Abstract

We present the theory of spherical holographic gratings recorded by use of a deformable plane mirror and consider its application to the optimized Rowland Mounting. We illustrate the efficiency of such a mounting by computing two high-resolution gratings (3800 grooves/mm) with f/24 and f/10 apertures.

© 1998 Optical Society of America

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References

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  1. 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]
  2. M. Duban, K. Dohlen, G. R. Lemaitre, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the COS gratings of HST,” Appl. Opt. (to be published).
  3. J. Green, “The Cosmic Origin Spectrograph,” Report P 97-752, 1, (Center for Astrophysics and Space Astronomy, Colorado University, Boulder, Colo., 1997).
  4. M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
    [CrossRef] [PubMed]
  5. M. Duban, “Comparison of grating designs for the Lyman Far-Ultraviolet Spectroscopic Explorer spectrograph,” Appl. Opt. 32, 4253–4264 (1993).
    [CrossRef] [PubMed]
  6. M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
    [CrossRef] [PubMed]

1998 (1)

1993 (1)

1991 (1)

1987 (1)

Dohlen, K.

M. Duban, K. Dohlen, G. R. Lemaitre, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the COS gratings of HST,” Appl. Opt. (to be published).

Duban, M.

Green, J.

J. Green, “The Cosmic Origin Spectrograph,” Report P 97-752, 1, (Center for Astrophysics and Space Astronomy, Colorado University, Boulder, Colo., 1997).

Lemai^tre, G. R.

Lemaitre, G. R.

M. Duban, K. Dohlen, G. R. Lemaitre, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the COS gratings of HST,” Appl. Opt. (to be published).

Malina, R. F.

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Figures (4)

Fig. 1
Fig. 1

Geometry of the recording setup.

Fig. 2
Fig. 2

Determination of the point M on the mirror corresponding to a given point P on the grating.

Fig. 3
Fig. 3

Spot diagrams obtained at 1150, 1194.4, 1300, 1405.9, and 1449 Å with an f/10 aperture.

Fig. 4
Fig. 4

Spot diagrams obtained at 1150, 1194.4, 1300, 1405.9, and 1449 Å with an f/24 aperture.

Tables (2)

Tables Icon

Table 1 Overall Image Dimensions and Effective Resolvant Width for f/10 Gratings (micrometers)

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Table 2 Overall Image Dimensions and Effective Resolvant Width for f/24 Gratings (micrometers)

Equations (31)

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X = K C 1 Y 3 + K C 2 YZ 2 + K S 1 Y 4 + K S 2 Y 2 Z 2 + K S 3 Z 4 ,
x = y 2 + z 2 / 2 R + y 4 + z 4 / 8 R 3 + y 2 z 2 / 4 R 3 .
Δ y ,   z = LM + MP - L Ω + Ω O ,
LM + MP / Y = 0 ,
LM + MP / Z = 0 .
Y = a 1 y + a 2 y 2 + a 3 z 2 + a 4 y 3 + a 5 yz 2 + a 6 y 4 + a 7 y 2 z 2 + a 8 z 4 ,
Z = b 1 y + b 2 z + b 3 y 2 + b 4 yz + b 5 y 3 + b 6 y 2 z + b 7 z 3 + b 8 y 4 + b 9 y 3 z + b 10 yz 3 .
Ty 3 = 2 K C 1 d 3 cos   u 3 / r 3 cos   i 2 ,
Tyz 2 = 2 K C 2 d 3   cos   u / r 3 ,
Ty 4 = 2 d 3 9 K C 1 2 d 2 cos   u 4 d - r + K C 1 r cos   u 3   cos   i 3   sin   u   cos   i + 2   cos   u   sin   i - 3 r   tan   u   cos   i / 2 R - K S 1 rd cos   u 4   cos   i / r 5 cos   i 4 ,
Ty 2 z 2 = d 3 8 K C 2 2 Rd 2 cos   u 2 cos   i 2 d - r + 12 K C 1 K C 2 Rd 2 cos   u 2 d - r - 3 K C 1 r 2   sin   u cos   u 2 + K C 2 r   cos   i 6 R   sin   u   cos   u   cos   i - r   sin   u   cos   i + 4 R cos   u 2   sin   i - 2 K S 2 Rrd cos   u 2   cos   i / Rr 5 cos   i 2 ,
Tz 4 = d 3 2 K C 2 2 Rd 2 d - r - K C 2 r 2   sin   u - 2 K S 3 Rrd   cos   i / Rr 5 ,
K C 1 = C 1 N R 3 cos   i 2 / 2 d 3 ,
K C 2 = C 2 N R 3 cos   u 2 / 2 d 3 ,
K S 1 = - S 1 N R 4 cos   i 3 / 2 d 4 + K C 1   cos   i 3   tan   u + 4   tan   i / 2 d + 9 K C 1 2 E / cos   i ,
K S 2 = - S 2 N R 4 cos   u 2   cos   i / 2 d 4 - K C 1 3   sin   u   cos   u / 2 d   cos   i + K C 2   cos   i 5   tan   u + 4   tan   i / 2 d + K C 1 K C 2 6 E / cos   i + K C 2 2 4 E   cos   i ,
K S 3 = - S 3 N R 4 cos   u 4 / 2 d 4   cos   i - K C 2 sin   u   cos   u / 2 d   cos   i + K C 2 2 E / cos   i ,
E = d d / R   cos   u - 1 .
A 31 = 3 K C 1 + K C 2 / 4 ,
A 33 = K C 1 - K C 2 / 4 ,
A 40 = 3 K S 1 + K S 2 + 3 K S 3 / 8 ,
A 42 = K S 1 - K S 2 / 2 ,
A 44 = K S 1 - K S 2 + K S 3 / 8 .
K S 1 = 7 K S 1 + K S 2 - K S 3 / 8 ,
K S 2 = 3 K S 1 + K S 2 + 3 K S 3 / 4 ,
K S 3 = - K S 1 + K S 2 + 7 K S 3 / 4 .
α = - 36.031   deg ,     β = 48.242   deg , λ 0 recording   laser = 3511   Å .
I = 20.177   deg ,     λ   min = 1150   Å , P 1 = 1194.4   Å ,     λ   med = 1295.5   Å , P 2 = 1405.9   Å ,     λ   max = 1449   Å ,
C 2 N = 2.028 × 10 - 7 ,     S 2 N = 8.558 × 10 - 11 , S 3 N = - 2.137 × 10 - 11 .
K C 2 = 2.246 × 10 - 7 ,     K S 2 = - 2.746 × 10 - 10 , K S 3 = 7.161 × 10 - 11 ,
A 31 = - A 33 = 5.615 × 10 - 8 ,     A 40 = - 7.47 × 10 - 12 , A 42 = - 3.58 × 10 - 11 ,     A 44 = 4.327 × 10 - 11 .

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