Abstract

Modifications to the surface of ellipsoidal gratings with straight rulings have been investigated. We find that with the addition of a term proportional to wl2 the stigmatic Rowland circle geometry can be greatly improved. We also show that with the addition of a term proportional to w3, comatic aberration can be corrected, and geometries outside the Rowland circle become well behaved. The modifications require only a few microns of figuring polish away from the nominal ellipsoid. Fabrication of these gratings is well within the capabilities of modern optics.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Final Report of the Science Working Group for the Far Ultraviolet Spectroscopic Explorer, NASA Publication (1983).
  2. W. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).
  3. “Conference on Optical Methods in Scientific and Industrial Measurements,” Jpn. J. Appl. Phys. (Suppl.) 14-1, Chap. 5 (1975).
  4. R. Iwanaga, T. Ashio, “Aberration Reduced Mechanically Ruled Grating for Simple Rotational Mounting,” J. Opt. Soc. Am. 69, 1538 (1979).
    [CrossRef]
  5. M. Hettrick, “Aberrations of Varied Line-Space Grazing Incidence Gratings in Converging Light Beams,” Appl. Opt. 23, 3221 (1984).
    [CrossRef] [PubMed]
  6. T. Namioka, “Theory of Ellipsoidal Concave Grating I,” J. Opt. Soc. Am. 51, 4 (1961).
    [CrossRef]
  7. T. Namioka, “Theory of Ellipsoidal Concave Grating II. Application of the Theory to the Specific Grating Mountings,” J. Opt. Soc. Am. 51, 13 (1961).
    [CrossRef]
  8. W. Werner, “The Geometrical Optical Aberration Theory of Diffraction Gratings,” Appl. Opt. 6, 1691 (1967).
    [CrossRef] [PubMed]

1984 (1)

1982 (1)

W. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).

1979 (1)

1975 (1)

“Conference on Optical Methods in Scientific and Industrial Measurements,” Jpn. J. Appl. Phys. (Suppl.) 14-1, Chap. 5 (1975).

1967 (1)

1961 (2)

Appl. Opt. (2)

J. Opt. Soc. Am. (3)

Jpn. J. Appl. Phys. (Suppl.) (1)

“Conference on Optical Methods in Scientific and Industrial Measurements,” Jpn. J. Appl. Phys. (Suppl.) 14-1, Chap. 5 (1975).

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

W. McClintock, W. Cash, “Grazing Incidence Optics: New Techniques for High Sensitivity Spectroscopy in the Space Ultraviolet,” Proc. Soc. Photo-Opt. Instrum. Eng. 331, 321 (1982).

Other (1)

Final Report of the Science Working Group for the Far Ultraviolet Spectroscopic Explorer, NASA Publication (1983).

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 (8)

Fig. 1
Fig. 1

Ray tracing of monochromatic light from a point entrance slit off a spherical grating showing astigmatism. (Left) image is from a conventional grating and shows line curvature. (Right) curvature has been canceled through use of the ɛ parameter.

Fig. 2
Fig. 2

Ellipsoidal grating where astigmatism is nearly corrected is ray traced. (Left) notice the severe effects of curvature. (Right) corrected grating image.

Fig. 3
Fig. 3

Fully stigmatic images are ray traced. Notice the dramatic improvement in resolution to the right where curvature is canceled.

Fig. 4
Fig. 4

Root mean square of the ray positions in the dispersion direction has been calculated by ray tracing for the curvature corrected grating. It shows that spectral performance is well behaved across the full 900–1200-Å band.

Fig. 5
Fig. 5

Schematic of ray paths for a non-Rowland circle geometry. The path length from entrance slit to grating may be made quite short compared with the overall spectrograph size.

Fig. 6
Fig. 6

Ray tracing of a non-Rowland circle mount. (Left) image showing the severe coma encountered with ellipsoidal gratings. (Right) the good image is the result of coma correction as described in the text.

Fig. 7
Fig. 7

Ray tracing of the coma and curvature correcting grating demonstrates good performance across the 900–1200-Å band.

Fig. 8
Fig. 8

Contours at 1-μm intervals show the deviation from the nominal ellipsoid of the surface of the coma and curvature corrected grating discussed in Sec. IV. Over most of the surface deviations amount to only a few microns.

Equations (12)

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

( u - a ) 2 a 2 + w 2 b 2 + l 2 c 2 = 1.
P = r + r + w ( n λ d - sin α - sin β ) + T 1 + T 2 + T 3 + higher - order terms ,
T 1 = ½ w 3 [ sin α r ( cos 2 α r - a cos α b 2 ) + sin β r ( cos 2 β r - a cos β b 2 ) ] , T 2 = ½ l 2 [ 1 r + 1 r - a c 2 ( cos α + cos β ) ] , T 3 = ½ l 2 w [ sin α r ( 1 r - a c 2 cos α ) + sin β r ( 1 r - a c 2 cos β ) ] .
S F = ( sec α + sec β ) ɛ w l 2 ,
u = a - a ( 1 - w 2 b 2 - l 2 c 2 ) 1 / 2 + ɛ w l 2 ,
ɛ = 1 2 ( sec α + sec β ) [ sin α r ( 1 r - a c 2 cos α ) + sin β r ( 1 r - a c 2 cos β ) ] .
C = R cos 1 / 2 β cos 1 / 2 α .
cos 2 α r - a b 2 cos α + cos 2 β r - a b 2 cos β = 0 ,
1 r - a c 2 cos α + 1 r - a c 2 cos β = 0 ,
a = r 2 cos α + r 2 cos β ,
ɛ = - [ sin α 4 r ( 1 r - a cos α c 2 ) + sin β 4 r ( 1 r - a cos β c 2 ) ] ,
δ = - [ sin α 4 r ( cos 2 α r - a cos α b 2 ) + sin β 4 r ( cos 2 β r - a cos β b 2 ) ] ,

Metrics