Abstract

The theory of three Cosmic Origin Spectrograph holographic gratings recorded with a deformable plane mirror is presented. Their working conditions are severe, since they have to correct the strong spherical aberration and the field astigmatism of the Hubble Space Telescope. Recorded on aspherized substrates, the gratings produce images that are diffraction limited with regard to spectral resolution.

© 1999 Optical Society of America

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References

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  1. J. C. Green, “HST Cosmic Origins Spectrograph: replacement instrument for the 2002 reservicing mission,” in Space Telescope and Instruments V, P. Y. Bely, B. Breckinridge, eds., Proc. SPIE3356, 265–270 (1998).
    [CrossRef]
  2. J. A. Morse, J. C. Green, “Performance and science goals of the Cosmic Origins Spectrograph for HST,” in Space Telescope and Instruments V, P. Y. Bely, B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
    [CrossRef]
  3. J. C. Green, “The Cosmic Origin Spectrograph,” (Colorado University, Boulder, Colo., 1997), pp. 97–752.
  4. 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.
  5. G. R. Lemaı̂tre, M. Wang, “Active mirrors warpedusing Clebsch–Zernike polynomials for correcting off-axisaberrations,” Astron. Astrophys. Suppl. Ser. 114, 373–378 (1995).
  6. 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]
  7. M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
    [CrossRef] [PubMed]
  8. M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
    [CrossRef] [PubMed]
  9. M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213.

1998 (1)

1995 (1)

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

1991 (1)

1987 (1)

Dohlen, K.

Duban, M.

Green, J. C.

J. A. Morse, J. C. Green, “Performance and science goals of the Cosmic Origins Spectrograph for HST,” in Space Telescope and Instruments V, P. Y. Bely, B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

J. C. Green, “HST Cosmic Origins Spectrograph: replacement instrument for the 2002 reservicing mission,” in Space Telescope and Instruments V, P. Y. Bely, B. Breckinridge, eds., Proc. SPIE3356, 265–270 (1998).
[CrossRef]

J. C. Green, “The Cosmic Origin Spectrograph,” (Colorado University, Boulder, Colo., 1997), pp. 97–752.

Lemai^tre, G. R.

Malina, R. F.

Morse, J. A.

J. A. Morse, J. C. Green, “Performance and science goals of the Cosmic Origins Spectrograph for HST,” in Space Telescope and Instruments V, P. Y. Bely, B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

Wang, M.

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

Appl. Opt. (5)

Astron. Astrophys. Suppl. Ser. (1)

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

Other (3)

J. C. Green, “HST Cosmic Origins Spectrograph: replacement instrument for the 2002 reservicing mission,” in Space Telescope and Instruments V, P. Y. Bely, B. Breckinridge, eds., Proc. SPIE3356, 265–270 (1998).
[CrossRef]

J. A. Morse, J. C. Green, “Performance and science goals of the Cosmic Origins Spectrograph for HST,” in Space Telescope and Instruments V, P. Y. Bely, B. Breckinridge, eds., Proc. SPIE3356, 361–368 (1998).
[CrossRef]

J. C. Green, “The Cosmic Origin Spectrograph,” (Colorado University, Boulder, Colo., 1997), pp. 97–752.

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Figures (5)

Fig. 1
Fig. 1

Geometry of the HST with a grating working on the telescope’s axis.

Fig. 2
Fig. 2

Any spherical aberration cancelled at λ m [curve (1)], shifted and optimized [curve (2)], and its holographic complementary correction [line (3)] versus λ.

Fig. 3
Fig. 3

Coordinate value y of image points plotted against pupil coordinate Y (when Z = 0) at λmin, λmed, and λmax, and image width versus λ compared with Airy disk radius and diameter (horizontal dotted lines). (a) Unoptimized parameters; (b) a, d, c 1, and s 1 optimized; (c) c 1 = 0, a, d, and s 1 optimized; (d) optimized parameters, off-axis image.

Fig. 4
Fig. 4

Geometry of the HST with a grating working off the telescope’s axis.

Fig. 5
Fig. 5

Spot diagrams given by grating 1 at λ = 1150, 1194.4 (p 1 point), 1200, 1250, 1300, 1350, 1400, 1405.9 (p 2 point), and 1449 Å. (a) On the HST axis, optimized parameters. (b) Off axis, unchanged parameters. (c) Astigmatism corrected. (d) All parameters optimized.

Tables (3)

Tables Icon

Table 1 Hubble Space Telescope Parameters

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Table 2 Spectral Data in (Å)

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Table 3 Grating Geometric Parameters

Equations (38)

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fj=cjρ2/1+1-1+kjcj2ρ21/2,
fj=cjρ2/2+cj31+kjρ4/8+cj51+kj2ρ6/16+.
F=2ER2-R1R2/2R1-R2-2E=6407.0084 mm.
x=y2+z2/2R+y4+z4/8R3+y2z2/4R3+.
p=a1y+a2y2+a3z2+a4y3+a5yz2+a6y4+a7y2z2+a8z4,
s=b1y+b2y2+b3z2+b4y3+b5yz2+b6y4+b7y2z2+b8z4.
T/p=0,  T/s=0.
ty4=G/8R4,  ty2z2=G/4R4 cos i2,  tz4=G/8R4 cos i4,
G=E/4K48mm2t2+2m+1+K316m2+16m-t1+K28m-3t1-3t1K-t1/1+K2m+14,
t1=1+k1,  t2=1+k2,  m=Ec2,  K=2Ec1-1.
G=199184 mm.
a1= st/2R,
c2= st2/2R2,
s1= st/8R3,  s2= st1+2t2/4R3,  s3= st1-t2/8R3,
sin β-sin α=Nλ0,
sin i+sin r=Nλ,
sin i tan i+sin r tan r+λ/λ0sin α tan α-sin β tan β=0.
i=20.1774 deg.
ty4=3.343×10-9,  ty2z2=7.589×10-9,  tz4=4.307×10-9.
s2M=-3.54×10-11,  s3M=8.93×10-12.
94, 214, and 122.
x=y2+z2/2R+1+ay4/8R3+1+by2z2/4R3+1+cz4/8R3+.
s1= st-a cos u/8R3,  s2= st1+2t2-b cos u/4R3,  s3= st1-t2-c cos u/8R3.
a=G/R+ st cos u,
b=G/R cos i2+ st1+2t2 cos u,
c=G/R cos i4+ st1-t2 cos u.
a=G/R+sin i tan i+sin r tan r+λa/λ0×sin α tan α - sin β tan β/cos i+cos r+λa/λ0cos α-cos β,
sin r=Nλa-sin i.
a=60.885,  b=68.817,  c=78.584,
a=59.9,  b=68.4,  c=77,
a=60.278,  b=68.428,  c=77.652.
x=y2+z2/2R+1+ay4/8R3+1+by2z2/4R3+1+cz4/8R3+1+dy6+31+ey4z2+31+fy2z4+1+gz6/16R5+.
a=60.144,  b=68.831,  c=77.518.
sin i tan i+sin r tan r+λ/λ0×sin α tan α - sin β tan β+δ/R cos i2=0.
a=60.06,  b=69.057,  c=78.054.
in+1=in+din,  βn+1=βn+dβn.
Vi=1/1+absdi3/di2,  Vβ=1/1+absdβ3/dβ2.
in+1=in+Vi din,  βn+1=βn+Vβ dβn.

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