i k x i ω t )  , H = H  exp ( i k x i ω t )  ,
2 E + ( ω 2 μ c / c 2 ) E = 0 , 2 H + ( ω 2 μ c / c 2 ) H = 0 ,
i k y E z E y / z = ( i ω μ / c ) H x , E x / z E z / x = ( i ω μ / c ) H y , E y / x i k y E x = ( i ω μ / c ) H z , i k y H z H y / z = ( i ω c / c ) E x , H x / x H z / x = ( i ω c / c ) E y , H y / x i k y H x = ( i ω c / c ) E z .
E ( x , z ) = n   E n ( z )  exp ( i α n x )
q ( x , z ) = n   q n ( z )  exp( 2 π i n x / d )  ,
q n ( z ) = ( 1 / d ) 0 d q ( x , z )  exp ( 2 π i n x / d ) d x .
n   E z n  exp ( i α n x ) = m   ( i α m H y m i k y H x m )   × exp  ( i α m x ) j   ( i c / ω c ) j  exp ( 2 π i j x / d ),
E z n = ( 1 / k 0 ) m   ( 1 / c ) n m ( k y H x m α m H y m ),
H z n = ( 1 / k 0 )     m   ( 1 / μ ) n m ( k y E x m α m E y m ) , d E y n / d z = i k y E z n i k 0   m   μ n m H x m , d H y n / d z = i k y H z n + i k 0   m   ( c ) n m E x m , d E x n / d z = i α n E z n + i k 0     m   μ n m H y m , d H x n / d z = i α n H z n i k 0     m   ( c ) n m E y m .
a 2 b 2 = R = real part of  [ ( β n λ / 2 π ) 2 ] , 2 a b = I =  imaginary part of  [ ( β n λ / 2 π ) 2 ] =  imaginary part of (n c 2 )  .
a = { [ R + ( R 2 + I 2 ) 1 / 2 ] / 2 } 1 / 2  , b = { [ R + ( R 2 + I 2 ) 1 / 2 ] / 2 } 1 / 2 .
E n = E o n (incident) exp ( i β n z ) + E o n ( reflected )  exp ( i β n z ) : ( z a ) , E n = E o n ( transmitted )  exp ( i β n z ) : ( z 0 )  ,
H x n = [ k 0 c β n E y n k y α n H y n ] / ( k 2 k y 2 )  , E x n = [ k 0 μ β n H y n + k y α n E y n ] / ( k 2 k y 2 )  , E z n = [ k y H x n α n H y n ] / k 0 c  , H z n = [ k y E x n α n E y n ] / k 0 μ .
d U n / d z = m   V n m ( z j ) U m ( z j )  ,
U n ( z j + h ) = U n ( z j ) + ( δ 1 + 2 δ 2 + 2 δ 3 + δ 4 ) / 6 +  order ( h 5 )  ,
δ 1 = h m   V n m ( z j ) U m ( z j )  , δ 2 = h m V n m ( z j + h / 2 )   [ U m ( z j ) + δ 1 / 2 ]  , δ 3 = h m   V n m ( z j + h / 2 )   [ U m ( z j ) + δ 2 / 2 ]  , δ 4 = h m   V n m ( z j + h ) [ U m ( z j ) + δ 3 ] .
E y n = A n  exp ( i β n a ) + B n  exp ( i β n a )  , H y n = C n  exp ( i β n a ) + D n  exp ( i β n a ) .
H x n ( k 2 k y 2 ) + α n k y H y n = k 0 c β n [ A n  exp ( i β n a ) B n   exp ( i β n a ) ]  , E x n ( k 2 k y 2 ) + α n k y E y n = k 0 μ β n [ C n  exp ( i β n a ) D n  exp ( i β n a ) ]  ,
Φ T = [ E y n H y n ] ( a t   z = 0 transmitted wave ) , Φ I = [ A n C n ] ( at  z  =  a , incident wave ) , Φ R = [ B n D n ] ( a t   z  =  a , reflected wave ) ,
Φ I = M A Φ T , Φ R = M B Φ T .
Φ T = T Φ I , Φ R = R Φ I  ,
E = E ( cos γ e ^ x +  sin γ e ^ y )  ,
H = H ( cos γ e ^ x + sin γ e ^ y )  ,
reflectivity for order  n = | F n ( reflected ) / F ( incident ) |  , transmissivity for order  n = | F n ( transmitted ) / F ( incident ) |  ,

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