Abstract

The third-generation holographic Rowland mount consists of a Rowland-mounted, optimally recorded holographic spherical grating, referred to as an optimized Rowland grating (ORG), whose recording sources are aberrated by two auxiliary ORG’s. The main purpose of this mount is to avoid any aspherical surface while providing control over all the parameters needed to correct the aberrations up to and including the fourth order. Earlier [Appl. Opt. 30, 4019–4025 (1991)], we considered the case of a moderate coma c2. We now give the fourth-order theory, apply it to the high-dispersion (4600 grooves/mm) grating considered previously, and obtain for it diffraction-limited images.

© 1999 Optical Society of America

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References

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  1. H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. A 64, 1031–1036 (1974).
    [CrossRef]
  2. T. Harada, T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980).
    [CrossRef] [PubMed]
  3. M. Duban, “Comparison of grating designs for the Lyman Far-Ultraviolet Spectroscopic Explorer spectrograph,” Appl. Opt. 32, 4253–4264 (1993).
    [CrossRef] [PubMed]
  4. W. C. Cash, “Aspheric concave grating spectrographs,” Appl. Opt. 23, 4518–4522 (1984).
    [CrossRef] [PubMed]
  5. D. Content, C. Trout, P. Davila, M. Wilson, “Aberration corrected aspheric gratings for far ultraviolet spectrographs: conventional approach,” Appl. Opt. 30, 801–806 (1991).
    [CrossRef] [PubMed]
  6. D. Content, T. Namioka, “Deformed ellipsoidal gratings for far-ultraviolet spectrographs: analytic optimization,” Appl. Opt. 32, 4881–4889 (1993).
    [CrossRef] [PubMed]
  7. M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
    [CrossRef] [PubMed]
  8. C. Palmer, “Theory of second-generation holographic diffraction gratings,” J. Opt. Soc. Am. A 6, 1175–1188 (1989).
    [CrossRef]
  9. R. Grange, M. Laget, “Holographic diffraction gratings generated by aberrated wave fronts: application to a high-resolution far-ultraviolet spectrograph,” Appl. Opt. 30, 3598–3603 (1991).
    [CrossRef] [PubMed]
  10. R. Grange, “Aberration-reduced holographic spherical gratings for Rowland circle spectrographs,” Appl. Opt. 31, 3744–3749 (1992).
    [CrossRef] [PubMed]
  11. R. Grange, “Holographic spherical gratings: a new family of quasi-stigmatic designs for the Rowland-circle mounting,” Appl. Opt. 32, 4875–4880 (1993).
    [CrossRef] [PubMed]
  12. W. Cash, “Far-ultraviolet spectrographs: the impact of holographic design,” Appl. Opt. 34, 2241–2246 (1995).
    [CrossRef] [PubMed]
  13. M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
    [CrossRef] [PubMed]
  14. M. Duban, G. R. Lemaı̂tre, R. F. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
    [CrossRef]
  15. M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
    [CrossRef]
  16. G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Clebsch–Zernike polynomials for correcting off-axis aberrations,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).
  17. M. Duban, K. Dohlen, G. R. Lemaı̂tre, “Illustration of the use of multimode deformable plane mirrors to record high- resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
    [CrossRef]
  18. J. C. Green, “The Cosmic Origin Spectrograph,” , 1 (Center for Astrophysics & Space Astronomy, Colorado University, Boulder, Colo., 1997).

1998 (3)

1995 (2)

W. Cash, “Far-ultraviolet spectrographs: the impact of holographic design,” Appl. Opt. 34, 2241–2246 (1995).
[CrossRef] [PubMed]

G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Clebsch–Zernike polynomials for correcting off-axis aberrations,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).

1993 (3)

1992 (1)

1991 (3)

1989 (1)

1987 (1)

1984 (1)

1980 (1)

1974 (1)

H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. A 64, 1031–1036 (1974).
[CrossRef]

Cash, W.

Cash, W. C.

Content, D.

Davila, P.

Dohlen, K.

Duban, M.

Grange, R.

Green, J. C.

J. C. Green, “The Cosmic Origin Spectrograph,” , 1 (Center for Astrophysics & Space Astronomy, Colorado University, Boulder, Colo., 1997).

Harada, T.

Kita, T.

Laget, M.

Lemai^tre, G. R.

Malina, R. F.

Namioka, T.

Noda, H.

H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. A 64, 1031–1036 (1974).
[CrossRef]

Palmer, C.

Seya, M.

H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. A 64, 1031–1036 (1974).
[CrossRef]

Trout, C.

Wang, M.

G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Clebsch–Zernike polynomials for correcting off-axis aberrations,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).

Wilson, M.

Appl. Opt. (14)

T. Harada, T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980).
[CrossRef] [PubMed]

W. C. Cash, “Aspheric concave grating spectrographs,” Appl. Opt. 23, 4518–4522 (1984).
[CrossRef] [PubMed]

M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
[CrossRef] [PubMed]

D. Content, C. Trout, P. Davila, M. Wilson, “Aberration corrected aspheric gratings for far ultraviolet spectrographs: conventional approach,” Appl. Opt. 30, 801–806 (1991).
[CrossRef] [PubMed]

R. Grange, M. Laget, “Holographic diffraction gratings generated by aberrated wave fronts: application to a high-resolution far-ultraviolet spectrograph,” Appl. Opt. 30, 3598–3603 (1991).
[CrossRef] [PubMed]

M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
[CrossRef] [PubMed]

R. Grange, “Aberration-reduced holographic spherical gratings for Rowland circle spectrographs,” Appl. Opt. 31, 3744–3749 (1992).
[CrossRef] [PubMed]

M. Duban, “Comparison of grating designs for the Lyman Far-Ultraviolet Spectroscopic Explorer spectrograph,” Appl. Opt. 32, 4253–4264 (1993).
[CrossRef] [PubMed]

R. Grange, “Holographic spherical gratings: a new family of quasi-stigmatic designs for the Rowland-circle mounting,” Appl. Opt. 32, 4875–4880 (1993).
[CrossRef] [PubMed]

D. Content, T. Namioka, “Deformed ellipsoidal gratings for far-ultraviolet spectrographs: analytic optimization,” Appl. Opt. 32, 4881–4889 (1993).
[CrossRef] [PubMed]

M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
[CrossRef]

W. Cash, “Far-ultraviolet spectrographs: the impact of holographic design,” Appl. Opt. 34, 2241–2246 (1995).
[CrossRef] [PubMed]

M. Duban, G. R. Lemaı̂tre, R. F. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
[CrossRef]

M. Duban, K. Dohlen, G. R. Lemaı̂tre, “Illustration of the use of multimode deformable plane mirrors to record high- resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
[CrossRef]

Astron. Astrophys. Suppl. Ser. (1)

G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Clebsch–Zernike polynomials for correcting off-axis aberrations,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).

J. Opt. Soc. Am. A (2)

H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. A 64, 1031–1036 (1974).
[CrossRef]

C. Palmer, “Theory of second-generation holographic diffraction gratings,” J. Opt. Soc. Am. A 6, 1175–1188 (1989).
[CrossRef]

Other (1)

J. C. Green, “The Cosmic Origin Spectrograph,” , 1 (Center for Astrophysics & Space Astronomy, Colorado University, Boulder, Colo., 1997).

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Figures (7)

Fig. 1
Fig. 1

Geometry of the main grating G recorded with an auxiliary grating g. (RC, Rowland circle).

Fig. 2
Fig. 2

Recording the main grating G at an arbitrary point M (schematic view: generally, m and M do not lie in the OXY plane).

Fig. 3
Fig. 3

Spot diagrams obtained at λ = 910 and 927.7 (P1 point); 940, 970, 1000, and 1012.5 (P2 point); 1030 Å, with λ j = 4879.9 Å (isotropic scales). (a) In Ref. 13. (simplified theory); (b) with ρ* = 1500 mm; (c) with ρ* = 3000 mm (exact theory).

Fig. 4
Fig. 4

Overall and resolvant width of an image, a and b. With an adequate detector, the spectral lines λ1, λ2, and λ3 are completely resolved.

Fig. 5
Fig. 5

Minimum and maximum global resolution versus ρ* for k j = ±3 and ±4, λj = 4879.9 Å.

Fig. 6
Fig. 6

Recording setup of the main grating G recorded by use of two auxiliary gratings g 1 and g 2 with the same radius of curvature ρ* = 1500 mm (exact theory).

Fig. 7
Fig. 7

Recording setup of the main grating G recorded by use of two auxiliary gratings g 1 and g 2 with ρ1 = 3765 mm and ρ2 = 3977.8 mm (simplified theory). RC, Rowland circle.

Tables (1)

Tables Icon

Table 1 Parameters of the Auxiliary Gratings

Equations (50)

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sin β-sin α=nλg,
sin i+sin r=knλG,
sin i tan i+sin r tan r+kλG/λgsin α tan α-sin β tan β=0.
σp=sin itan ip+kλG/λgsin αtan αp-sin βtan βp,
Σp=σp+sin rtan rp.
Σ0=0,
Σ1=0.
TY, Z=Lm+mM+kλG/λgcm-dm,
T0=Lo+oO+kλG/λgco-do.
X=Y2+Z2/2R+Y4+Z4/8R3+Y2Z2/4R3+,
x=y2+z2/2ρ+y4+z4/8ρ3+y2z2/4ρ3+.
y=a1Y+a2Y2+a3Z2+a4Y3+a5YZ2+a6Y4+a7Y2Z2+a8Z4,
z=b1Z+b2YZ+b3Y2Z+b4Z3+b5Y3Z+b6YZ3.
z=b1Z+b2YZ+b3Y2Z+b4Z3.
T/y=0,  T/z=0.
T=T1i+kλG/λgT1α-T1β+T2.
y=a1Y+a2Y2+a3Z2,
z=b1Z+b2YZ.
a1=ρ/R,
b1=-ρ cos r/R cos a,
a2=ρ/2R2tan a-tan r,
b2=-ρ cos r/R2 cos aΣ2 cos r+tan a-tan r-ρ2 cos r3/R3 cos a2Σ2,
a3=ρ/2R2 cos a2sin r cos r-sin a cos a+Σ2 cos r+ρ2 cos r2/2R3 cos a2Σ2,
ρ cos r2/2R2 cos a2Σ1-a3Σ0+sin a tan a/2R,
C20=sin a tan a2/2R2,
S20=sin a tan a1+2 tan a2/4R3,
S30=sin a tan a1-tan a2/8R3.
C2=ρΣ2 cos r2/2R3 cos a2,
S2=Eρ2/2R5 cos a3+ρ sin r3/4R4 cos a25 tan a-tan r1+2 cos r2+ρ cos r5 sina-r+4 cos a sin r3σ2/4R4 cos a3+ρ cos r2/2R4 cos a2σ22 cos r+σ3,
S3=Eρ2/8R5 cos a5+ρ sin r3/8R4 cos a4tan r-2 sin a cos a+ρ cos r2tan r-sin a cos aσ2/4R4 cos a4+ρ cos r3/8R4 cos a4σ22-σ3 cos r,
E=sin r6+2 sin r3 cos r2σ2+cos r4σ22.
C2D=Σ2/2ρ2.
C2=C2Dρ3 cos r2/R3 cos a2.
C2j=Ajρj,
S2j=Bjρj+Cjρj2,
S3j=Djρj+Ejρj2.
C2G=kλ/λGC21-C22,
S2G=kλ/λGS21-S22,
S3G=kλ/λGS31-S32.
C2N=-1/2R2sin i tan i2+sin rC tan rC2+kλC/λGsin α tan α2-sin β tan β2,
S2N=-1/4R3sin i tan i1+2 tan i2+sin rS2 tan rS21+2 tan rS22+kλS2/λGsin α tan α1+2 tan α2-sin β tan β(1+2 tan β2,
S3N=-1/8R3sin i tan i1-tan i2+sin rS3 tan rS31-tan rS32+kλS3/λGsin α tan α1-tan α2-sin β tan β(1-tan β2,
sin i+sin rC=knλC,
sin i+sin rS2=knλS2,
sin i+sin rS3=knλS3.
kλC/λGC21-C22=C2N,
kλS2/λGS21-S22=S2N,
kλS3/λGS31-S32=S3N.
R=1750 mm,  n=4600 grooves/mm, λG=3336 Å,  α=-45.862°, β=54.775°,  i=18.225°,  k=1. Spectral range: 9101030 Å. Elliptical pupil of 170×135 mm. Needed resolution λ/dλ: 30,000.
α=-45.872°,  β=54.763°,  i=18.235°.

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