Abstract

The optical design of a Wolter type 1 glancing incidence x-ray telescope for the wavelength region 6–100 Å is described. The theoretical performance of the instrument is evaluated by ray tracing. The results of laboratory and rocket flight tests on a prototype instrument are briefly described.

© 1969 Optical Society of America

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References

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  1. For a review, see V. E. Coslett, W. C. Nixon, X-ray Microscopy (Cambridge University Press, New York, 1960).
  2. H. Wolter, Ann. Phys. 10, 94 (1952).
    [CrossRef]
  3. H. Wolter, Ann. Phys. 10, 286 (1952).
    [CrossRef]
  4. R. Giacconi, N. F. Harmon, R. F. Lacey, Z. Szilagyi, J. Opt. Soc. Amer. 55, 345 (1965).
    [CrossRef]
  5. R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
    [CrossRef]
  6. J. H. Underwood, W. S. Muney, Solar Phys. 1, 129 (1967).
    [CrossRef]
  7. See A. H. Compton, S. K. Allison, X-rays in Theory and Experiment (Van Nostrand Company, Inc., New York, 1935).
  8. H. E. Bennett, J. O. Porteus, J. Opt. Soc. Amer. 51, 123 (1961).
    [CrossRef]
  9. W. F. Koehler, W. C. White, J. Opt. Soc. Amer. 45, 1011 (1955).
    [CrossRef]
  10. W. F. Koehler, J. Opt. Soc. Amer. 43, 743 (1953).
    [CrossRef]
  11. J. B. Schroeder, R. G. Klimasewski, Appl. Opt. 7, 1921 (1968).
    [CrossRef] [PubMed]
  12. R. W. Dietz, J. M. Bennett, Appl. Opt. 5, 881 (1966).
    [PubMed]
  13. R. W. Dietz, J. M. Bennett, Appl. Opt. 6, 1275 (1967).
    [CrossRef] [PubMed]
  14. L. M. Rieser, J. Opt. Soc. Amer. 47, 987 (1967).
  15. S. B. Elliott, X-ray Optics and Microanalysis (Academic Press Inc., New York, 1963).
  16. E. A. Stewardson, J. H. Underwood, Brit. J. Appl. Phys. 16, 1877 (1965).
    [CrossRef]
  17. A. P. Lukirskii, E. P. Savinov, Opt. Spectrosc. 14, 152 (1964).
  18. J. O. Porteus, J. Opt. Soc. Amer. 5, 1394 (1963).
  19. W. Augustyn, J. Vrabel, J. H. Underwood, J. Opt. Soc. Amer. 56, 1425 (1966).

1968 (1)

1967 (3)

R. W. Dietz, J. M. Bennett, Appl. Opt. 6, 1275 (1967).
[CrossRef] [PubMed]

L. M. Rieser, J. Opt. Soc. Amer. 47, 987 (1967).

J. H. Underwood, W. S. Muney, Solar Phys. 1, 129 (1967).
[CrossRef]

1966 (2)

R. W. Dietz, J. M. Bennett, Appl. Opt. 5, 881 (1966).
[PubMed]

W. Augustyn, J. Vrabel, J. H. Underwood, J. Opt. Soc. Amer. 56, 1425 (1966).

1965 (3)

E. A. Stewardson, J. H. Underwood, Brit. J. Appl. Phys. 16, 1877 (1965).
[CrossRef]

R. Giacconi, N. F. Harmon, R. F. Lacey, Z. Szilagyi, J. Opt. Soc. Amer. 55, 345 (1965).
[CrossRef]

R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
[CrossRef]

1964 (1)

A. P. Lukirskii, E. P. Savinov, Opt. Spectrosc. 14, 152 (1964).

1963 (1)

J. O. Porteus, J. Opt. Soc. Amer. 5, 1394 (1963).

1961 (1)

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Amer. 51, 123 (1961).
[CrossRef]

1955 (1)

W. F. Koehler, W. C. White, J. Opt. Soc. Amer. 45, 1011 (1955).
[CrossRef]

1953 (1)

W. F. Koehler, J. Opt. Soc. Amer. 43, 743 (1953).
[CrossRef]

1952 (2)

H. Wolter, Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, Ann. Phys. 10, 286 (1952).
[CrossRef]

Allison, S. K.

See A. H. Compton, S. K. Allison, X-rays in Theory and Experiment (Van Nostrand Company, Inc., New York, 1935).

Augustyn, W.

W. Augustyn, J. Vrabel, J. H. Underwood, J. Opt. Soc. Amer. 56, 1425 (1966).

Bennett, H. E.

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Amer. 51, 123 (1961).
[CrossRef]

Bennett, J. M.

Compton, A. H.

See A. H. Compton, S. K. Allison, X-rays in Theory and Experiment (Van Nostrand Company, Inc., New York, 1935).

Coslett, V. E.

For a review, see V. E. Coslett, W. C. Nixon, X-ray Microscopy (Cambridge University Press, New York, 1960).

Dietz, R. W.

Elliott, S. B.

S. B. Elliott, X-ray Optics and Microanalysis (Academic Press Inc., New York, 1963).

Giacconi, R.

R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
[CrossRef]

R. Giacconi, N. F. Harmon, R. F. Lacey, Z. Szilagyi, J. Opt. Soc. Amer. 55, 345 (1965).
[CrossRef]

Harmon, N. F.

R. Giacconi, N. F. Harmon, R. F. Lacey, Z. Szilagyi, J. Opt. Soc. Amer. 55, 345 (1965).
[CrossRef]

Klimasewski, R. G.

Koehler, W. F.

W. F. Koehler, W. C. White, J. Opt. Soc. Amer. 45, 1011 (1955).
[CrossRef]

W. F. Koehler, J. Opt. Soc. Amer. 43, 743 (1953).
[CrossRef]

Lacey, R. F.

R. Giacconi, N. F. Harmon, R. F. Lacey, Z. Szilagyi, J. Opt. Soc. Amer. 55, 345 (1965).
[CrossRef]

Lindsay, J. C.

R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
[CrossRef]

Lukirskii, A. P.

A. P. Lukirskii, E. P. Savinov, Opt. Spectrosc. 14, 152 (1964).

Muney, W. S.

J. H. Underwood, W. S. Muney, Solar Phys. 1, 129 (1967).
[CrossRef]

R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
[CrossRef]

Nixon, W. C.

For a review, see V. E. Coslett, W. C. Nixon, X-ray Microscopy (Cambridge University Press, New York, 1960).

Porteus, J. O.

J. O. Porteus, J. Opt. Soc. Amer. 5, 1394 (1963).

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Amer. 51, 123 (1961).
[CrossRef]

Reidy, W. P.

R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
[CrossRef]

Rieser, L. M.

L. M. Rieser, J. Opt. Soc. Amer. 47, 987 (1967).

Savinov, E. P.

A. P. Lukirskii, E. P. Savinov, Opt. Spectrosc. 14, 152 (1964).

Schroeder, J. B.

Stewardson, E. A.

E. A. Stewardson, J. H. Underwood, Brit. J. Appl. Phys. 16, 1877 (1965).
[CrossRef]

Szilagyi, Z.

R. Giacconi, N. F. Harmon, R. F. Lacey, Z. Szilagyi, J. Opt. Soc. Amer. 55, 345 (1965).
[CrossRef]

Underwood, J. H.

J. H. Underwood, W. S. Muney, Solar Phys. 1, 129 (1967).
[CrossRef]

W. Augustyn, J. Vrabel, J. H. Underwood, J. Opt. Soc. Amer. 56, 1425 (1966).

E. A. Stewardson, J. H. Underwood, Brit. J. Appl. Phys. 16, 1877 (1965).
[CrossRef]

Vrabel, J.

W. Augustyn, J. Vrabel, J. H. Underwood, J. Opt. Soc. Amer. 56, 1425 (1966).

White, W. C.

W. F. Koehler, W. C. White, J. Opt. Soc. Amer. 45, 1011 (1955).
[CrossRef]

Wolter, H.

H. Wolter, Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, Ann. Phys. 10, 286 (1952).
[CrossRef]

Zehnpfennig, T.

R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
[CrossRef]

Ann. Phys. (2)

H. Wolter, Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, Ann. Phys. 10, 286 (1952).
[CrossRef]

Appl. Opt. (3)

Astrophys. J. (1)

R. Giacconi, W. P. Reidy, T. Zehnpfennig, J. C. Lindsay, W. S. Muney, Astrophys. J. 142, 1274 (1965).
[CrossRef]

Brit. J. Appl. Phys. (1)

E. A. Stewardson, J. H. Underwood, Brit. J. Appl. Phys. 16, 1877 (1965).
[CrossRef]

J. Opt. Soc. Amer. (7)

J. O. Porteus, J. Opt. Soc. Amer. 5, 1394 (1963).

W. Augustyn, J. Vrabel, J. H. Underwood, J. Opt. Soc. Amer. 56, 1425 (1966).

R. Giacconi, N. F. Harmon, R. F. Lacey, Z. Szilagyi, J. Opt. Soc. Amer. 55, 345 (1965).
[CrossRef]

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Amer. 51, 123 (1961).
[CrossRef]

W. F. Koehler, W. C. White, J. Opt. Soc. Amer. 45, 1011 (1955).
[CrossRef]

W. F. Koehler, J. Opt. Soc. Amer. 43, 743 (1953).
[CrossRef]

L. M. Rieser, J. Opt. Soc. Amer. 47, 987 (1967).

Opt. Spectrosc. (1)

A. P. Lukirskii, E. P. Savinov, Opt. Spectrosc. 14, 152 (1964).

Solar Phys. (1)

J. H. Underwood, W. S. Muney, Solar Phys. 1, 129 (1967).
[CrossRef]

Other (3)

See A. H. Compton, S. K. Allison, X-rays in Theory and Experiment (Van Nostrand Company, Inc., New York, 1935).

S. B. Elliott, X-ray Optics and Microanalysis (Academic Press Inc., New York, 1963).

For a review, see V. E. Coslett, W. C. Nixon, X-ray Microscopy (Cambridge University Press, New York, 1960).

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Figures (18)

Fig. 1
Fig. 1

Reflection of soft x–rays. In this diagram, the reflectance R = I/I0 is plotted against the normalized glancing angle θ/θc for various values of the absorption parameter Y.

Fig. 2
Fig. 2

Schematic diagram of the Wolter type 1 x-ray telescope. The angles of glancing incidence have been exaggerated for clarity.

Fig. 3
Fig. 3

Reflection efficiency of glass or quartz surfaces as a function of wavelength. θ = 54 min of arc. Open circles: one reflection. Closed circles: two reflections. The points represent experimental data taken from published work on the reflection of x-rays (See Refs. 16 and 17). Note the large dip around the oxygen K-edge.

Fig. 4
Fig. 4

This figure shows the notation used in the calculations.

Fig. 5
Fig. 5

Spot diagrams computed for the x-ray telescope at various off-axis angles δ. The left and center columns show the appearance of the spot diagrams in the gaussian plane and in the optimum focal plane, respectively. The right-hand column shows the effect of vignetting by reducing the length of the hyperboloid. The bar to the left of each spot diagram represents 1 sec of arc. δ a is in milliradians.

Fig. 6
Fig. 6

Tangential image size plotted against focal plane shift for various off-axis object points.

Fig. 7
Fig. 7

Half-aperture spot diagram for δ = 6 mrad, m = 1.65 mm.

Fig. 8
Fig. 8

Diagram showing how the point of intersection of a ray with the hyperboloid moves as the entrance point moves around the entrance pupil.

Fig. 9
Fig. 9

Paths of tangential rays in the vicinity of the focus. δ = 4 mrad.

Fig. 10
Fig. 10

Vignetting diagram. The energy lost from the image is plotted as a function of the length of the second element for various values of δ.

Fig. 11
Fig. 11

Tangential image size plotted against δ: (a) at gaussian focal plane; (b) at optimum focal surface, unvignetted; (c) at optimum focal surface, vignetted; (d) at optimum focal surface, vignetted, one-half intensity width.

Fig. 12
Fig. 12

Distribution of energy in the image in the gaussian plane (broken line) and in the optimum focal plane (solid line). The energy has been summed in strips parallel to the z-axis and so this figure is equivalent to a microdensitometer trace along the y direction.

Fig. 13
Fig. 13

Fraunhofer diffraction patterns of an unobscured circular aperture and a thin annulus.

Fig. 14
Fig. 14

Modulation transfer function of a perfect imaging system with a highly obscured annular pupil. Inset: modulation transfer functions for other annular pupils. f/f0 is the normalized spatial frequency.

Fig. 15
Fig. 15

Schematic diagram of laboratory setup used for making x-ray tests of the telescopes.

Fig. 16
Fig. 16

Photographs taken in visible light with the x-ray telescopes. Above: diffraction pattern surrounding image of a point source, taken at 5461 Å. Below: USAF test target photographed in a band around 5461 Å.

Fig. 17
Fig. 17

X-ray photographs obtained using the setup shown in Fig. 15. Above: Al Kα radiation (8.34 Å), below: C Kα radiation (44 Å).

Fig. 18
Fig. 18

X-ray photograph of the sun obtained using a glancing incidence x-ray telescope. The wavelength bandpass is 44–60 Å. The exposure lasted 15 sec. In this photograph solar north is at the top and east is at the left.

Tables (1)

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Table I Roughness of Optically Polished Surfaces

Equations (9)

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cos θ c = n = 1 - Δ ,
θ c = ( 2 Δ ) 1 2 .
h / sin α = constant = r
Δ r = r Δ α tan ( α / 2 ) .
A 2 π y p min r Δ α ,
Δ r A θ max / y p min .
y p min = f sin ( 4 θ max ) = y h max p = y p min tan θ max c = f / 2 a = f ( 2 cos 2 θ max - 1 ) / 2 b = ( c 2 - a 2 ) 1 2 y p max = ( A / π + y p 2 min ) 1 2 } .
τ = f sin δ ( 1 - cos 4 θ max 2 cos 4 θ max ) .
( x + a ) 2 / a 2 - y 2 / b 2 = 1 ,

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