Abstract

Efficiencies for diffraction of 45–275-eV x rays into orders by interferometrically formed, electrodeposited, gold transmission gratings have been measured on the 4° beam line at the Stanford Synchrotron Radiation Project (SSRP). Anomalous dispersion affects the observed efficiency since the gold is partially transmitting to x rays. Model calculations which include anomalous dispersion are in good agreement with observations. With a suitable choice of material and thickness, a grating can be optimized for a given wavelength range by reducing the zero order transmission and enhancing the higher orders. Even orders are suppressed for a grating with equal slit and wire sizes.

© 1977 Optical Society of America

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References

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  1. J. H. Dijkstra, W. de Graaff, L. J. Lantwaard, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (Reidel, Dordrecht, 1971), p. 207.
  2. R. Giacconi, B. rossi, J. Geophys. Res. 65, 773 (1960).
    [CrossRef]
  3. R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
    [CrossRef]
  4. H. Gursky, T. Zehnpfennig, Appl. Opt. 5, 875 (1966).
    [PubMed]
  5. J. A. Dijkstra, L. J. Lantwaard, Opt. Commun. 15, 300 (1975).
    [CrossRef]
  6. J. H. Dijkstra, Space Sci. Instrum. 2, 363 (1976).
  7. H. I. Smith, Proc. IEEE 62, 1361 (1974).
    [CrossRef]
  8. H. I. Smith, H. Efremow, P. C. Kelly, J. Electrochem. Soc. 121, 1503 (1974).
    [CrossRef]
  9. H. Winick, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 776.
  10. F. C. Brown, R. Z. Bachrach, S. B. M. Hagström, N. Lien, C. H. Pruett, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 785.
  11. R. Z. Bachrach in Proceedings of Synchrotion Radiation Facilities Quebec Summer Workshop, J. W. McGowan, E. M. Rowe, Eds. (Université Laval, Quebec, 1976).
  12. M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap. 8.
  13. H.-J. Hagemann, W. Gudat, C. Kunz, Preprint DESY SR-74/7 (1974).

1976 (1)

J. H. Dijkstra, Space Sci. Instrum. 2, 363 (1976).

1975 (1)

J. A. Dijkstra, L. J. Lantwaard, Opt. Commun. 15, 300 (1975).
[CrossRef]

1974 (3)

H. I. Smith, Proc. IEEE 62, 1361 (1974).
[CrossRef]

H. I. Smith, H. Efremow, P. C. Kelly, J. Electrochem. Soc. 121, 1503 (1974).
[CrossRef]

H.-J. Hagemann, W. Gudat, C. Kunz, Preprint DESY SR-74/7 (1974).

1969 (1)

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
[CrossRef]

1966 (1)

1960 (1)

R. Giacconi, B. rossi, J. Geophys. Res. 65, 773 (1960).
[CrossRef]

Bachrach, R. Z.

R. Z. Bachrach in Proceedings of Synchrotion Radiation Facilities Quebec Summer Workshop, J. W. McGowan, E. M. Rowe, Eds. (Université Laval, Quebec, 1976).

F. C. Brown, R. Z. Bachrach, S. B. M. Hagström, N. Lien, C. H. Pruett, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 785.

Born, M.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap. 8.

Brown, F. C.

F. C. Brown, R. Z. Bachrach, S. B. M. Hagström, N. Lien, C. H. Pruett, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 785.

de Graaff, W.

J. H. Dijkstra, W. de Graaff, L. J. Lantwaard, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (Reidel, Dordrecht, 1971), p. 207.

Dijkstra, J. A.

J. A. Dijkstra, L. J. Lantwaard, Opt. Commun. 15, 300 (1975).
[CrossRef]

Dijkstra, J. H.

J. H. Dijkstra, Space Sci. Instrum. 2, 363 (1976).

J. H. Dijkstra, W. de Graaff, L. J. Lantwaard, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (Reidel, Dordrecht, 1971), p. 207.

Efremow, H.

H. I. Smith, H. Efremow, P. C. Kelly, J. Electrochem. Soc. 121, 1503 (1974).
[CrossRef]

Giacconi, R.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
[CrossRef]

R. Giacconi, B. rossi, J. Geophys. Res. 65, 773 (1960).
[CrossRef]

Gudat, W.

H.-J. Hagemann, W. Gudat, C. Kunz, Preprint DESY SR-74/7 (1974).

Gursky, H.

Hagemann, H.-J.

H.-J. Hagemann, W. Gudat, C. Kunz, Preprint DESY SR-74/7 (1974).

Hagström, S. B. M.

F. C. Brown, R. Z. Bachrach, S. B. M. Hagström, N. Lien, C. H. Pruett, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 785.

Kelly, P. C.

H. I. Smith, H. Efremow, P. C. Kelly, J. Electrochem. Soc. 121, 1503 (1974).
[CrossRef]

Kunz, C.

H.-J. Hagemann, W. Gudat, C. Kunz, Preprint DESY SR-74/7 (1974).

Lantwaard, L. J.

J. A. Dijkstra, L. J. Lantwaard, Opt. Commun. 15, 300 (1975).
[CrossRef]

J. H. Dijkstra, W. de Graaff, L. J. Lantwaard, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (Reidel, Dordrecht, 1971), p. 207.

Lien, N.

F. C. Brown, R. Z. Bachrach, S. B. M. Hagström, N. Lien, C. H. Pruett, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 785.

Pruett, C. H.

F. C. Brown, R. Z. Bachrach, S. B. M. Hagström, N. Lien, C. H. Pruett, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 785.

Reidy, W. P.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
[CrossRef]

rossi, B.

R. Giacconi, B. rossi, J. Geophys. Res. 65, 773 (1960).
[CrossRef]

Smith, H. I.

H. I. Smith, Proc. IEEE 62, 1361 (1974).
[CrossRef]

H. I. Smith, H. Efremow, P. C. Kelly, J. Electrochem. Soc. 121, 1503 (1974).
[CrossRef]

Vaiana, G. S.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
[CrossRef]

Van Speybroeck, L. P.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
[CrossRef]

Winick, H.

H. Winick, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 776.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap. 8.

Zehnpfennig, T.

Zehnpfennig, T. F.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
[CrossRef]

Appl. Opt. (1)

J. Electrochem. Soc. (1)

H. I. Smith, H. Efremow, P. C. Kelly, J. Electrochem. Soc. 121, 1503 (1974).
[CrossRef]

J. Geophys. Res. (1)

R. Giacconi, B. rossi, J. Geophys. Res. 65, 773 (1960).
[CrossRef]

Opt. Commun. (1)

J. A. Dijkstra, L. J. Lantwaard, Opt. Commun. 15, 300 (1975).
[CrossRef]

Preprint DESY SR-74/7 (1)

H.-J. Hagemann, W. Gudat, C. Kunz, Preprint DESY SR-74/7 (1974).

Proc. IEEE (1)

H. I. Smith, Proc. IEEE 62, 1361 (1974).
[CrossRef]

Space Sci. Instrum. (1)

J. H. Dijkstra, Space Sci. Instrum. 2, 363 (1976).

Space Sci. Rev. (1)

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, Space Sci. Rev. 9, 3 (1969).
[CrossRef]

Other (5)

H. Winick, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 776.

F. C. Brown, R. Z. Bachrach, S. B. M. Hagström, N. Lien, C. H. Pruett, in Vacuum Ultraviolet Radiation Physics, E.-E. Koch, R. Haensel, C. Kunz, Eds. (Pergamon, Vieweg, 1975), p. 785.

R. Z. Bachrach in Proceedings of Synchrotion Radiation Facilities Quebec Summer Workshop, J. W. McGowan, E. M. Rowe, Eds. (Université Laval, Quebec, 1976).

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap. 8.

J. H. Dijkstra, W. de Graaff, L. J. Lantwaard, in New Techniques in Space Astronomy, F. Labuhn, R. Lüst, Eds. (Reidel, Dordrecht, 1971), p. 207.

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Figures (5)

Fig. 1
Fig. 1

A schematic representation of the basic components required to produce a set of interference fringes in the photoresist (not to scale).

Fig. 2
Fig. 2

An electron micrograph of a small portion of a 1000-l/mm grating. Coarse and fine support structures are seen in addition to the grating wires. Note the rounding of the grating wires.

Fig. 3
Fig. 3

The experiment as installed on the 4° beam line at SPEAR (not to scale).

Fig. 4
Fig. 4

(a) Grating 1, E = 95 eV in first order and E = 190 eV in second oder. In the labeling of the orders, the top number refers to 95 eV and the lower one to 190-eV x rays. (b) Grating 1, E = 190 eV. Little second order radiation from the monochromator is present. (c) Grating 2, E = 190 eV. Note the difference in intensity relative to first order for orders 2 through 5 of the data in (c) when compared with the same orders in (b). This is indicative of a different fractional open grating space a/d for each grating. The 0.5-mm detector slit is equivalent to 5.2 detector index units.

Fig. 5
Fig. 5

Experimental and theoretical results. (a) The ratios are energy dependent, an indication of a nonrectangular wire cross section. The choice of a/d = 0.64 gives a better fit at E = 137 eV. The best fit a/d value is obtained from the data between 155 eV and 225 eV. (b) First order to zero order ratio values are used to obtain the grating thickness. Using the value of a/d obtained from (a), the best fit of the experimental data yields the grating thickness z. (c) Absolute efficiencies for first order. The values for the experimental data may be low because of difficulties in obtaining absolute normalization to the incident beam. Values of N0(q) = (1 − f)n0(q)t may, therefore, be too high. For thick gratings the order ratios 0:1:2:3 ⋯ m should be ¼: 1/π2: 1/(4π2): 1/(9π2) ⋯ 1/(m2π2). A value of f = 0.25 was used.

Equations (7)

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n ( m ) ( q ) N 0 ( q ) = ( [ sin ( M m π ) M sin ( m π ) ] 2 { sin [ ( a / d ) m π ] ( m π ) } 2 × [ 1 + exp ( - 2 q z k ) - 2 exp ( - q z k ) cos ( q z δ ) ] ) ,
n ( 0 ) ( q ) N 0 ( q ) = ( a d ) 2 + ( 1 - a d ) 2 exp ( - 2 q z k ) + 2 ( a 2 ) ( 1 - a d ) exp ( - q z k ) cos ( q z δ ) .
n ( m ) ( q ) N 0 ( q ) = 1 π 2 m 2 [ 1 + exp ( - 2 q z k ) - 2 exp ( - q z k ) cos ( q z δ ) ]
n ( m ) ( q ) N 0 ( q ) = 0 ,             for m = even integer .
n ( 0 ) ( q ) N 0 ( q ) = ¼ [ 1 + exp ( - 2 q z k ) + 2 exp ( - q z k ) cos ( q z δ ) ] .
n ( m ) ( q ) n ( 1 ) ( q ) = [ sin [ ( a / d ) m π m sin ( a / d ) ] 2
n ( 1 ) ( q ) n ( 0 ) ( q ) = [ sin ( a d π ) π ] 2 [ 1 + exp ( - 2 q z k ) - 2 exp ( - q z k ) cos ( q z δ ) ] [ ( a d ) 2 + ( 1 - a d ) 2 exp ( - 2 q z k ) + 2 ( a d ) ( 1 - a d ) exp ( - q z k ) cos ( q z δ ) ] .

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