Abstract

A detailed comparison of the performance of uniform and graded multilayers as soft x-ray monochromators and normal incidence collectors has been made. In particular, the responses of flat depth-, and laterally graded multilayers to Al Kα radiation, λ = 8.34 Å, have been computed and compared with the corresponding uniform multilayer. Furthermore, the efficiency of graded and uniform multilayers as normal incidence x-ray collectors has been calculated in terms of effective areas for parabolic reflectors tuned to the O Kα line, λ = 23.7 Å. Finally, the effective areas of four strong solar emission lines in the 30–60 Å region have been computed for uniform multilayers. Normal incidence multilayer mirrors are well suited for spectroheliograph type of applications.

© 1983 Optical Society of America

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References

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  1. T. W. Barbee, in Proceedings of the Topical Conference on Low Energy X-Ray Diagnostics, D. T. Attwood, B. L. Henke, Eds. (American Institute of Physics, New York, 1981); I. K. Schuller, Phys. Rev. Lett. 44, 1597 (1980).
    [CrossRef]
  2. E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
    [CrossRef]
  3. S. V. Gaponov, S. A. Gusev, B. M. Luskin, N. N. Salashchenko, Opt. Commun. 38, 7 (1981);see also Refs. 1 and 2.
    [CrossRef]
  4. J. H. Underwood, T. W. Barbee, Nature 294, 429 (1981).
    [CrossRef]
  5. J. P. Henry, E. Spiller, M. Weisskopf, Appl. Phys. Lett. 40, 25 (1982).
    [CrossRef]
  6. D. J. Nagel, T. W. Barbee, J. V. Gilfrich, Nucl. Instrum. Methods 195, 63 (1982).
    [CrossRef]
  7. A. E. Rosenbluth, J. M. Forsyth, in Proceedings of the Topical Conference on Low Energy X-Ray Diagnostics, D. T. Attwood, B. L. Henke, Eds. (American Institute of Physics, New York, 1981); J. H. Underwood, T. W. Barbee, in same Proceedings.
  8. P. Lee, Opt. Commun. 37, 159 (1981).
    [CrossRef]
  9. Detailed discussions of the matrix A and AN for bilayer systems are given in Ref. 8 and P. Lee, Opt. Commun. 43, 237 (1982).
    [CrossRef]
  10. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuru, B. K. Fujikawa, Atomic and Nuclear Data Table 27 (1982).
  11. J. H. Underwood, T. W. Barbee, D. L. Shealy, Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).
  12. W. E. Austin, J. D. Purcell, R. Tousey, K. G. Widing, Astrophys. 145, 373 (1966).
    [CrossRef]

1982

J. P. Henry, E. Spiller, M. Weisskopf, Appl. Phys. Lett. 40, 25 (1982).
[CrossRef]

D. J. Nagel, T. W. Barbee, J. V. Gilfrich, Nucl. Instrum. Methods 195, 63 (1982).
[CrossRef]

Detailed discussions of the matrix A and AN for bilayer systems are given in Ref. 8 and P. Lee, Opt. Commun. 43, 237 (1982).
[CrossRef]

1981

J. H. Underwood, T. W. Barbee, D. L. Shealy, Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

P. Lee, Opt. Commun. 37, 159 (1981).
[CrossRef]

S. V. Gaponov, S. A. Gusev, B. M. Luskin, N. N. Salashchenko, Opt. Commun. 38, 7 (1981);see also Refs. 1 and 2.
[CrossRef]

J. H. Underwood, T. W. Barbee, Nature 294, 429 (1981).
[CrossRef]

1980

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

1966

W. E. Austin, J. D. Purcell, R. Tousey, K. G. Widing, Astrophys. 145, 373 (1966).
[CrossRef]

Austin, W. E.

W. E. Austin, J. D. Purcell, R. Tousey, K. G. Widing, Astrophys. 145, 373 (1966).
[CrossRef]

Barbee, T. W.

D. J. Nagel, T. W. Barbee, J. V. Gilfrich, Nucl. Instrum. Methods 195, 63 (1982).
[CrossRef]

J. H. Underwood, T. W. Barbee, Nature 294, 429 (1981).
[CrossRef]

J. H. Underwood, T. W. Barbee, D. L. Shealy, Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

T. W. Barbee, in Proceedings of the Topical Conference on Low Energy X-Ray Diagnostics, D. T. Attwood, B. L. Henke, Eds. (American Institute of Physics, New York, 1981); I. K. Schuller, Phys. Rev. Lett. 44, 1597 (1980).
[CrossRef]

Forsyth, J. M.

A. E. Rosenbluth, J. M. Forsyth, in Proceedings of the Topical Conference on Low Energy X-Ray Diagnostics, D. T. Attwood, B. L. Henke, Eds. (American Institute of Physics, New York, 1981); J. H. Underwood, T. W. Barbee, in same Proceedings.

Fujikawa, B. K.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuru, B. K. Fujikawa, Atomic and Nuclear Data Table 27 (1982).

Gaponov, S. V.

S. V. Gaponov, S. A. Gusev, B. M. Luskin, N. N. Salashchenko, Opt. Commun. 38, 7 (1981);see also Refs. 1 and 2.
[CrossRef]

Gilfrich, J. V.

D. J. Nagel, T. W. Barbee, J. V. Gilfrich, Nucl. Instrum. Methods 195, 63 (1982).
[CrossRef]

Gusev, S. A.

S. V. Gaponov, S. A. Gusev, B. M. Luskin, N. N. Salashchenko, Opt. Commun. 38, 7 (1981);see also Refs. 1 and 2.
[CrossRef]

Haelbich, R-P.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

Henke, B. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuru, B. K. Fujikawa, Atomic and Nuclear Data Table 27 (1982).

Henry, J. P.

J. P. Henry, E. Spiller, M. Weisskopf, Appl. Phys. Lett. 40, 25 (1982).
[CrossRef]

Lee, P.

Detailed discussions of the matrix A and AN for bilayer systems are given in Ref. 8 and P. Lee, Opt. Commun. 43, 237 (1982).
[CrossRef]

P. Lee, Opt. Commun. 37, 159 (1981).
[CrossRef]

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuru, B. K. Fujikawa, Atomic and Nuclear Data Table 27 (1982).

Luskin, B. M.

S. V. Gaponov, S. A. Gusev, B. M. Luskin, N. N. Salashchenko, Opt. Commun. 38, 7 (1981);see also Refs. 1 and 2.
[CrossRef]

Nagel, D. J.

D. J. Nagel, T. W. Barbee, J. V. Gilfrich, Nucl. Instrum. Methods 195, 63 (1982).
[CrossRef]

Purcell, J. D.

W. E. Austin, J. D. Purcell, R. Tousey, K. G. Widing, Astrophys. 145, 373 (1966).
[CrossRef]

Rife, J.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

Rosenbluth, A. E.

A. E. Rosenbluth, J. M. Forsyth, in Proceedings of the Topical Conference on Low Energy X-Ray Diagnostics, D. T. Attwood, B. L. Henke, Eds. (American Institute of Physics, New York, 1981); J. H. Underwood, T. W. Barbee, in same Proceedings.

Salashchenko, N. N.

S. V. Gaponov, S. A. Gusev, B. M. Luskin, N. N. Salashchenko, Opt. Commun. 38, 7 (1981);see also Refs. 1 and 2.
[CrossRef]

Segmuller, A.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

Shealy, D. L.

J. H. Underwood, T. W. Barbee, D. L. Shealy, Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

Shimabukuru, R. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuru, B. K. Fujikawa, Atomic and Nuclear Data Table 27 (1982).

Spiller, E.

J. P. Henry, E. Spiller, M. Weisskopf, Appl. Phys. Lett. 40, 25 (1982).
[CrossRef]

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

Tanaka, T. J.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuru, B. K. Fujikawa, Atomic and Nuclear Data Table 27 (1982).

Tousey, R.

W. E. Austin, J. D. Purcell, R. Tousey, K. G. Widing, Astrophys. 145, 373 (1966).
[CrossRef]

Underwood, J. H.

J. H. Underwood, T. W. Barbee, D. L. Shealy, Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

J. H. Underwood, T. W. Barbee, Nature 294, 429 (1981).
[CrossRef]

Weisskopf, M.

J. P. Henry, E. Spiller, M. Weisskopf, Appl. Phys. Lett. 40, 25 (1982).
[CrossRef]

Widing, K. G.

W. E. Austin, J. D. Purcell, R. Tousey, K. G. Widing, Astrophys. 145, 373 (1966).
[CrossRef]

Appl. Phys. Lett.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

J. P. Henry, E. Spiller, M. Weisskopf, Appl. Phys. Lett. 40, 25 (1982).
[CrossRef]

Astrophys.

W. E. Austin, J. D. Purcell, R. Tousey, K. G. Widing, Astrophys. 145, 373 (1966).
[CrossRef]

Nature

J. H. Underwood, T. W. Barbee, Nature 294, 429 (1981).
[CrossRef]

Nucl. Instrum. Methods

D. J. Nagel, T. W. Barbee, J. V. Gilfrich, Nucl. Instrum. Methods 195, 63 (1982).
[CrossRef]

Opt. Commun.

P. Lee, Opt. Commun. 37, 159 (1981).
[CrossRef]

Detailed discussions of the matrix A and AN for bilayer systems are given in Ref. 8 and P. Lee, Opt. Commun. 43, 237 (1982).
[CrossRef]

S. V. Gaponov, S. A. Gusev, B. M. Luskin, N. N. Salashchenko, Opt. Commun. 38, 7 (1981);see also Refs. 1 and 2.
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

J. H. Underwood, T. W. Barbee, D. L. Shealy, Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

Other

T. W. Barbee, in Proceedings of the Topical Conference on Low Energy X-Ray Diagnostics, D. T. Attwood, B. L. Henke, Eds. (American Institute of Physics, New York, 1981); I. K. Schuller, Phys. Rev. Lett. 44, 1597 (1980).
[CrossRef]

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuru, B. K. Fujikawa, Atomic and Nuclear Data Table 27 (1982).

A. E. Rosenbluth, J. M. Forsyth, in Proceedings of the Topical Conference on Low Energy X-Ray Diagnostics, D. T. Attwood, B. L. Henke, Eds. (American Institute of Physics, New York, 1981); J. H. Underwood, T. W. Barbee, in same Proceedings.

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Figures (9)

Fig. 1
Fig. 1

Diffraction from a set of thin films. E k ± represents the amplitude and phase of the transmitted and reflected waves in the kth medium. rk,k+1 is the Fresnel reflection coefficient at the interface of the kth and k + 1th layers.

Fig. 2
Fig. 2

Models of depth- and laterally graded multilayers. Parallel beams of x rays strike the surfaces at an angle θ in each case.

Fig. 3
Fig. 3

Schematic of a parabolic collector with focal length f and diameter D. θ is the Bragg angle and ϕ is the polar coordinate angle.

Fig. 4
Fig. 4

Comparison of the calculated x-ray responses of flat depth-graded multilayers to uniform multilayers near the Al Kα line.

Fig. 5
Fig. 5

Comparison of the calculated x-ray responses of flat laterally graded multilayers to uniform multilayers near the Al Kα line.

Fig. 6
Fig. 6

Collection efficiencies of depth-graded multilayers and uniform multilayers tuned to the O Kα line for a 10-m focal length, 1-m diam parabolic collector.

Fig. 7
Fig. 7

Collection efficiencies of laterally graded multilayers and corresponding uniform multilayers for a 10-m focal length, 1-m diam parabolic collector tuned to the O Kα line.

Fig. 8
Fig. 8

Comparison of the effective areas for uniform W/C multilayers to uniform V/Be multilayers each tuned to the C VI (λ = 33.74 Å) line.

Fig. 9
Fig. 9

Collection efficiencies of uniform W/C multilayers tuned to Si XI (λ = 49.22 Å), Si X (λ = 50.52 Å), and Si IX (λ = 55.34 Å).

Tables (3)

Tables Icon

Table I Summary of Flat Multilayer Responses Near the Al Kα Line

Tables Icon

Table II Normal Incidence Collection Efficiencies of 10-m Focal Length and 1-m Diam Parabolic Reflectors Tuned to the O Kα Line; Total Collecting Area is 7836 cm2

Tables Icon

Table III Summary of Uniform W/C Multilayer Collection Efficiencies for Four Strong Solar Emission Lines; Total Collecting Area is 7836 cm2

Equations (10)

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r k , k + 1 s = n k + 1 sin θ k + 1 n k sin θ k n k + 1 sin θ k + 1 + n k sin θ k ,
r k , k + 1 p = n k sin θ k + 1 n k + 1 sin θ k n k sin θ k + 1 + n k + 1 sin θ k
r k , k + 1 = ( Δ δ + i Δ β ) P ( 2 θ ) 2 sin 2 θ ,
( χ k + χ k ) = 1 1 r k , k + 1 ( exp ( i ψ k + 1 ) r k , k + 1 exp ( i ψ k + 1 ) r k , k + 1 exp ( i ψ k + 1 ) exp ( i ψ k + 1 ) ) ( χ k + 1 + χ k + 1 ) ,
ψ k = 2 π λ d k sin θ k ( 1 δ k + i β k sin 2 θ k ) ,
R = 2 i r exp ( i ψ 2 ) sin ψ 1 S N 1 ( x ) exp ( i ψ ) [ 1 r 2 exp ( 2 i ψ 1 ) ] S N 1 ( x ) Δ S N 2 ( x ) ,
T = Δ exp ( i ψ ) [ 1 r 2 exp ( 2 i ψ 1 ) ] S N 1 ( x ) Δ S N 2 ( x ) ,
S N ( x ) = sin [ ( N + 1 ) cos 1 ( x ) ] / sin [ cos 1 ( x ) ] , Δ ( 1 r 2 ) 2 , x [ cos ψ r 2 cos ( ψ 1 ψ 2 ) ] / Δ , ψ ψ 1 + ψ 2 .
A = 8 π f 2 0 ϕ 0 I ( ϕ , λ ) sin ϕ cos ϕ / 2 ( 1 + cos ϕ ) 2 d ϕ .
R 0 ( λ ) = 1 L 0 L I ( λ, x ) d x ,

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