Abstract

Holographic gratings using aspheric blanks and/or aberrated laser recording sources are most often required to achieve high spectral resolution over a large spectral range. We propose a configuration derived from the optimized holographic Rowland mounting, where the grating is recorded by the interference of two aberrated wave fronts diffracted from concave holographic gratings. These two auxiliary gratings are recorded with laser point sources, and the three blanks are spherical, which is well suited to the severe far-UV constraints on shape and polishing. In addition to the correction of astigmatism, coma C1, and spherical aberration S1 given by the optimized Rowland mounting, this mounting cancels, at least at one point of the spectrum, coma C2 and spherical aberrations S2 and S3.

© 1991 Optical Society of America

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References

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  1. M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
    [CrossRef] [PubMed]
  2. M. Duban, “Calcul et réalisation de spectrographes à réseaux holographiques asphériques destins à 1'astronomie spatiale,” Thèse (Laboratoire d'Astronomie Spatiale du Centre National de la Recherche Scientifique, Marseille, France, 1988).
  3. B. Brown, I. Wilson, “Holographic grating aberration correction for a Rowland circle mount,” Opt. Acta 28, 1587–1599, 1601–1610 (1981).
    [CrossRef]
  4. M. Duban, “Les réseaux holographiques asphériques enregistrés avec des ondes laser aberrantes: un outil efficace pour la haute résolution spectrale,” J. Opt. 20, 269–279 (1989).
    [CrossRef]
  5. H. Noda, Y. Harada, M. Koike, “Holographic grating recorded using aspheric wavefronts for a Seya-Namioka monochromator,” Appl. Opt. 28, 4375–4380 (1989).
    [CrossRef] [PubMed]
  6. C. Palmer, “Theory of second-generation holographic diffraction gratings,” J. Opt. Soc. Am. A 6, 1175–1188 (1989).
    [CrossRef]
  7. R. Grange, M. Laget, “Second-generation holography applied to a high resolution concave grating spectrograph,” submitted to Appl. Opt.
  8. M. Duban, “Some reflections about a high resolution spectrograph,” Appl. Opt. (to be published).

1989 (3)

1987 (1)

1981 (1)

B. Brown, I. Wilson, “Holographic grating aberration correction for a Rowland circle mount,” Opt. Acta 28, 1587–1599, 1601–1610 (1981).
[CrossRef]

Brown, B.

B. Brown, I. Wilson, “Holographic grating aberration correction for a Rowland circle mount,” Opt. Acta 28, 1587–1599, 1601–1610 (1981).
[CrossRef]

Duban, M.

M. Duban, “Les réseaux holographiques asphériques enregistrés avec des ondes laser aberrantes: un outil efficace pour la haute résolution spectrale,” J. Opt. 20, 269–279 (1989).
[CrossRef]

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

M. Duban, “Calcul et réalisation de spectrographes à réseaux holographiques asphériques destins à 1'astronomie spatiale,” Thèse (Laboratoire d'Astronomie Spatiale du Centre National de la Recherche Scientifique, Marseille, France, 1988).

M. Duban, “Some reflections about a high resolution spectrograph,” Appl. Opt. (to be published).

Grange, R.

R. Grange, M. Laget, “Second-generation holography applied to a high resolution concave grating spectrograph,” submitted to Appl. Opt.

Harada, Y.

Koike, M.

Laget, M.

R. Grange, M. Laget, “Second-generation holography applied to a high resolution concave grating spectrograph,” submitted to Appl. Opt.

Noda, H.

Palmer, C.

Wilson, I.

B. Brown, I. Wilson, “Holographic grating aberration correction for a Rowland circle mount,” Opt. Acta 28, 1587–1599, 1601–1610 (1981).
[CrossRef]

Appl. Opt. (2)

J. Opt. (1)

M. Duban, “Les réseaux holographiques asphériques enregistrés avec des ondes laser aberrantes: un outil efficace pour la haute résolution spectrale,” J. Opt. 20, 269–279 (1989).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

B. Brown, I. Wilson, “Holographic grating aberration correction for a Rowland circle mount,” Opt. Acta 28, 1587–1599, 1601–1610 (1981).
[CrossRef]

Other (3)

M. Duban, “Calcul et réalisation de spectrographes à réseaux holographiques asphériques destins à 1'astronomie spatiale,” Thèse (Laboratoire d'Astronomie Spatiale du Centre National de la Recherche Scientifique, Marseille, France, 1988).

R. Grange, M. Laget, “Second-generation holography applied to a high resolution concave grating spectrograph,” submitted to Appl. Opt.

M. Duban, “Some reflections about a high resolution spectrograph,” Appl. Opt. (to be published).

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Figures (13)

Fig. 1
Fig. 1

Geometry of tho aberrations on focus F.

Fig. 2
Fig. 2

Geometryof the Rowland mounting.

Fig. 3
Fig. 3

Determination of the laser ray mM that crosses G at a given point M.

Fig. 4
Fig. 4

Astigmatism a2 and spherical aberration s1 given by G: (a) basic configuration and (b) modified configuration.

Fig. 5
Fig. 5

Coma c2 and spherical aberrations s2 and s3 given by G when using recording sources: (a) punctual and (b) aberrated.

Fig. 6
Fig. 6

Image boundaries given by G with punctual recording sources.

Fig. 7
Fig. 7

Spot diagrams given by G with aberrated recording sources.

Fig. 8
Fig. 8

Spot diagrams given by G when recorded using g: (a) full aperture and (b) half-pupil.

Fig. 9
Fig. 9

Schematic view of the mounting using two auxiliary gratings g1 and g2.

Fig. 10
Fig. 10

Images of L1 and L2 given by (a) g1, and (b) g2.

Fig. 11
Fig. 11

Spot diagrams given by modified G with theoretical aberrated laser sources.

Fig. 12
Fig. 12

Spot diagrams actually given by G when recorded with g1 and g2.

Fig. 13
Fig. 13

Half-image boundaries given by G with a 50-mm pupil.

Equations (41)

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sin β sin α = n λ 0 ,
sin i + sin r = k λ n .
Δ = ( M S O S ) + ( M S O S ) + ( k λ / λ 0 ) [ ( M C O C ) ( M D O D ) ] ,
Δ = D ( S ) + D ( S ) + ( k λ / λ 0 ) [ D ( C ) D ( D ) ] ,
Δ = [ D ( Q ) ] ,
Δ = a 1 y 2 + a 2 z 2 + c 1 y 3 + c 2 y z 2 + s 1 y 4 + s 2 y 2 z 2 + s 3 z 4 + ,
Δ = A 1 Y 2 + A 2 Z 2 + C 1 Y 3 + C 2 Y Z 2 + S 1 Y 4 + S 2 Y 2 Z 2 + S 3 Z 4 + .
[ q / 2 d ] = 0 ,
( 1 R ρ cos 2 i ) / R cos i + ( 1 R ρ cos 2 r ) / R cos r = 0 ,
ρ = R cos i cos r .
[ sin u tan u ] = 0 .
[ s t ] = 0 .
[ s t ] = sin i tan i + sin r tan r + ( sin i + sin r ) ( sin β sin α ) × ( sin α tan α sin β tan β ) .
sin r tan r + A sin r + B = 0 ,
s 1 = [ s t ] / 8 R 3 .
c 2 = [ s t 2 ] / 2 R 2 .
s 2 = [ s t ( 1 + 2 t 2 ) ] / 4 R 3 , s 3 = [ s t ( 1 t 2 ) ] / 8 R 3 .
s 2 = [ s t 3 ] / 2 R 3 , s 3 = [ s t 3 ] / 8 R 3 .
Δ = y 2 ( A 1 cos 2 u ) + z 2 ( A 2 ) + y 3 ( C 1 cos 3 u ) + y z 2 ( C 2 cos u ) + y 4 ( S 1 cos 4 u ) + y 2 z 2 ( 5 C 2 sin u / 2 R + S 2 cos 2 u ) + z 4 ( C 2 sin u / 2 R + S 3 ) .
C 2 = c 2 / cos r , S 2 = ( s 2 5 c 2 sin r / 2 R cos r ) / cos 2 r , S 3 = s 2 / 4 + c 2 sin r / 2 R cos r .
C 2 * = c 2 R 3 cos 2 r , S 2 * = ( 5 c 2 tan r / 2 R s 2 ) R 4 cos 2 r , S 3 * = ( s 2 / 4 c 2 tan r / 2 R ) R 4 cos 4 r .
C 2 * = R cos 2 r [ s t 2 ] / 2 , S 2 * = R cos 2 r ( 5 tan r [ s t 2 ] / 2 [ s t 3 ] ) / 2 , S 3 * = R cos 4 r ( [ s t 3 ] / 2 tan r [ s t 2 ] ) / 4 .
[ s t ] = 0 ,
R = 2 C 2 * / cos 2 r [ s t 2 ] ,
[ s t 3 ] / [ s t 2 ] 5 tan r / 2 = S 2 * / C 2 * ,
cos 2 r ( tan r [ s t 3 ] / 2 [ s t 2 ] ) / 2 = S 3 * / C 2 *
( 8 S 3 * ) T 2 + C 2 * T + ( 8 S 3 * + 2 S 2 * ) = 0 ,
( C 2 * ) 2 > 64 S 3 * ( 4 S 3 * + S 2 * ) ,
K = [ s t 3 ] / [ s t 2 ] ,
K ( r ) = 5 T / 2 + S 2 * / C 2 * .
sin i = k λ G λ g ( sin β sin α ) sin r
R = 1750 mm , n = 4600 grooves / mm , λ G = 3336 Å α = 45.862 ° , β = 54.775 ° , i = 18.225 ° , k = 1 ,
on only C : 965.513 , 3121.979 , 318.211 ;
on only D : 662.24 , 1909.582 , 119.797.
r 1 = 45.86 ° , k positive , R 62 73 m , r 2 = 54.65 ° , k negative , R 66 78 m .
r 2 = 54.778 ° , k positive , R 11 13 m , inconvenient , r 1 = 64.615 ° , R = 3481.5 mm for k = 3 , λ g = 4879.9 Å .
α = 71.107 ° , β = 1.912 ° , i = 75.568 , n = 1870.4 grooves / mm .
aberrations ( C 2 * , S 2 * , S 3 * ) on C : 420 , 530 , 134 ;
aberrations on D : 373.88 , 509.88 , 65.6 .
grating k α β i r R ( mm ) n ( g / mm ) g 1 + 3 5.022 38.443 49.131 19.838 3765.04 1094.7 g 2 3 60.918 1.8 66.348 54.279 3977.8 1726.5
α = 45.872 ° , β = 54.763 ° , i = 18.235 ° .

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