Abstract

We used a numerical minimization method to design a Rowland holographic spherical grating that is recorded with two stigmatic laser sources. The method aims at simultaneously reducing all aberrations up to fourth order over a significant spectral range. In the context of a high spectral resolution, far-ultraviolet spectrograph, an original solution is found that implies a nonclassical recording geometry with one virtual source. This solution satisfies the requirement of a resolving power of ~ 30 000 with the unquestionable advantage of manufacturing and testing simplicity. Finally, another example, which is obtained in a different context, shows that the properties of this recording geometry probably have a general applicability.

© 1992 Optical Society of America

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References

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1992 (1)

1991 (2)

1989 (1)

1987 (1)

1984 (1)

1983 (1)

1980 (1)

1974 (1)

1945 (1)

Beutler, H.

Bowyer, S.

S. Bowyer, Center for EUV Astrophysics, University of California, Berkeley, Berkeley, Calif. 94720 (personal communication, 1990).

Cash, W. C.

Chrisp, M.

Content, D.

Davila, P.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 289.

Grange, R.

Harada, T.

Hettrick, M. C.

M. C. Hettrick, “Varied line-space gratings: past, present and future,” in Diffraction Phenomena in Optical Engineering Applications, D. M. Byrne, J. E. Harvey, eds., Proc. Soc. Photo-Opt. Instrum. Eng.560, 96–108 (1985).

Kita, T.

Laget, M.

McKinney, W. R.

Moos, H. W.

H. W. Moos, “Lyman, the far ultraviolet spectroscopic explorer,” Phase A: Study Final Rep. (NASA Goddard Space Flight Center, Greenbelt, Md, 1989), vols. I and II.

Namioka, T.

Noda, H.

Palmer, C.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 289.

Seya, M.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 289.

Trout, C.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 289.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986), pp. 75–78.

Wilson, M.

Appl. Opt. (7)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Other (5)

M. C. Hettrick, “Varied line-space gratings: past, present and future,” in Diffraction Phenomena in Optical Engineering Applications, D. M. Byrne, J. E. Harvey, eds., Proc. Soc. Photo-Opt. Instrum. Eng.560, 96–108 (1985).

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986), pp. 75–78.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, London, 1986), p. 289.

H. W. Moos, “Lyman, the far ultraviolet spectroscopic explorer,” Phase A: Study Final Rep. (NASA Goddard Space Flight Center, Greenbelt, Md, 1989), vols. I and II.

S. Bowyer, Center for EUV Astrophysics, University of California, Berkeley, Berkeley, Calif. 94720 (personal communication, 1990).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the Rowland circle mount. The entrance slit A and the image B are on the Rowland circle. The laser sources C and D can be located anywhere in the dispersion plane xOy.

Fig. 2
Fig. 2

Geometric (solid curve) and holographic (dashed curve) astigmatism coefficients versus wavelength for α = 22.953°. Astigmatism is canceled at 92.8 nm and 101.2 nm.

Fig. 3
Fig. 3

Spot diagrams for an on-axis point source and five wavelengths in the spectrum corresponding to the Lyman/Fuse 5764 mm−1 grating.

Fig. 4
Fig. 4

Schematic diagram of the recording geometry for the Lyman/Fuse 5764 mm−1 grating. The spherical mirror gives a quasi-stigmatic image C of the laser source located in C′. The scale of the optical components does not apply to the distances from C′ to the vertex mirror (3600 mm) and to the vertex grating (300 mm). The mirror diameter of 300 mm and the radius of 5124 mm give a focal ratio of f/8.5; its useful aperture is only 290 mm × 77 mm. The other source D does not need any auxiliary optic. The laser wavelength is 333.6 nm.

Fig. 5
Fig. 5

Spot diagrams for an on-axis point source for two gratings with the same Rowland circle diameter (400 mm) and the same groove density (2500 mm−1): (a) toroidal grating recorded with straight and equally spaced grooves (minor radius ρ = 368.486 mm and α = 22.8°), (b) holographic spherical grating (α = 15.736°).

Tables (2)

Tables Icon

Table I Mounting and Recording Parameters for Lyman/Fuse 5764 mm−1 Grating

Tables Icon

Table II Mounting and Recording Parameters for 2500 mm−1 Grating

Equations (12)

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F = A P + P B + n m λ .
n λ 0 = ( C P - D P ) - ( C O - D O ) ,
( x - R ) 2 + y 2 + z 2 = R 2 .
x ( y , z ) = 1 / 2 R y 2 + 1 / 2 R z 2 + 1 / 8 R 3 y 4 + 1 / 4 R 3 y 2 z 2 + 1 / 8 R 3 z 4 .
F ( y , z ) = F 00 + F 10 + 1 / 2 y 2 F 20 + 1 / 2 z 2 F 02 + 1 / 2 y 3 F 30 + 1 / 2 y z 2 F 12 + 1 / 8 y 4 F 40 + 1 / 4 y 2 z 2 F 22 + 1 / 8 z 4 F 04 .
F i j = M i j + ( m λ / λ 0 ) H i j .
sin α + sin β = ( m λ / λ 0 ) ( sin δ - sin γ ) .
N = ( sin δ - sin γ ) / λ 0 .
δ y = ( R b - y sin β ) R b cos β [ ( R b - y sin β ) F y - y sin β F z ] , z = ( R b - y sin β ) F z .
Φ = Σ w i Σ ( δ y + f δ z ) 2 .
M 02 = 1 / R [ 1 / cos α + 1 / cos β - cos α - cos β ] ,
β = A S N ( N m λ - sin α ) .

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