Abstract

Aberration-corrected concave gratings with curved and variable spacing grooves are ruled with a numerically controlled ruling engine. In the design of aberration-corrected concave gratings, mechanical methods allow more freedom to choose the amount of space variation than do holographic methods. A highly efficient visible–UV monochromator and a coma-type aberration-reduced Seya-Namioka monochromator have been designed and fabricated using mechanically ruled aberration-corrected concave gratings. The gratings can be used with VUV monochromators and spectrographs with improved image focusing properties.

© 1980 Optical Society of America

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References

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  1. J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Newcastle-upon-Tyne, England, 1970), p. 117.
  2. H. Noda, T. Namioka, M. Seya, J. Opt. Soc. Am. 64, 1031 (1974).
    [CrossRef]
  3. F. Masuda, H. Noda, T. Namioka, J. Spectrosc. Soc. Jpn. 27, 311 (1978).
    [CrossRef]
  4. T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).
  5. T. Harada, S. Moriyama, T. Kita, Y. Kondo, J. Jpn. Soc. Precision Eng. 42, 888 (1976).
    [CrossRef]
  6. F. M. Gerasimov, E. A. Yakovlev, B. K. Koshlev, Opt. Spectrosc. 46, 665 (1979).
  7. G. W. Stroke, Handbuch der Pysik, Vol. 29 (Springer, Berlin, 1967), p. 664.
  8. T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).
    [CrossRef]
  9. T. Harada, T. Kita, in Extended Abstracts, Fifth International Conference on VUV Radiation Physics, Montpellier, 1977, Vol. 3, p. 58.
  10. H. Noda, T. Namioka, M. Seya, J. Opt. Soc. Am. 64, 1043 (1974).
    [CrossRef]
  11. R. Iwanaga, T. Oshio, J. Opt. Soc. Am. 69, 1538 (1979).
    [CrossRef]
  12. T. Kita, T. Harada, J. Spectrosc. Soc. Jpn. 29, 256 (1980).
    [CrossRef]

1980 (1)

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn. 29, 256 (1980).
[CrossRef]

1979 (2)

F. M. Gerasimov, E. A. Yakovlev, B. K. Koshlev, Opt. Spectrosc. 46, 665 (1979).

R. Iwanaga, T. Oshio, J. Opt. Soc. Am. 69, 1538 (1979).
[CrossRef]

1978 (1)

F. Masuda, H. Noda, T. Namioka, J. Spectrosc. Soc. Jpn. 27, 311 (1978).
[CrossRef]

1976 (1)

T. Harada, S. Moriyama, T. Kita, Y. Kondo, J. Jpn. Soc. Precision Eng. 42, 888 (1976).
[CrossRef]

1975 (1)

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

1974 (2)

1959 (1)

Cordelle, J.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Newcastle-upon-Tyne, England, 1970), p. 117.

Flamand, J.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Newcastle-upon-Tyne, England, 1970), p. 117.

Gerasimov, F. M.

F. M. Gerasimov, E. A. Yakovlev, B. K. Koshlev, Opt. Spectrosc. 46, 665 (1979).

Harada, T.

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn. 29, 256 (1980).
[CrossRef]

T. Harada, S. Moriyama, T. Kita, Y. Kondo, J. Jpn. Soc. Precision Eng. 42, 888 (1976).
[CrossRef]

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

T. Harada, T. Kita, in Extended Abstracts, Fifth International Conference on VUV Radiation Physics, Montpellier, 1977, Vol. 3, p. 58.

Iwanaga, R.

Kita, T.

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn. 29, 256 (1980).
[CrossRef]

T. Harada, S. Moriyama, T. Kita, Y. Kondo, J. Jpn. Soc. Precision Eng. 42, 888 (1976).
[CrossRef]

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

T. Harada, T. Kita, in Extended Abstracts, Fifth International Conference on VUV Radiation Physics, Montpellier, 1977, Vol. 3, p. 58.

Kondo, Y.

T. Harada, S. Moriyama, T. Kita, Y. Kondo, J. Jpn. Soc. Precision Eng. 42, 888 (1976).
[CrossRef]

Koshlev, B. K.

F. M. Gerasimov, E. A. Yakovlev, B. K. Koshlev, Opt. Spectrosc. 46, 665 (1979).

Labeyrie, A.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Newcastle-upon-Tyne, England, 1970), p. 117.

Masuda, F.

F. Masuda, H. Noda, T. Namioka, J. Spectrosc. Soc. Jpn. 27, 311 (1978).
[CrossRef]

Moriyama, S.

T. Harada, S. Moriyama, T. Kita, Y. Kondo, J. Jpn. Soc. Precision Eng. 42, 888 (1976).
[CrossRef]

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

Namioka, T.

Noda, H.

Oshio, T.

Pieuchard, G.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Newcastle-upon-Tyne, England, 1970), p. 117.

Seya, M.

Stroke, G. W.

G. W. Stroke, Handbuch der Pysik, Vol. 29 (Springer, Berlin, 1967), p. 664.

Yakovlev, E. A.

F. M. Gerasimov, E. A. Yakovlev, B. K. Koshlev, Opt. Spectrosc. 46, 665 (1979).

J. Jpn. Soc. Precision Eng. (1)

T. Harada, S. Moriyama, T. Kita, Y. Kondo, J. Jpn. Soc. Precision Eng. 42, 888 (1976).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Spectrosc. Soc. Jpn. (2)

T. Kita, T. Harada, J. Spectrosc. Soc. Jpn. 29, 256 (1980).
[CrossRef]

F. Masuda, H. Noda, T. Namioka, J. Spectrosc. Soc. Jpn. 27, 311 (1978).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Harada, S. Moriyama, T. Kita, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 175 (1975).

Opt. Spectrosc. (1)

F. M. Gerasimov, E. A. Yakovlev, B. K. Koshlev, Opt. Spectrosc. 46, 665 (1979).

Other (3)

G. W. Stroke, Handbuch der Pysik, Vol. 29 (Springer, Berlin, 1967), p. 664.

T. Harada, T. Kita, in Extended Abstracts, Fifth International Conference on VUV Radiation Physics, Montpellier, 1977, Vol. 3, p. 58.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel, Newcastle-upon-Tyne, England, 1970), p. 117.

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Figures (13)

Fig. 1
Fig. 1

Numerically controlled ruling engine.

Fig. 2
Fig. 2

Control system of the ruling engine.

Fig. 3
Fig. 3

Mechanism for ruling curved grooves.

Fig. 4
Fig. 4

Mechanism for lifting tool carriage.

Fig. 5
Fig. 5

Schematic diagram of optical system.

Fig. 6
Fig. 6

Definition of groove position.

Fig. 7
Fig. 7

Horizontal focal condition of concave grating monochromator: 600 g/mm, r = r′, αβ = 6°.

Fig. 8
Fig. 8

Comparison of image focusing properties: A.C., aberration-corrected monochromator; S.N., Seya-Namioka monochromator; 600 g/mm, R = 150 mm, 20 × 20-mm2 ruled area.

Fig. 9
Fig. 9

Optimum space variation for Seya-Namioka monochromator: 600 g/mm, R = 500 mm, 50-mm ruled width.

Fig. 10
Fig. 10

Spectral images of mercury lines obtained with Seya-Namioka monochromator: 600 g/mm; R = 500 mm; 50 × 30-mm2 ruled area.

Fig. 11
Fig. 11

Ray-traced spectral images obtained with Seya-Namioka monochromator: 1200 g/mm; R = 500 mm; 50 × 30-mm2 ruled area.

Fig. 12
Fig. 12

Horizontal focal curves of grazing incidence spectrograph obtained with a varied spacing concave grating: 1200 g/mm; R = 6 m; α = 87°.

Fig. 13
Fig. 13

Ray-traced spectral images obtained with a grazing incidence spectrograph using an aberration-corrected concave grating: 1200 g/mm; R = 6m; 50 × 18-mm2 ruled area; α = 87°.

Tables (1)

Tables Icon

Table I Specifications of the Concave Gratings Ruled with the Numerically Controlled Ruling Engine

Equations (27)

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F = A P + P B + n m λ
F / w = 0 and F / l = 0 ,
A P = [ ( x u ) 2 + ( y w ) 2 + l 2 ] 1 / 2 , P B = [ ( x u ) 2 + ( y w ) 2 + l 2 ] 1 / 2 .
A P 2 = r 2 + u 2 + w 2 + l 2 2 u r cos α 2 w r sin α , P B 2 = r 2 + u 2 + w 2 + l 2 2 u r cos β 2 w r sin β ,
( u R ) 2 + w 2 + l 2 = R 2 .
u = w 2 + l 2 2 R + ( w 2 + l 2 ) 2 8 R 3 + ( w 2 + l 2 ) 3 16 R 5 + .
w θ = w u tan θ .
n = 1 σ 0 ( w θ + b 2 R w θ 2 + b 3 R 2 w θ 3 + b 4 R 3 w θ 4 + ) ,
σ = σ 0 / ( 1 + 2 b 2 R w θ + 3 b 3 R 2 w θ 3 + 4 b 4 R 3 w θ 3 + ) .
F = r + r + w F 10 + w 2 F 20 + l 2 F 02 + w 3 F 30 + w l 2 F 12 + w 2 l 2 F 22 + w 4 F 40 + w 2 l 2 F 22 + l 4 F 04 + O ( w 5 ) ,
F i j = C i j + [ ( m λ ) / σ 0 ] M i j ,
C 10 = sin α sin β ,
M 10 = 1 ,
C 20 = 1 2 ( cos 2 α r cos α R ) + 1 2 ( cos 2 β r cos β R ) ,
M 20 = 1 R ( b 2 tan θ 2 ) ,
C 02 = 1 2 ( 1 r cos α R ) + 1 2 ( 1 r cos β R ) ,
M 02 = tan θ 2 R ,
C 30 = 1 2 sin α r ( cos 2 α r cos α R ) + 1 2 sin β r ( cos 2 β r cos β R ) ,
M 30 = 1 R 2 ( b 3 b 2 tan 2 θ ) ,
C 12 = 1 2 sin α r ( 1 r cos α R ) + 1 2 sin β r ( 1 r cos β R ) ,
M 12 = b 2 tan θ R 2 ,
C 40 = 1 8 [ 4 sin 4 α r 2 ( cos 2 α r cos α R ) 1 r ( cos 2 α r cos α R ) 2 + 1 R 2 ( 1 r cos α R ) ] + 1 8 [ 4 sin 2 β r 2 ( cos 2 β r cos β R ) 1 r ( cos 2 β r cos β R ) 2 + 1 R 2 ( 1 r cos β R ) ] ,
M 40 = 1 R 3 ( b 4 3 b 3 tan θ 2 + b 2 tan 2 θ 4 tan θ 8 ) ,
C 22 = 1 4 [ 2 sin 2 α r 2 ( 1 r cos α R ) 1 r ( cos 2 α r cos α R ) ( 1 r cos α R ) + 1 R 2 ( 1 r cos α R ) ] + 1 4 [ 2 sin 2 β r 2 ( 1 r cos β R ) 1 r ( cos 2 β r cos β R ) ( 1 r cos β R ) + 1 R 2 ( 1 r cos β R ) ] ,
M 22 = 1 2 R 3 ( 3 b 3 tan θ + b 2 tan 2 θ tan θ 2 ) ,
C 04 = 1 8 [ 1 r ( 1 r cos α R ) 2 + 1 R 2 ( 1 r cos α R ) ] + 1 8 [ 1 r ( 1 r cos β R ) 2 + 1 R 2 ( 1 r cos β R ) ] ,
M 04 = 1 4 R 3 ( b 2 tan 2 θ tan θ 2 ) .

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