Abstract

An aberration theory is applied to spectrograph design. The initial system considered has a toroidal mirror in front of a concave grating spectrograph, giving spatial resolution perpendicular to the dispersion direction. The accuracy of the theory is shown by comparison of spot diagrams obtained from the aberrations with those produced by raytracing. The major aberrations affecting the vignetting at the intermediate slit and the spatial resolution are identified. A new system, using a holographic grating to give a flat focal plane, is then designed and optimized. It has increased spatial resolution over the wavelength range and is particularly suitable for microchannel array detectors.

© 1983 Optical Society of America

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References

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  1. W. A. Rense, T. Violett, J. Opt. Soc. Am. 49, 139 (1959).
    [CrossRef]
  2. L. Garifo, A. M. Malvezzi, G. Tondello, Appl. Opt. 18, 1900 (1979).
    [CrossRef] [PubMed]
  3. M. P. Chrisp, Appl. Opt. 22, 1508 (1983).
    [CrossRef] [PubMed]
  4. G. Tondello, Opt. Acta 26, 357 (1979).
    [CrossRef]
  5. J. Meiron, Appl. Opt. 7, 667 (1968).
    [CrossRef] [PubMed]
  6. A. Takashi, T. Katayama, J. Opt. Soc. Am. 68, 1254 (1978).
    [CrossRef]
  7. J. G. Timothy, R. L. Bybee, Soc. Photo-Opt. Instrum. Eng. 265, 93 (1981).
  8. M. P. Chrisp, “The Theory of Holographic Toroidal Grating Systems,” Ph.D. Thesis, London U. (June1981).

1983 (1)

1981 (1)

J. G. Timothy, R. L. Bybee, Soc. Photo-Opt. Instrum. Eng. 265, 93 (1981).

1979 (2)

1978 (1)

1968 (1)

1959 (1)

Bybee, R. L.

J. G. Timothy, R. L. Bybee, Soc. Photo-Opt. Instrum. Eng. 265, 93 (1981).

Chrisp, M. P.

M. P. Chrisp, Appl. Opt. 22, 1508 (1983).
[CrossRef] [PubMed]

M. P. Chrisp, “The Theory of Holographic Toroidal Grating Systems,” Ph.D. Thesis, London U. (June1981).

Garifo, L.

Katayama, T.

Malvezzi, A. M.

Meiron, J.

Rense, W. A.

Takashi, A.

Timothy, J. G.

J. G. Timothy, R. L. Bybee, Soc. Photo-Opt. Instrum. Eng. 265, 93 (1981).

Tondello, G.

Violett, T.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Opt. Acta (1)

G. Tondello, Opt. Acta 26, 357 (1979).
[CrossRef]

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

J. G. Timothy, R. L. Bybee, Soc. Photo-Opt. Instrum. Eng. 265, 93 (1981).

Other (1)

M. P. Chrisp, “The Theory of Holographic Toroidal Grating Systems,” Ph.D. Thesis, London U. (June1981).

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Figures (9)

Fig. 1
Fig. 1

Tondello’s x-ray spectrograph.

Fig. 2
Fig. 2

Spot diagrams from Tondello’s system for different object point heights. Wavelength λ = 44 Å, and the image plane is perpendicular to the base ray. All axes are in millimeters.

Fig. 3
Fig. 3

Vignetting at the entrance slit for different object point heights. Slit width sw = 0.01 mm. All axes are in millimeters.

Fig. 4
Fig. 4

Variation of the aberrations of Tondello’s system with wavelength (Å). Object point η0 = 0.4 mm. Aberrations W040,W022,W013,W031 are <0.1 Å.

Fig. 5
Fig. 5

Ray pencil through toroidal mirror.

Fig. 6
Fig. 6

Optimization of a Seya-Namioka monochromator; results from OPT and Takashi.6 (γ, δ, rc, rd are shown in Appendix B)

Fig. 7
Fig. 7

Variation of the holographic and surface meridional defocus contributions with wavelength.

Fig. 8
Fig. 8

Variation of the aberrations of the final design with wavelength (Å). Object point η0 = 0.4 mm. Aberrations W040,W022,W013,W031 are <0.1 Å.

Fig. 9
Fig. 9

Variation of the spatial resolution with wavelength for in-plane and off-plane object points. Percentage slit transmission is shown at side: —, flat-field design; - - - Tondello’s system.

Equations (26)

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1 R 1 = cos ϑ 2 ( 1 r + 1 r m 1 ) ,
r = R c cos β s .
r s 1 = d + r .
1 ρ 1 = 1 2 cos ϑ ( 1 r + 1 r s 1 ) ,
1 ρ 1 = 1 2 cos ϑ ( 1 r + 1 d + R c cos β s ) .
L = area of field stop × solid angle of aperture stop subtended at field stop .
L = 16 H s H m ,
E = 4 ν m ν s cos β .
W = i j k 4 K i j k W i j k x n i y n j u n k ,
i j k 4 = i j k with i + j + k 4 ;
d W d x n = i j k 4 K i j k W i j k i x n i - 1 y n j u n k , d W d y n = i j k 4 K i j k W i j k j x n i y n j - 1 u n k .
[ W 300 ] 1 = [ - T ( ϑ , r ) sin ϑ r + T ( - ϑ , r m 1 ) sin ϑ r m 1 ] X 1 3 .
[ W 300 ] 1 = sin ϑ cos 2 ϑ 2 ( 1 r m 1 2 - 1 r 2 ) X 1 3 .
[ W 120 ] 1 = sin ϑ ( 1 r s 1 + 1 r ) ( 1 r s 1 - 1 2 r - 1 2 r m 1 ) X 1 Y 1 2 .
δ x 120 = - r m 1 2 X 1 [ W 120 ] y 1 n 2 .
[ W 111 ] 1 = sin ϑ ( 1 r + 1 r s 1 ) X 1 Y 1 U 1 ,
δ x 111 = - r m 1 X 1 [ W 111 ] 1 y n u n .
δ λ = ζ cos α m δ α ,
Ω = i j k 4 V i j k ( Λ 1 [ W i j k 2 ] λ 1 + Λ 2 [ W i j k 2 ] λ 2 + + Λ n [ W i j k 2 ] λ n ) ,
M λ = ( 1 S s W 2 d s ) 1 / 2 .
Ω = n ( W 200 2 + W 020 2 + W 300 2 ) λ n ,
Y 1 = v s r             X 1 = ( ν m r m 1 ) / ( cos ϑ ) .
1 R 2 = 1 cos α + cos β ( cos 2 α r m 2 + cos 2 β r ) .
W 200 = ( M 200 - m λ λ 0 H 200 ) X 2 2 ,
δ y = - r Y 2 d W d y n ;
δ y = - r M Y 2 W 020 y n .

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