Abstract

For holographic gratings requiring an extreme dispersion, I consider a modified Rowland mounting, in which the recording laser sources are moved away from the grating, to reduce the uncorrected higher-order aberrations. In addition, I choose the geometric parameters such that first-type coma is corrected. Then a plane multimode deformable mirror (MDM) or two auxiliary spherical holographic gratings (R3 device) are used to aberrate the grating’s recording sources; correction up to the fourth order is sufficient to obtain high image quality. Applied to the FUSE–Lyman (FUSE is Far Ultraviolet Spectroscopic Explorer) grating, with a groove density as high as 5767 grooves/mm, these recording devices produce a resolution (chromatic resolving power) as great as 611,000 with the MDM and 3,030,000 with the R3 device. These results far exceed the specified performance of 30,000. Since diffraction limits the resolution to 482,000, the images are diffraction limited with both devices.

© 2001 Optical Society of America

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References

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  1. M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
    [CrossRef]
  2. G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373 (1995).
  3. M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
    [CrossRef] [PubMed]
  4. M. Duban, “Third-generation holographic Rowland mounting: fourth-order theory,” Appl. Opt. 38, 3443–3449 (1999).
    [CrossRef]
  5. 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]
  6. G. Lemaı̂tre, M. Duban, “A general method of holographic grating recording with a null-powered multimode deformable mirror,” Astron. Astrophys. 339, L89–L93 (1998).
  7. M. Duban, “Theory and computation of three Cosmic Origin Spectrograph aspheric gratings recorded with a multimode deformable mirror,” Appl. Opt. 38, 1096–1102 (1999).
    [CrossRef]
  8. M. Duban, “Recording high-dispersion spherical holographic gratings in a modified Rowland mounting by use of a multimode deformable mirror,” Appl. Opt. 39, 16–19 (2000).
    [CrossRef]
  9. See the following URL: http://violet.pha.jhu.edu/papers/papers.html .
  10. M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
    [CrossRef] [PubMed]
  11. R. Grange, “Aberration-reduced holographic spherical gratings for Rowland circle spectrographs,” Appl. Opt. 31, 3744–3749 (1992).
    [CrossRef] [PubMed]
  12. 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]

2000 (1)

1999 (2)

1998 (3)

1995 (1)

G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373 (1995).

1993 (1)

1992 (1)

1991 (1)

1987 (1)

Dohlen, K.

Duban, M.

Grange, R.

Lemai^tre, G.

G. Lemaı̂tre, M. Duban, “A general method of holographic grating recording with a null-powered multimode deformable mirror,” Astron. Astrophys. 339, L89–L93 (1998).

Lemai^tre, G. R.

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]

G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373 (1995).

Wang, M.

G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373 (1995).

Appl. Opt. (9)

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

M. Duban, “Third-generation holographic Rowland mounting: fourth-order theory,” Appl. Opt. 38, 3443–3449 (1999).
[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]

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

M. Duban, “Theory and computation of three Cosmic Origin Spectrograph aspheric gratings recorded with a multimode deformable mirror,” Appl. Opt. 38, 1096–1102 (1999).
[CrossRef]

M. Duban, “Recording high-dispersion spherical holographic gratings in a modified Rowland mounting by use of a multimode deformable mirror,” Appl. Opt. 39, 16–19 (2000).
[CrossRef]

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

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

Astron. Astrophys. (1)

G. Lemaı̂tre, M. Duban, “A general method of holographic grating recording with a null-powered multimode deformable mirror,” Astron. Astrophys. 339, L89–L93 (1998).

Astron. Astrophys. Suppl. Ser. (1)

G. R. Lemaı̂tre, M. Wang, “Active mirrors warped using Zernike polynomials for correcting off-axis aberrations of fixed primary mirrors. I. Theory and elasticity design,” Astron. Astrophys. Suppl. Ser. 114, 373 (1995).

Other (1)

See the following URL: http://violet.pha.jhu.edu/papers/papers.html .

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Figures (11)

Fig. 1
Fig. 1

Geometry of the grating G in Rowland mounting (recording laser sources C 0 and D 0) and in first-type modified Rowland mounting (sources C and D). The source S to be analyzed and the spectrum remain unchanged on the Rowland circle. We set OC = H 1, OD = H 2.

Fig. 2
Fig. 2

Spot diagrams computed for the FUSE–Lyman grating G at λ = 91, 92.9, 94, 97, 100, 101.1, and 103 nm (isotropic scales, step 20 µm). (a) Initial mounting (only coma C1 is corrected). With theoretical supplementary corrections: (b) C2 corrected; (c) C2, S2, S3 corrected; (d) C2, S1, S2, S3 corrected.

Fig. 3
Fig. 3

Global (dashed curves) and effective (solid curves) resolution λ/Δλ versus λ, for the FUSE–Lyman grating with partial corrections. (a) Initial mounting (only C1 is corrected); (b) C1, C2, S2, S3 corrected by a R3 device, with auxiliary gratings in Rowland mounting. A resolution of [30] was required.

Fig. 4
Fig. 4

Global (dashed curves) and effective (solid curves) resolution λ/Δλ versus λ, for the FUSE–Lyman grating with complete corrections: (a) theoretical, (b) by MDM, (c) by R3 with second-type modified Rowland auxiliary gratings, (d) by compact R3 devices (with the same unities for the four diagrams).

Fig. 5
Fig. 5

Working and recording setup of the grating G recorded with a MDM. L 1 and L 2 are the laser sources. We have schematically introduced an auxiliary concave spherical mirror to produce the virtual source C. S is the source to be analysed; RC, the Rowland circle; C and D, the recording sources of G. (The dimensions of the optical components are exaggereted.)

Fig. 6
Fig. 6

Interferogramm at λHe–Ne = 632.8 nm, showing the computed shape of the MDM with a 60-mm diameter. The maximum deformations are -4.75 and +1.6 µm.

Fig. 7
Fig. 7

Spot diagrams computed with the grating G completely corrected by (a) a MDM (b) a R3 device with second-type modified Rowland auxiliary gratings (isotropic scales, step 20 µm).

Fig. 8
Fig. 8

Geometry of the main grating G aberrated by an auxiliary grating g, at an arbitrary point M of G, corresponding to the point m on g (schematic view: generally, m and M do not lie in the OXY plane). L is the laser source; c and d, the recording sources of g; RC(g), its Rowland circle; L′ the aberrated image of L given by g; D, the recording source of G here considered. (L′ is set on D).

Fig. 9
Fig. 9

Recording setup of the main grating G recorded with two auxiliary gratings g 1 and g 2 in Rowland mounting. L 1, L 2 are the two laser sources; c i , d i , the recording sources of g i ; RC, the Rowland circles; C and D, the recording sources of G. (The dimensions of the gratings are exaggerated.)

Fig. 10
Fig. 10

Recording setup of the grating G recorded with two auxiliary gratings g 1 and g 2 in second-type modified Rowland mounting (same conventions as in Fig. 9).

Fig. 11
Fig. 11

Compact recording setup of the grating G recorded with two auxiliary gratings g 1 and g 2 in second-type modified Rowland mounting (same conventions as in Fig. 9). g 2 gives a virtual image L 2′ of the laser source L 2. C is 4535.54 mm distant from G; D is 3040.88 mm distant from g 2.

Tables (3)

Tables Icon

Table 1 Parameters of the Auxiliary Gratings in a Rowland Mountinga

Tables Icon

Table 2 Parameters of the Auxiliary Gratings in a Second-Type Modified Rowland Mountinga

Tables Icon

Table 3 Parameters of the Auxiliary Gratings in a Compact Second-Type Modified Rowland Mountinga

Equations (60)

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H1=N/P sin2 βG-Q cos2 βG,
H2=N/P sin2 αG-Q cos2 αG,
N=Rcos2 αG-cos2 βG,
P=cos αG-cos βG,
Q=sin α0 tan α0-sin β0 tan β0.
sin βG-sin αG=sin β0-sin α0=nGλG
R=1750 mm; nG=5764 grooves/mm; λG=333.6 nm; working order, kG=1; spectral range, 91103 nm; elliptical pupil of 170×135 mm; needed resolution, 30,000.
R=1631.3 mm, nG=5767 grooves/mm, and an elliptical pupil of 204 mm×187 mm,
sin αG cos αGcos αG-H1/R/H12=sin βG cos βGcos βG-H2/R/H22,
αG=-75.8344,  βG=72.6073°, H1=-4535.542, H2=4463.876 mm.
C2N=4.832×10-9,  S1N=1.47×10-12, S2N=5.755×10-12,  S3N=8.036×10-13.
imir=30°,  dm=1400 mm,
A31=6.55×10-8,  A33=-A31, A40=-2.937×10-9,  A42=-2.887×10-9,A44=-3.558×10-10.
sin β-sin α=nλg,
sin i+sin r=knλG,
TY, Z=Lm+mM+Kcm-dm
T0=Lo+oO+Kco-do,
X=Y2+Z2/2R+Y4+Z4/8R3+Y2Z2/4R3+,
y=a1Y+a2Y2+a3Z2,
z=b1Z+b2YZ.
T/y=0,  T/z=0.
C2=Σ2ρ cos a cos r2/2H3+sin a1/H-cos a/R/2H,
S2=Σ3ρ cos a2 cos r2/2H4+Σ22ρ cos a2 cos r3H+ρ cos r/2H5+Σ2ρ cos a cos r2cos a6 tan a-5 tan r/H-tan a/R/4H3+3 sin a2-1/4H3+cos a3 cos a2-1/4RH2+sin a2/4R2H-cos a/4R3,
S3=-Σ3ρ cos r4/8H4+Σ22ρ cos r3H+ρ cos r/8H5+Σ2ρ cos r2sin r cos r/H-sin a/R/4H3-1/8H3+cos a/4RH2+sin a2/8R2H-cos a/8R3,
Σj=sin i tan ij+sin r tan rj+Ksin α tan αj-sin β tan βj j=13.
C20=U sin a/2H2,
S10=UV+6 sin a2-5 sin a4/8H3,
S20=UV+3 sin a2/4H3,
S30=UV/8H3,
U=1-H cos a/R,
V=H2/R2-U.
KC2-C20g1-C2-C20g2=C2N
cos i2/p+cos r2/q=cos i+cos r/ρ,
sin i cos icos i-p/ρ/p2+sin r cos rcos r-q/ρ/q2=0,
p=ρE/sin r,  q=ρE/sin i,
where E=sin i cos r2+sin r cos i2/cos i+cos r.
Ksin α tan α-sin β tan β=-sin i sin rcos i+cos r/1-sin i sin r.
a1=q cos a/H cos r,  b1=-q/H
na2=E1sina-r-3E2 cos r/2F2+sin a cos a/R+a13E1-cos asin r/ρ/2F+3a12E3 sin i cos i/2p, da2=cos i2/p+cos r2/F-cos i+cos r/ρ,
a3=E5 cos r/2F-sin r1-b12/2F2-b1E6/2/da2,
b2=E21-b1/F2+b1E1 sin r/ρF-a1E6/Σ1-cos i-cos r/ρ+1/F+1/p,
F=Oo=H+q, Σj=Ksin α tan αj-sin β tan βj
E1=cos a+a1 cos r, E2=sin a+a1 sin r, E3=1/ρ-cos i/p, E4=1/p-cos i/ρ, E5=sin a/R+b12 sin r/ρ, E6=b1E4 sin i/p+Σ2/ρ2, E7=a1a3+b1b2, E8=1-2 tan a tan r,  E9=tan a+tan r, E10=a32+b14/4ρ2/2ρ, E11=a22+a14/4ρ2/2ρ, E12=b12E4-2a3 sin i, E13=pa12E4-2a2 sin i.
T1C2=-a1a3E3 cos i+b1E4b2+a1b1 sin i/2p,
T1S1=-E11 cos i+cos i2a12 tan i/2ρ-a22-2a12a2 tan i/ρ/2p+a12 cos i3a2 sin i cos i+a121-3 sin i2/2ρ/2p2+a14 cos i25 sin i2-1/8p3,
T1S2=E123 a12 sin i2-E13/4p2+E4b22/2+a1b12/4ρ2+a2a3+a1E7 sin i/p,
T1S3=-E122/8p+ρE4E10.
T2C2=-E7 cos r/ρ+E7-b2+a3E1 cos r-a1-E1E5/2/F+E21-b12/2F2,
T2S1=-cos a/8R3-E11 cos r+sin asin a/4R+a12 sin r/2ρ-a2 cos r/R+a14 sin r2/4ρ2+a1a2 sin rcos a-3E1/ρ+a22 cos r2/2F+a2E13 E1 sin r/2+sina-r+a12E13E1 cos r-2 cosa-r-2a1/4ρ+E1E1 cos a-2E2 sin a/4R/F2+E128E2 sin a-2E1 cos a+1-5 sin a2-a121-5 sin r2/8F3,
T2S2=-cos a/4R3-a12b12 cos r/4ρ3-cos rb22/2+a2a3/ρ+a2a3 cos r2+b22/2-a2+a3sin a cos r/2R+sin a2/4R2+sin ra12E5+b12sin a/R-4E1E7-2 cos ra2b12+a3a12/4ρ/F+b2E2b1-1+a3E1 sin a cos r+sin ra2+a3 cos a2+a2b1b1-2+a1a3 cos r3E1+cos a/2+cos aa1a1E8 cos r2+2 cos a cos r1-E9 tan a+1-b12+1-3 sin a2/4R+cos ra121-2b1+b12{a1a13 cos r2-1+2 cos a cos r1-E9 tan r+E8 cos a2)/4ρ/F2+1-b12a123 sin r2-1-2a1E8 cos a cos r+3 sin a2-1/4F3,
T2S3=-cos a/8R3-E10 cos r+E5-2a3 cos r2/8F+1-b12cos a/R+b12 cos r/ρ+2a3 sin r/4F2-1-b14/8F3,
T3C2=b1a1b1Σ2+2ρb2Σ1/2ρ2,
T3S1=a14Σ1/8ρ3,
T3S2=Σ1ρb22+a12b12/2ρ+Σ2b12a1b2+a2b1+Σ3a12b12/ρ/2ρ,
T3S3=b12b12Σ1-Σ3/ρ+4a3Σ2/8ρ2.
C2S=q3 cos a/2H3 cos rsin i1-p cos i/ρ/p2+sin r1-q cos r/ρ/q2+Σ2/ρ2.
KC2Sg1-C2Sg2=C2N,
KS1-S10g1-S1-S10g2=S1N,
KS2-S20g1-S2-S20g2=S2N,
dS3=KS3-S30g1-S3-S30g2-S3N/S3N

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