Abstract

Using two optical toroidal elements, a mirror and a grating, both working at grazing incidence, a spectrometer can be built that is stigmatic in the XUV region at one wavelength. Good compensation of the aberrations is achieved when the intermediate sagittal image is nearly at infinity. By varying the angle of incidence on the grating with simple movements, a given couple of optical elements could cover stigmatically a rather extended spectral range. If coupled with bidimensional array detectors, such a spectrograph could find applications in planned solar XUV telescopes.

© 1981 Optical Society of America

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References

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  1. T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).
    [CrossRef]
  2. R. J. Speer, Space Sci. Instrum. 2, 463 (1976).
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    [CrossRef]
  4. S. O. Kastner, C. Wade, Appl. Opt. 17, 1252 (1978).
    [CrossRef] [PubMed]
  5. M. Pouey, J. Phys C Suppl. 4188 (1978).
  6. G. Tondello, Opt. Acta 26, 357 (1979).
    [CrossRef]
  7. H. Haber, J. Opt. Soc. Am. 40, 153 (1950).
    [CrossRef]
  8. L. Garifo, A. M. Malvezzi, CISE Report N-185, 1977 (unpublished).
  9. G. P. Haskell, Ed., “Grazing Incidence Solar Telescope, GRIST,” Report DP/PS(78)11 (European Space Agency, Paris, 1978).
  10. J. G. Timothy, J. Opt. Soc. Am. 68, 1441 (1978).
  11. M. C. E. Huber, G. Tondello, Appl. Opt. 18, 3948 (1979).
    [CrossRef] [PubMed]
  12. L. Garifo, A. M. Malvezzi, G. Tondello, Appl. Opt. 18, 1900 (1979).
    [CrossRef] [PubMed]
  13. G. Passerau, A. Thevenon, J. Flamand, in Proceedings, Conference on Synchrotron Radiation Instrumentation, 4–6 June 1979, Gaithersburg, Maryland.

1979 (3)

1978 (3)

J. G. Timothy, J. Opt. Soc. Am. 68, 1441 (1978).

S. O. Kastner, C. Wade, Appl. Opt. 17, 1252 (1978).
[CrossRef] [PubMed]

M. Pouey, J. Phys C Suppl. 4188 (1978).

1976 (1)

R. J. Speer, Space Sci. Instrum. 2, 463 (1976).

1961 (1)

1959 (1)

1950 (1)

Flamand, J.

G. Passerau, A. Thevenon, J. Flamand, in Proceedings, Conference on Synchrotron Radiation Instrumentation, 4–6 June 1979, Gaithersburg, Maryland.

Garifo, L.

L. Garifo, A. M. Malvezzi, G. Tondello, Appl. Opt. 18, 1900 (1979).
[CrossRef] [PubMed]

L. Garifo, A. M. Malvezzi, CISE Report N-185, 1977 (unpublished).

Haber, H.

Huber, M. C. E.

Kastner, S. O.

Malvezzi, A. M.

L. Garifo, A. M. Malvezzi, G. Tondello, Appl. Opt. 18, 1900 (1979).
[CrossRef] [PubMed]

L. Garifo, A. M. Malvezzi, CISE Report N-185, 1977 (unpublished).

Namioka, T.

Passerau, G.

G. Passerau, A. Thevenon, J. Flamand, in Proceedings, Conference on Synchrotron Radiation Instrumentation, 4–6 June 1979, Gaithersburg, Maryland.

Pouey, M.

M. Pouey, J. Phys C Suppl. 4188 (1978).

Speer, R. J.

R. J. Speer, Space Sci. Instrum. 2, 463 (1976).

Thevenon, A.

G. Passerau, A. Thevenon, J. Flamand, in Proceedings, Conference on Synchrotron Radiation Instrumentation, 4–6 June 1979, Gaithersburg, Maryland.

Timothy, J. G.

J. G. Timothy, J. Opt. Soc. Am. 68, 1441 (1978).

Tondello, G.

Wade, C.

Appl. Opt. (3)

J. Opt. Soc. Am. (4)

J. Phys C Suppl. (1)

M. Pouey, J. Phys C Suppl. 4188 (1978).

Opt. Acta (1)

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

Space Sci. Instrum. (1)

R. J. Speer, Space Sci. Instrum. 2, 463 (1976).

Other (3)

L. Garifo, A. M. Malvezzi, CISE Report N-185, 1977 (unpublished).

G. P. Haskell, Ed., “Grazing Incidence Solar Telescope, GRIST,” Report DP/PS(78)11 (European Space Agency, Paris, 1978).

G. Passerau, A. Thevenon, J. Flamand, in Proceedings, Conference on Synchrotron Radiation Instrumentation, 4–6 June 1979, Gaithersburg, Maryland.

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Figures (6)

Fig. 1
Fig. 1

Configuration of the system in the sagittal and meridional planes: S, entrance slit; M, mirror; G, grating; H. position of the intermediate sagittal focuses; ϕ, angle of incidence on M; α, angle of incidence on G; β, angle of diffraction for λst; entrance (Ω, Ω) and exit (ω, ω) aperture angles are shown with relevant distances between the source/images and the optical elements.

Fig. 2
Fig. 2

Spectral (- - -) blur ax and spatial (—) blur ay on the focal surface in the vicinity of the central stigmatic wavelength λst = 150 Å. Each set of curves refers to, from bottom to top, a point source located at 0, 0.25, and 0.75 mm from the meridional plane in the center of the entrance slit. The arrow on the left gives the equivalent spectral blur size for a 20-μm wide entrance slit (corresponding to 5.4 × 10−2 Å). The double arrow at the bottom corresponds to twenty spectral resolution elements. The arrow on the right corresponds to a single spatial resolution element.

Fig. 3
Fig. 3

Mechanism for varying the stigmatic wavelength λst: S, entrance slit; M, mirror. The rail R rotates around pivot S* into position R′. The grating G slides along the rail to G′, thus changing the angle of incidence αα′ and the stigmatic wavelength λ st λ st .

Fig. 4
Fig. 4

Spectral (- - -) ax and spatial (—) ay blurs in the vicinity of the two extreme stigmatic positions λst = 171 Å and λst = 128.4 Å. Each set of curves refers to (bottom to top) a point source located at 0, 0.25, and 0.75 mm from the meridional plane. The arrow on the left gives the equivalent spectral blur size for a 20-μm wide entrance slit.

Fig. 5
Fig. 5

Geometry of the two-mirror system.

Fig. 6
Fig. 6

Sketch of the possible stigmatic configurations for the two-mirror system. The system is completely symmetric with respect to its middle point both in the sagittal plane (upper) and in the meridional plane (lower). Two configurations, one U shaped (solid lines) and one Z shaped (dotted lines) are possible in the meridional plane.

Tables (2)

Tables Icon

Table I Values of Parameters Used in the Present Study of the Proposed Configuration

Tables Icon

Table II Comparison of the Optical Configuration of Table I with a Single Toroidal and a Spherical Grating

Equations (16)

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1 p + 1 p = 2 R m cos ϕ ,
1 p + 1 p ̅ = 2 cos ϕ ρ m ,
p ̅ = R g cos α + p ρ g cos β cos β ( cos α + cos β ) ρ g / R g .
λ = d ( sin α + sin β ) ,
F = A P ¯ + P P ¯ + P B ¯ ,
A P ¯ = A 0 + A 1 + A 2 + A 3 + A 4 + O ( w 5 / R 4 ) ,
A 0 = R cos ϕ ; A 1 = w sin ϕ ; A 2 = l 2 2 R cos ϕ ( 1 R cos 2 ϕ / ρ ) + z 2 2 z l 2 R cos ϕ ; A 3 = w l 2 sin ϕ 2 R cos 2 ϕ ( 1 R cos 2 ϕ / ρ ) + w ( z 2 2 z l ) sin ϕ 2 R 2 cos 2 ϕ ; A 4 = w 4 sin 2 ϕ 8 R 2 cos ϕ + l 4 8 R cos ϕ × [ 1 ρ 2 1 R 2 ( 1 R cos 2 ϕ / ρ ) ] ( 1 R cos 2 ϕ / ρ ) + w 2 l 2 sin 2 ϕ 2 R 2 cos ϕ [ 1 2 ρ + 1 R cos ϕ ( 1 R cos 2 ϕ / ρ ) ] + w 2 ( z 2 2 z l ) sin 2 ϕ 2 R 3 cos 3 ϕ + l 2 ( z 2 2 z l ) 4 R 4 cos 4 ϕ ( 1 R cos 2 ϕ / ρ ) ( z 2 2 z l ) 2 8 R 4 cos 4 ϕ .
P P x = B 1 x + C 0 B 2 + C 0 B 3 x + C 0 B 4 x C 1 B 3 x + C 2 B 2 C 0 3 B 2 2 + O ( w 5 / R 4 ) ,
C 0 = 1 8 R cos ϕ ; C 1 = ( w w ) sin ϕ 8 R 2 cos 2 ϕ ; C 2 = ( w w ) 2 sin 2 ϕ 16 R 3 cos 3 ϕ ; B 1 U = 2 R cos ϕ + ( w w ) sin ϕ ; B 1 Z = 2 R cos ϕ + ( w + w ) sin ϕ ; B 2 = ( w w ) 2 cos 2 ϕ + ( l 2 + l 2 ) ( 1 2 R cos 2 ϕ / ρ ) 2 l l ; B 3 U = 2 sin ϕ cos ϕ [ w ( w 2 / R + l 2 / ρ ) w ( w 2 / R + l 2 / ρ ) ] ; B 3 Z = 0 ; B 4 U = ( 1 / 2 cos 2 ϕ ) [ ( w 2 w 2 ) 2 2 R 2 l 2 l 2 ρ 2 + ( l 2 l 2 ) ( w 2 w 2 ) ρ R ] + ( 1 / 2 R cos 2 ϕ / ρ ) l 4 + l 4 2 ρ 2 ; B 4 Z = ( 1 / 2 cos 2 ϕ ) ( w 4 + w 4 2 R 2 + w 2 l 2 + w 2 l 2 ρ R ) + ( 1 / 2 cos 2 ϕ / ρ ) l 4 + l 4 2 ρ 2 + w 2 w 2 2 R 2 + w 2 l 2 + l 2 w 2 2 R ρ + l 2 l 2 2 ρ 2 .
w = w ; l = ( 3 4 R cos 2 ϕ / ρ ) l .
( K 2 1 ) 1 2 R cos ϕ ,
Δ w = w w , Δ l = K l l
F / w = 0 ; F / l = 0 .
F / w = 0 ; F / l = 0 .
z = ( k 1 ) w 2 l sin 2 ϕ R 2 cos 2 ϕ + l 3 8 R 2 cos 4 ϕ [ ( 5 K 3 ) sin 2 ϕ + ( 3 K 5 ) cos 2 ϕ + 4 ( 1 K ) ] , Δ ϕ = ( 1 K ) w l 2 sin 2 ϕ R 3 cos 4 ϕ + 2 w 3 sin 2 ϕ R 3 cos 2 ϕ ,
z = ( K 1 ) l w sin ϕ R cos ϕ + 3 K 1 2 w 2 l sin 2 ϕ R 2 cos 2 ϕ + K + 1 8 l 3 R 2 cos 4 ϕ ( 1 2 cos 2 ϕ ) , Δ ϕ = K 1 2 l 2 sin ϕ R 2 cos 2 ϕ 2 w 3 sin 2 ϕ R 3 cos 2 ϕ 3 K + 7 2 w l 2 sin 2 ϕ R 3 cos 4 ϕ .

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