Abstract

The eight distinct reflection configurations for pairs of toroidal mirrors are investigated by numerically calculating their aberration patterns for on- and off-axis source points. The best performance is obtained for a Z-shaped configuration where the two mirrors deflect in opposite directions across a common interior sagittal and tangential focus. Imaging properties can be improved significantly in some cases by replacing the toroidal elements with their elliptical or parabolic equivalents. The best overall performance is obtained with parabolic mirrors in a U-shaped configuration.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Wolter, Ann. Phys. 10, 94 (1952).
    [CrossRef]
  2. M. J. Boyer, H. G. Ahlstrom, Rev. Sci. Instrum. 49, 746 (1978).
    [CrossRef]
  3. D. E. Aspnes, S. M. Kelso, J. Opt. Soc. Am. 71, 997 (1981).
    [CrossRef]
  4. D. E. Aspnes, S. M. Kelso, Nucl. Instrum. Methods 195, 175 (1982).
    [CrossRef]
  5. D. E. Aspnes, S. M. Kelso, Proc. Soc. Photo-Opt. Instrum. Eng. 315, 30 (1982).
  6. A. M. Malvezzi, L. Garifo, G. Tondello, Appl. Opt. 20, 2560 (1981).
    [CrossRef] [PubMed]
  7. See, for example, various papers in Nucl. Instrum. Methods 172 (1980).
  8. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945);M. R. Howells, Appl. Opt. 19, 4027 (1980).
    [CrossRef] [PubMed]
  9. J. H. Underwood, X-ray and Extreme Ultraviolet Optics (Wiley, New York, to be published 1983), Chap. 3.
  10. H. P. Brueggeman, Conic Mirrors (Focal Press, New York, 1968).
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

1982 (2)

D. E. Aspnes, S. M. Kelso, Nucl. Instrum. Methods 195, 175 (1982).
[CrossRef]

D. E. Aspnes, S. M. Kelso, Proc. Soc. Photo-Opt. Instrum. Eng. 315, 30 (1982).

1981 (2)

1980 (1)

See, for example, various papers in Nucl. Instrum. Methods 172 (1980).

1978 (1)

M. J. Boyer, H. G. Ahlstrom, Rev. Sci. Instrum. 49, 746 (1978).
[CrossRef]

1952 (1)

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

1945 (1)

Ahlstrom, H. G.

M. J. Boyer, H. G. Ahlstrom, Rev. Sci. Instrum. 49, 746 (1978).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, S. M. Kelso, Nucl. Instrum. Methods 195, 175 (1982).
[CrossRef]

D. E. Aspnes, S. M. Kelso, Proc. Soc. Photo-Opt. Instrum. Eng. 315, 30 (1982).

D. E. Aspnes, S. M. Kelso, J. Opt. Soc. Am. 71, 997 (1981).
[CrossRef]

Beutler, H. G.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Boyer, M. J.

M. J. Boyer, H. G. Ahlstrom, Rev. Sci. Instrum. 49, 746 (1978).
[CrossRef]

Brueggeman, H. P.

H. P. Brueggeman, Conic Mirrors (Focal Press, New York, 1968).

Garifo, L.

Kelso, S. M.

D. E. Aspnes, S. M. Kelso, Proc. Soc. Photo-Opt. Instrum. Eng. 315, 30 (1982).

D. E. Aspnes, S. M. Kelso, Nucl. Instrum. Methods 195, 175 (1982).
[CrossRef]

D. E. Aspnes, S. M. Kelso, J. Opt. Soc. Am. 71, 997 (1981).
[CrossRef]

Malvezzi, A. M.

Tondello, G.

Underwood, J. H.

J. H. Underwood, X-ray and Extreme Ultraviolet Optics (Wiley, New York, to be published 1983), Chap. 3.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Wolter, H.

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

Ann. Phys. (1)

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

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Nucl. Instrum. Methods (2)

D. E. Aspnes, S. M. Kelso, Nucl. Instrum. Methods 195, 175 (1982).
[CrossRef]

See, for example, various papers in Nucl. Instrum. Methods 172 (1980).

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

D. E. Aspnes, S. M. Kelso, Proc. Soc. Photo-Opt. Instrum. Eng. 315, 30 (1982).

Rev. Sci. Instrum. (1)

M. J. Boyer, H. G. Ahlstrom, Rev. Sci. Instrum. 49, 746 (1978).
[CrossRef]

Other (3)

J. H. Underwood, X-ray and Extreme Ultraviolet Optics (Wiley, New York, to be published 1983), Chap. 3.

H. P. Brueggeman, Conic Mirrors (Focal Press, New York, 1968).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Tangential plane cross sections for the eight types of toroidal mirror pairs. The rotational symmetry axes of the individual elements are shown as dashed lines.

Fig. 2
Fig. 2

Aberration patterns in the image plane for a toroidal (TO) mirror pair in a Z-shaped configuration with intermediate sagittal and tangential foci between the elements. The Gaussian images (●) of a nine-point source array on a 0,±1-mm grid in the object plane are shown together with the intersection loci for all conjugate rays making an inclination of 8 mrad at the source. Dimensional units are: length, millimeters; angle, milliradians. The aberration patterns for a Gaussian-optical equivalent pair of elliptical (EL) mirrors, calculated for a ray inclination of 25 mrad, are also shown.

Fig. 3
Fig. 3

As Fig. 2, but for a U-shaped configuration and a ray inclination of 5 mrad.

Fig. 4
Fig. 4

As Fig. 2, but for a Z-shaped configuration with the intermediate sagittal focus at infinity and the intermediate tangential focus between the elements. The ray inclination is 5 mrad.

Fig. 5
Fig. 5

As Fig. 4, but for a U-shaped configuration and a ray inclination of 8 mrad.

Fig. 6
Fig. 6

As Fig. 2, but for a Z-shaped configuration with the intermediate sagittal focus between the elements and the intermediate tangential focus at infinity. The ray inclination is 8 mrad.

Fig. 7
Fig. 7

As Fig. 6, but for a U-shaped configuration and a ray inclination of 5 mrad.

Fig. 8
Fig. 8

As Fig. 2, but for both intermediate foci at infinity. The ray inclination is 8 mrad. For comparison, aberration patterns for the parabolic (PA) equivalent mirrors are shown for 5-mrad inclination for the three source points on (not above) the horizontal axis.

Fig. 9
Fig. 9

As Fig. 8, but for a U-shaped configuration and ray inclinations of 2.5 and 5.0 mrad. The aberration patterns for the parabolic equivalents are calculated for a ray inclination of 25 mrad for the four corner object points.

Metrics