Abstract

Two approaches to reducing optical aberrations of concave grating spectrographs have been used, holographically controlling the groove curvature and spacing and reshaping the optical substrate while ruling the grooves conventionally. The latter approach, slightly deforming an ellipsoidal grating blank, can lead to diffraction-limited performance at a single far ultraviolet wavelength. When such a grating is used in a slitted Rowland circle spectrograph, the result is an extremely efficient spectrograph with spectral resolving power of ~30,000 and low astigmatism. Optical fabrication technology has advanced to the point where these exotic surface gratings are becoming practical.

© 1991 Optical Society of America

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References

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  1. H. W. Moos et al., “LYMAN, the Far Ultraviolet Spectroscopic Explorer, Phase A Study Final Report,” NASA Goddard Space Flight Center, Greenbelt, MD (1989).
  2. C. Martin, “The Pan-American Astrophysics Explorer (PAX),” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 878–894 (1990).
  3. T. Namioka, “Theory of the Ellipsoidal Concave Grating I,” J. Opt. Soc. Am. 51, 4–12 (1961).
    [CrossRef]
  4. T. Namioka, “Theory of the Concave Grating,” J. Opt. Soc. Am. 49, 446–460 (1959).
    [CrossRef]
  5. W. C. Cash, “Aspheric Concave Grating Spectrographs,” Appl. Opt. 23, 4518–4522 (1984).
    [CrossRef] [PubMed]
  6. P. Davila, “Aberration Corrected Aspheric Gratings for Far Ultraviolet Spectrographs: Holographic Approach,” submitted to Appl. Opt. (1990).
  7. R. Grange, M. Laget, “Second Generation Holography Applied to a High Resolution Concave Grating Spectrograph,” submitted to Appl. Opt. (1990).
  8. D. Content et al., “Optical Design of Lyman/FUSE,” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 943–952 (1990).
  9. T. T. Saha, “General Surface Equations for Glancing Incidence Telescopes,” Appl. Opt. 26, 658–663 (1987).
    [CrossRef] [PubMed]
  10. SYNOPSYS, Product of Optical Systems Design, East Boothbay, ME.
  11. M. Duban, “Improved Wadsworth mounting with aspherical holographic grating,” Appl. Opt. 19, 2488–2489 (1980).
    [CrossRef] [PubMed]
  12. B. Bach, Hyperfine, Inc.; private communication (1990).
  13. P. Z. Takacs, S. K. Feng, “Long Trace Profile Measurements on Cylindrical Aspheres,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 354–364 (1988).
  14. P. Z. Takacs, K. Furenlid, R. A. Debiasse, “Surface Topography Measurements over the 1 Meter to 10 Micrometer Spatial Period Bandwidth,” Proc. Soc. Photo-Opt. Instrum. Eng. 1164, 203–208 (1989).
  15. P. Glenn, “Å Level Profilometry for Submillimeter to Meter Scale Surface Errors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1333, (1990).
  16. S. Wong, “Fringe Analysis for Testing Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 316–321 (1988).
  17. S. M. Arnold, “How to Test an Asphere with a Computer Generated Hologram,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 191–197 (1989).
  18. E. J. Danielewicz, D. Selman, “Computer-Generated Holograms Test Aspheric Optics,” Laser Focus World 26, 143–147 (1990).
  19. M. Hurwitz, S. Bowyer, J. Edelstein, T. Harada, T. Kita, “EUV Efficiency of a 6000-Grooves mm−1 Diffraction Grating,” Appl. Opt. 29, 1866–1867 (1990).
    [CrossRef] [PubMed]

1990 (5)

C. Martin, “The Pan-American Astrophysics Explorer (PAX),” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 878–894 (1990).

D. Content et al., “Optical Design of Lyman/FUSE,” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 943–952 (1990).

P. Glenn, “Å Level Profilometry for Submillimeter to Meter Scale Surface Errors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1333, (1990).

E. J. Danielewicz, D. Selman, “Computer-Generated Holograms Test Aspheric Optics,” Laser Focus World 26, 143–147 (1990).

M. Hurwitz, S. Bowyer, J. Edelstein, T. Harada, T. Kita, “EUV Efficiency of a 6000-Grooves mm−1 Diffraction Grating,” Appl. Opt. 29, 1866–1867 (1990).
[CrossRef] [PubMed]

1989 (2)

P. Z. Takacs, K. Furenlid, R. A. Debiasse, “Surface Topography Measurements over the 1 Meter to 10 Micrometer Spatial Period Bandwidth,” Proc. Soc. Photo-Opt. Instrum. Eng. 1164, 203–208 (1989).

S. M. Arnold, “How to Test an Asphere with a Computer Generated Hologram,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 191–197 (1989).

1988 (2)

S. Wong, “Fringe Analysis for Testing Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 316–321 (1988).

P. Z. Takacs, S. K. Feng, “Long Trace Profile Measurements on Cylindrical Aspheres,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 354–364 (1988).

1987 (1)

1984 (1)

1980 (1)

1961 (1)

1959 (1)

Arnold, S. M.

S. M. Arnold, “How to Test an Asphere with a Computer Generated Hologram,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 191–197 (1989).

Bach, B.

B. Bach, Hyperfine, Inc.; private communication (1990).

Bowyer, S.

Cash, W. C.

Content, D.

D. Content et al., “Optical Design of Lyman/FUSE,” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 943–952 (1990).

Danielewicz, E. J.

E. J. Danielewicz, D. Selman, “Computer-Generated Holograms Test Aspheric Optics,” Laser Focus World 26, 143–147 (1990).

Davila, P.

P. Davila, “Aberration Corrected Aspheric Gratings for Far Ultraviolet Spectrographs: Holographic Approach,” submitted to Appl. Opt. (1990).

Debiasse, R. A.

P. Z. Takacs, K. Furenlid, R. A. Debiasse, “Surface Topography Measurements over the 1 Meter to 10 Micrometer Spatial Period Bandwidth,” Proc. Soc. Photo-Opt. Instrum. Eng. 1164, 203–208 (1989).

Duban, M.

Edelstein, J.

Feng, S. K.

P. Z. Takacs, S. K. Feng, “Long Trace Profile Measurements on Cylindrical Aspheres,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 354–364 (1988).

Furenlid, K.

P. Z. Takacs, K. Furenlid, R. A. Debiasse, “Surface Topography Measurements over the 1 Meter to 10 Micrometer Spatial Period Bandwidth,” Proc. Soc. Photo-Opt. Instrum. Eng. 1164, 203–208 (1989).

Glenn, P.

P. Glenn, “Å Level Profilometry for Submillimeter to Meter Scale Surface Errors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1333, (1990).

Grange, R.

R. Grange, M. Laget, “Second Generation Holography Applied to a High Resolution Concave Grating Spectrograph,” submitted to Appl. Opt. (1990).

Harada, T.

Hurwitz, M.

Kita, T.

Laget, M.

R. Grange, M. Laget, “Second Generation Holography Applied to a High Resolution Concave Grating Spectrograph,” submitted to Appl. Opt. (1990).

Martin, C.

C. Martin, “The Pan-American Astrophysics Explorer (PAX),” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 878–894 (1990).

Moos, H. W.

H. W. Moos et al., “LYMAN, the Far Ultraviolet Spectroscopic Explorer, Phase A Study Final Report,” NASA Goddard Space Flight Center, Greenbelt, MD (1989).

Namioka, T.

Saha, T. T.

Selman, D.

E. J. Danielewicz, D. Selman, “Computer-Generated Holograms Test Aspheric Optics,” Laser Focus World 26, 143–147 (1990).

Takacs, P. Z.

P. Z. Takacs, K. Furenlid, R. A. Debiasse, “Surface Topography Measurements over the 1 Meter to 10 Micrometer Spatial Period Bandwidth,” Proc. Soc. Photo-Opt. Instrum. Eng. 1164, 203–208 (1989).

P. Z. Takacs, S. K. Feng, “Long Trace Profile Measurements on Cylindrical Aspheres,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 354–364 (1988).

Wong, S.

S. Wong, “Fringe Analysis for Testing Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 316–321 (1988).

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

Laser Focus World (1)

E. J. Danielewicz, D. Selman, “Computer-Generated Holograms Test Aspheric Optics,” Laser Focus World 26, 143–147 (1990).

Proc. Soc. Photo-Opt. Instrum. Eng. (7)

D. Content et al., “Optical Design of Lyman/FUSE,” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 943–952 (1990).

P. Z. Takacs, S. K. Feng, “Long Trace Profile Measurements on Cylindrical Aspheres,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 354–364 (1988).

P. Z. Takacs, K. Furenlid, R. A. Debiasse, “Surface Topography Measurements over the 1 Meter to 10 Micrometer Spatial Period Bandwidth,” Proc. Soc. Photo-Opt. Instrum. Eng. 1164, 203–208 (1989).

P. Glenn, “Å Level Profilometry for Submillimeter to Meter Scale Surface Errors,” Proc. Soc. Photo-Opt. Instrum. Eng. 1333, (1990).

S. Wong, “Fringe Analysis for Testing Optical Surface,” Proc. Soc. Photo-Opt. Instrum. Eng. 966, 316–321 (1988).

S. M. Arnold, “How to Test an Asphere with a Computer Generated Hologram,” Proc. Soc. Photo-Opt. Instrum. Eng. 1052, 191–197 (1989).

C. Martin, “The Pan-American Astrophysics Explorer (PAX),” Proc. Soc. Photo-Opt. Instrum. Eng. 1235, 878–894 (1990).

Other (5)

H. W. Moos et al., “LYMAN, the Far Ultraviolet Spectroscopic Explorer, Phase A Study Final Report,” NASA Goddard Space Flight Center, Greenbelt, MD (1989).

SYNOPSYS, Product of Optical Systems Design, East Boothbay, ME.

P. Davila, “Aberration Corrected Aspheric Gratings for Far Ultraviolet Spectrographs: Holographic Approach,” submitted to Appl. Opt. (1990).

R. Grange, M. Laget, “Second Generation Holography Applied to a High Resolution Concave Grating Spectrograph,” submitted to Appl. Opt. (1990).

B. Bach, Hyperfine, Inc.; private communication (1990).

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Figures (6)

Fig. 1
Fig. 1

Spot diagrams for third-order deformed ellipsoidal grating for a point source on-axis. Astigmatism is canceled at the wavelength shown, 97.0 nm: (a) 0 = 0.93410−8 mm−2 (analytic value); (b) 0 = 1.128 × 10−8 mm−2 (optimized value). Root-mean-square radii are 22 and 7 μm, respectively.

Fig. 2
Fig. 2

Spot diagrams for a point source on-axis at 91.0, 93.7, 97.0, 100.3 and 103.0 nm for the third-order grating design (0 = 1.128 × 10−8 mm−2). Astigmatism is canceled at 93.7 and 100.3 nm (βc = ±1.09°). Images are placed on the same horizontal axis for clarity and are all plotted to the same scale.

Fig. 3
Fig. 3

Spot diagram for a point source on-axis at 97.0 nm for the fourth-order deformed grating optimized for stigmatic imaging at 97.0 nm (βc = 0): (a) scale is the same as in Fig. 1; (b) magnified 10 times. Root mean square radius is 0.3 μm.

Fig. 4
Fig. 4

Spectral resolving power of fourth-order grating optimized for 97.0 nm vs entrance slit width at 97.0 nm. A Gaussian intensity profile for an input beam with 50% EE in a 1-arcsec diameter is assumed. The resolving power at the 0 slit width is determined using a diffraction model and the Rayleigh criterion.

Fig. 5
Fig. 5

Spot diagrams for a point source on-axis at 91.0, 93.7, 97.0, 100.3, and 103.0 nm for the fourth-order design. Astigmatism is canceled at 93.7 and 100.3 nm or βc = ±1.09°. The scale is the same as in Fig. 2.

Fig. 6
Fig. 6

Spectral resolving power of third- and fourth-order grating designs vs wavelength assuming a 1 arcsec entrance slit width: +, third-order design, βc = ±1.09°; *, fourth-order counterpart, βc = ±1.09°. Canceling astigmatism at a different wavelength does not change the resolving power by more than 100 at any wavelength shown.

Tables (4)

Tables Icon

Table I Design Parameters for Third-Order Grating

Tables Icon

Table II Performance of Third-Order Grating; the Source Is a Wolter Type II Telescope with 50% EE Inside a 1 arcsec Diameter; Astigmatism Is Canceled at βc = ±1.09°

Tables Icon

Table III Deformation Coefficients for Fourth-Order Grating, Canceling Sagittal Coma and Spherical Aberration at 97.0 nm

Tables Icon

Table IV Performance of Fourth-Order Grating Using the Same Methods as In Table II; Astigmatism Is Again Canceled at βc = ±1.09°

Equations (15)

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U = a a [ 1 ( W b ) 2 ( L c ) 2 ] ,
A 1 = 0 ( tangential astigmatism ) ,
A 2 = ( cos α + cos β ) ( sec α sec β R 2 c 2 ) ( sagittal astigmatism ) ,
C 1 = 0 ( tangential coma ) ,
C 2 = sin α cos 2 α + sin β cos 2 β R 2 c 2 ( sin α + sin β ) ( sagittal coma ) ,
S 1 = ( cos α + cos β ) ( sec α sec β 1 ) ( spherical aberration ) ,
S 2 = R 2 c 2 [ ( cos α + cos β ) ( sec α sec β 1 ) 2 ( sin 2 α cos α + sin 2 β cos β ) ] + 2 ( sin 2 α cos 3 α + sin 2 β cos 3 β ) ( spherical aberration ) ,
S 3 = R 4 c 4 ( cos α + cos β ) ( sec α sec β 2 ) , + 2 ( R 2 c 2 ) ( sec α + sec β ) ( sec 3 α + sec 3 β ) , ( spherical aberration ) ,
Δ = W ( sin α sin β ) + W 2 2 R A 1 + L 2 2 R A 2 + W 3 2 R 2 C 1 + W L 2 2 R 2 C 2 + W 4 8 R 3 S 1 + W 2 L 2 4 R 3 S 2 + L 4 8 R 3 S 3 .
c = R cos α cos β .
0 = 1 2 R 2 [ sec α + sec β ] × [ sin α cos 2 α + sin β cos 2 β R 2 c 2 ( sin α + sin β ) ] .
1 = 1 8 R 3 cos α + cos β sec α + sec β ( sec α sec β 1 ) ;
2 = 1 4 R 3 1 sec α + sec β { R 2 c 2 [ 2 ( cos α + cos β ) ( sec α sec β 1 ) 2 ( sin 2 α cos α + sin 2 β cos β ) ] + 2 ( sin 2 α cos 3 α + sin 2 β cos 3 β ) } ;
3 = 1 8 R 3 1 sec α + sec β [ R 4 c 4 ( cos α + cos β ) ( sec α + sec β 2 ) + 2 ( R 2 c 2 ) ( sec α + sec β ) ( sec 3 α + sec 3 β ) ]
U = a a [ 1 ( W b ) 2 ( L c ) 2 ] + 0 W L 2 + 1 W 4 + 2 W 2 L 2 + 3 L 4 .

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