Abstract

Spherical and paraboloidal diffraction gratings are considered for use on an experiment involving a collection of satelliteborne spectrographs that will investigate astrophysical plasmas in the spectral region from approximately 100 to 300 Å. We shall use eight spectrographs: Wadsworth mounts in near-normal incidence with effective focal lengths of 3 m, each centered on a chosen wavelength in this spectral range. Ray tracings show that paraboloidal gratings used in the Wadsworth mount have a significant increase in resolution over spherical gratings of the same effective focal length, used in the same mounting, as long as the spectral ranges are small (approximately 10% of the central wavelength). This increase in resolution is due to the spatial extent of coma for a paraboloidal grating that is less than the circle of least confusion of spherical gratings.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Tousey, J.-D. F. Bartoe, G. E. Brueckner, J. D. Purcell, “Extreme ultraviolet spectroheliograph ATM experiment S082A,” Appl. Opt. 16, 870–878 (1977).
    [PubMed]
  2. R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
    [CrossRef]
  3. J. L. Sirks, “On the astigmatism of Rowland’s concave gratings,” Astron. Astrophys. 13, 763–768 (1894).
  4. F. L. O. Wadsworth, “The modern spectroscope. XV,” Astrophys. J. 3, 47–62 (1896).
    [CrossRef]
  5. M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
    [CrossRef]
  6. beam 4 is available from Stellar Software, P.O. Box 10183, Berkeley, Calif. 94709, www.stellarsoftware.com .
  7. G. H. Spencer, M. V. R. K. Murty, “General ray-tracing procedure,” J. Opt. Soc. Am. 52, 672–678 (1962).
    [CrossRef]
  8. D. Korsch, Reflective Optics (Academic, New York, 1991), p. 82.

2002 (1)

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

1977 (1)

1962 (1)

1896 (1)

F. L. O. Wadsworth, “The modern spectroscope. XV,” Astrophys. J. 3, 47–62 (1896).
[CrossRef]

1894 (1)

J. L. Sirks, “On the astigmatism of Rowland’s concave gratings,” Astron. Astrophys. 13, 763–768 (1894).

Bannister, N. P.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Barbee, T. W.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Barstow, M. A.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Bartoe, J.-D. F.

Brown, C. M.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

Brueckner, G. E.

Cruddace, R. G.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Culhane, J. L.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Fraser, G. W.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

Fritz, G. G.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Goldstein, W.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

Goldstein, W. H.

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Gursky, H.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Hunter, W. R.

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Kordas, J. F.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Korsch, D.

D. Korsch, Reflective Optics (Academic, New York, 1991), p. 82.

Kowalski, M. P.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Lapington, J. S.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Murty, M. V. R. K.

Purcell, J. D.

Sanderson, B.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

Sirks, J. L.

J. L. Sirks, “On the astigmatism of Rowland’s concave gratings,” Astron. Astrophys. 13, 763–768 (1894).

Spencer, G. H.

Spragg, J. E.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

Tandy, J. A.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

Tousey, R.

Wadsworth, F. L. O.

F. L. O. Wadsworth, “The modern spectroscope. XV,” Astrophys. J. 3, 47–62 (1896).
[CrossRef]

Wood, K. S.

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Yentis, D.

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

Yentis, D. J.

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (1)

J. L. Sirks, “On the astigmatism of Rowland’s concave gratings,” Astron. Astrophys. 13, 763–768 (1894).

Astrophys. J. (1)

F. L. O. Wadsworth, “The modern spectroscope. XV,” Astrophys. J. 3, 47–62 (1896).
[CrossRef]

Astrophys. J. Lett. (1)

R. G. Cruddace, M. P. Kowalski, D. Yentis, C. M. Brown, H. Gursky, M. A. Barstow, N. P. Bannister, G. W. Fraser, J. E. Spragg, J. S. Lapington, J. A. Tandy, B. Sanderson, J. L. Culhane, T. W. Barbee, J. F. Kordas, W. Goldstein, G. G. Fritz, “High resolution spectroscopy of G191-B2B in the extreme ultraviolet,” Astrophys. J. Lett. 565, L47–L50 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (3)

M. P. Kowalski, R. G. Cruddace, K. S. Wood, D. J. Yentis, H. Gursky, T. W. Barbee, W. H. Goldstein, J. F. Kordas, G. G. Fritz, W. R. Hunter, M. A. Barstow, N. P. Bannister, J. L. Culhane, J. S. Lapington, “The Astrophysical Plasmadynamic Explorer (APEX): a high-resolution spectroscopic observatory,” in Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation, J. C. Blades, O. H. W. Siegmund, eds., Proc. SPIE4854, 640–653 (2003).
[CrossRef]

beam 4 is available from Stellar Software, P.O. Box 10183, Berkeley, Calif. 94709, www.stellarsoftware.com .

D. Korsch, Reflective Optics (Academic, New York, 1991), p. 82.

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

Schematic diagram of the ray-tracing setup in the Z, X plane. Ng is the grating normal that is inclined 5.45° to the Z axis. Parallel radiation is incident on the grating G as shown by the lines parallel to Z and is diffracted up to the plane detector D at 0 (zero order) and at the second order of 160, 174, and 190 Å. The figure is not to scale and the dimensions given are nominal.

Fig. 2
Fig. 2

Spot diagrams for a Wadsworth mount with a spherical grating. The direction of dispersion is horizontal and all units are in centimeters. Wavelength increases to the left. All wavelengths are inside second order. The central wavelength is 175 Å, shown at the lower right, and the wavelength decreases in 3-Å increments to 160 Å at the upper left. The scales for all diagrams are the same for easy comparison. The circular areas show little astigmatism and have increased in diameter by approximately 8% at 160 Å.

Fig. 3
Fig. 3

Spot diagrams for a Wadsworth mount with a paraboloidal grating. The direction of dispersion is horizontal and all units are in centimeters. Wavelength increases to the left. All wavelengths are inside second order. The central wavelength is 175 Å shown at the lower right, and the wavelength decreases in 3-Å increments to 160 Å at the upper left. The scales for all diagrams are the same for easy comparison except at 175 Å where they were increased by a factor of 275 to show details.

Fig. 4
Fig. 4

(a) Spot diagram for a spherical grating at 160 Å and (b) its projection onto the axis of dispersion. Wavelength increases to the left. The units are in centimeters except for the vertical axis of the projection that is in events per bin. The vertical line shows the abscissal value separating the 10% discarded points, to the right, from those used in calculating the image width to obtain the resolution.

Fig. 5
Fig. 5

(a) Spot diagram for a paraboloidal grating at 160 Å and (b) its projection onto the axis of dispersion. Wavelength increases to the left. The units are in centimeters except for the vertical axis of the projection that is in events per bin. The vertical line shows the abscissal value separating the 10% discarded points, to the right, from those used to calculate the image width to obtain the resolving power.

Fig. 6
Fig. 6

Comparison of the effective dimensions of the spot diagrams in the dispersion direction for the spherical (S) and paraboloidal (P) gratings. The large data circles represent the widths when no pointing errors occur, and the small data points show the effect of a 1-arc min pointing error (see the discussion in the text).

Fig. 7
Fig. 7

Comparison of the resolution of a spherical (S) and a paraboloidal (P) grating in a Wadsworth mount. The large data circles represent the resolutions when no pointing errors occur, and the small data points show the effect of a 1-arc min pointing error (see the discussion in the text).

Fig. 8
Fig. 8

Spot diagrams showing the evolution of the aureole of points at 160 Å as the aperture of a spherical grating is increased from 20 to 30 cm. Direction of dispersion is horizontal and the units are in centimeters. Wavelength increases to the left.

Fig. 9
Fig. 9

Spot diagrams and aberration curves for paraboloidal gratings, 160 Å in the right column and 174 Å in the left column. At the top are the aberration curves obtained when the gratings are illuminated with a circular cylinder of parallel rays 34 cm in diameter. The middle diagrams show the result of illuminating the grating with five concentric circular cylinders of rays with diameters 6.8, 13.6, 20.4, 27.2, and 34 cm. At the bottom are spot diagrams. Direction of dispersion is horizontal and the units are in centimeters. Wavelength increases to the left.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

r=R cos2 β/cos α+cos β,
R=nrλG/δx,

Metrics