Abstract

The theory developed by Seya, Namioka, and Sai has been numerically evaluated with the purpose of furnishing practical data for designing a Monk-Gillieson monochromator, in which coma-type aberration is eliminated at one specific wavelength of the designer’s choice. The numerical results are conveniently arranged in the form of graphs and tables so as to facilitate estimation of the optimum instrumental constants and the performance to be expected. The calculations included here have been verified experimentally with a monochromator whose instrumental constants were so chosen, in accordance with the theory, as to eliminate the coma-type aberration at 3000 Å. For practical interest, the performance of the above monochromator has also been compared with that of a Schroeder-type monochromator.

© 1971 Optical Society of America

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References

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  1. G. S. Monk, J. Opt. Soc. Amer. 17, 358 (1928).
    [CrossRef]
  2. H. T. Smyth, J. Opt. Soc. Amer. 25, 312 (1935).
    [CrossRef]
  3. A. H. C. P. Gillieson, J. Sci. Instrum. 26, 335 (1949).
    [CrossRef]
  4. E. W. T. Richards, A. R. Thomas, W. Weinstein, AERE Rep. C/R 2152 (AERE, Harwell, Eng., 7Jan.1957).
  5. G. R. Rosendahl, J. Opt. So c. Amer. 52, 412 (1962).
    [CrossRef]
  6. M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
    [CrossRef]
  7. D. J. Schroeder, Appl. Opt. 5, 545 (1966).
    [CrossRef] [PubMed]
  8. J. T. Hall, Appl. Opt. 5, 1051 (1966).
    [CrossRef] [PubMed]
  9. J. N. Howard, Appl. Opt. 5, 1466 (1966).
    [CrossRef] [PubMed]
  10. M. Seya, T. Namioka, T. Sai, Sci. Light (Tokyo) 16, 138 (1967).
  11. P. D. Johnson, Rev. Sci. Instrum. 28, 833 (1957).
    [CrossRef]
  12. R. Onaka, Sci. Light (Tokyo) 7, 23 (1958).
  13. In Schroeder’s paper7 (the 4th line in Result), “grating to mirror distance = 20.5 cm” should be changed to 20.25 cm in order to have the consistency among the instrumental constants.

1967 (1)

M. Seya, T. Namioka, T. Sai, Sci. Light (Tokyo) 16, 138 (1967).

1966 (3)

1962 (2)

G. R. Rosendahl, J. Opt. So c. Amer. 52, 412 (1962).
[CrossRef]

M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
[CrossRef]

1958 (1)

R. Onaka, Sci. Light (Tokyo) 7, 23 (1958).

1957 (1)

P. D. Johnson, Rev. Sci. Instrum. 28, 833 (1957).
[CrossRef]

1949 (1)

A. H. C. P. Gillieson, J. Sci. Instrum. 26, 335 (1949).
[CrossRef]

1935 (1)

H. T. Smyth, J. Opt. Soc. Amer. 25, 312 (1935).
[CrossRef]

1928 (1)

G. S. Monk, J. Opt. Soc. Amer. 17, 358 (1928).
[CrossRef]

Gillieson, A. H. C. P.

A. H. C. P. Gillieson, J. Sci. Instrum. 26, 335 (1949).
[CrossRef]

Hall, J. T.

Howard, J. N.

Johnson, P. D.

P. D. Johnson, Rev. Sci. Instrum. 28, 833 (1957).
[CrossRef]

Monk, G. S.

G. S. Monk, J. Opt. Soc. Amer. 17, 358 (1928).
[CrossRef]

Murty, M. V. R. K.

M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
[CrossRef]

Namioka, T.

M. Seya, T. Namioka, T. Sai, Sci. Light (Tokyo) 16, 138 (1967).

Onaka, R.

R. Onaka, Sci. Light (Tokyo) 7, 23 (1958).

Richards, E. W. T.

E. W. T. Richards, A. R. Thomas, W. Weinstein, AERE Rep. C/R 2152 (AERE, Harwell, Eng., 7Jan.1957).

Rosendahl, G. R.

G. R. Rosendahl, J. Opt. So c. Amer. 52, 412 (1962).
[CrossRef]

Sai, T.

M. Seya, T. Namioka, T. Sai, Sci. Light (Tokyo) 16, 138 (1967).

Schroeder, D. J.

Seya, M.

M. Seya, T. Namioka, T. Sai, Sci. Light (Tokyo) 16, 138 (1967).

Smyth, H. T.

H. T. Smyth, J. Opt. Soc. Amer. 25, 312 (1935).
[CrossRef]

Thomas, A. R.

E. W. T. Richards, A. R. Thomas, W. Weinstein, AERE Rep. C/R 2152 (AERE, Harwell, Eng., 7Jan.1957).

Weinstein, W.

E. W. T. Richards, A. R. Thomas, W. Weinstein, AERE Rep. C/R 2152 (AERE, Harwell, Eng., 7Jan.1957).

Appl. Opt. (3)

J. Opt. So c. Amer. (1)

G. R. Rosendahl, J. Opt. So c. Amer. 52, 412 (1962).
[CrossRef]

J. Opt. Soc. Amer. (3)

M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
[CrossRef]

G. S. Monk, J. Opt. Soc. Amer. 17, 358 (1928).
[CrossRef]

H. T. Smyth, J. Opt. Soc. Amer. 25, 312 (1935).
[CrossRef]

J. Sci. Instrum. (1)

A. H. C. P. Gillieson, J. Sci. Instrum. 26, 335 (1949).
[CrossRef]

Rev. Sci. Instrum. (1)

P. D. Johnson, Rev. Sci. Instrum. 28, 833 (1957).
[CrossRef]

Sci. Light (Tokyo) (2)

R. Onaka, Sci. Light (Tokyo) 7, 23 (1958).

M. Seya, T. Namioka, T. Sai, Sci. Light (Tokyo) 16, 138 (1967).

Other (2)

E. W. T. Richards, A. R. Thomas, W. Weinstein, AERE Rep. C/R 2152 (AERE, Harwell, Eng., 7Jan.1957).

In Schroeder’s paper7 (the 4th line in Result), “grating to mirror distance = 20.5 cm” should be changed to 20.25 cm in order to have the consistency among the instrumental constants.

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Figures (25)

Fig. 1
Fig. 1

Schematic diagram of a Monk-Gillieson monochromator. For the symbols, refer to Sec. II.A.

Fig. 2
Fig. 2

Dependence of r, D0, and r0′ on n.

Fig. 3
Fig. 3

Allowed ranges of α0 and θ for negative A0’s. The ranges restricted by Eqs. (4) and (18) are marked with hatching. The crisscrossed portions indicate the allowed ranges further restricted by the condition l/R ≤ 0.5 (refer to Sec. III.D).

Fig. 4
Fig. 4

Allowed ranges of α0 and θ for positive A0′s. The ranges restricted by Eq. (18) are marked with hatching. The crisscrossed portions indicate the allowed ranges further restricted by the condition l/R ≤ 0.5 (refer to Sec. III.D).

Fig. 5
Fig. 5

Level curves of r/R. The dash–dot curves are the wavelength isochromats expressed in terms of A0. The level curve r/R = ∞ is independent of θ.

Fig. 6
Fig. 6

Level curves of D0/R. The dash–dot curves are the wavelength isochromats expressed in terms of A0. The level curve D0/R = ∞ is independent of θ.

Fig. 7
Fig. 7

Level curves of r0′/R. The dash–dot curves are the wavelength isochromats expressed in terms of A0. The open circles indicate the terminal points due to Eq. (18). The level curve r0′/R = 0 is independent of θ.

Fig. 8
Fig. 8

Level curves of l/R. The dash–dot curves are the wavelength isochromats expressed in terms of A0. The open circles indicate the terminal points due to Eq. (18). The level curves l/R = 0 and ∞ are independent of θ.

Fig. 9
Fig. 9

The variation of with α0. The open circles indicate the terminal points due to Eq. (4). (The curve for A0 = −0.18 is the one not expressed by the arrow.)

Fig. 10
Fig. 10

The amount of defocusing for A0 = ± 0.06.

Fig. 11
Fig. 11

The amount of defocusing for A0 = ± 0.18.

Fig. 12
Fig. 12

The amount of defocusing for A0 = ± 0.30.

Fig. 13
Fig. 13

The amount of coma for A0 = ± 0.06.

Fig. 14
Fig. 14

The amount of coma for A0 = ± 0.12.

Fig. 15
Fig. 15

The amount of coma for A0 = ± 0.18.

Fig. 16
Fig. 16

The amount of coma for A0 = ± 0.24. Note that Δp·R/s2 for A0 = − 0.24, θ = 10°, and α0 = 15° is double-valued for certain A’s. This is due to the fact that, in this particular case, A reaches its maximum value at a certain δ value and then decreases as δ increases further.

Fig. 17
Fig. 17

The amount of coma for A0 = ± 0.30.

Fig. 18
Fig. 18

Relationship between A (= mλ/σ) and the angle of grating rotation δ.

Fig. 19
Fig. 19

The amount of change in the angle of emergence of the exit beam with A (= mλ/σ). γ is independent of θ.

Fig. 20
Fig. 20

Values of θ and α0 which provide the minimum reciprocal linear dispersion at A = A0(> 0).

Fig. 21
Fig. 21

Recorder trace of the Hg spectrum obtained with monochromator I. Intensities are in arbitrary units. The experimental conditions are: illuminated area on the mirror = 10 mm (H) by 45 mm (W); openings of the entrance and exit slits = 3 mm by 15 μ; scanning speed = 50 Å/min.

Fig. 22
Fig. 22

Recorder trace of the Schumann-Runge bands of the O2 molecule obtained with monochromator I. The experimental conditions are same as those given in the caption of Fig. 21.

Fig. 23
Fig. 23

Recorder trace made with monochromator I of the Hg spectrum showing the effect of masking the mirror surface. The slit openings and the scanning speed are same as those given in the caption of Fig. 21.

Fig. 24
Fig. 24

Recorder trace of the Hg spectrum obtained with monochromator II. Intensities are in arbitrary units. The experimental conditions are same as those given in the caption of Fig. 21.

Fig. 25
Fig. 25

The amount of coma-type aberration, Δp, calculated for monochromators I and II.

Tables (3)

Tables Icon

Table I Proper Values of α0, Judged from the Amount of Defocusing

Tables Icon

Table II Proper Values of α0 and θ, Judged from the Amount of Coma

Tables Icon

Table III Typical Values of the Optimum Instrumental Constants and the Performance to be Expected

Equations (20)

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r = R Γ cos θ , θ 0 ,
Γ = 1 2 [ 1 + ( sin θ Λ ) 1 2 ] ,
Λ = sin θ - 2 ( 1 - 1 n ) cos θ ( tan α 0 + tan β 0 cos α 0 cos β 0 ) > 0
sin α 0 + sin β 0 = m λ 0 / σ A 0 .
D 0 = O A n = R Γ cos θ n ( 2 Γ - 1 ) and n > 1
r 0 = ( 1 - 1 n ) R Γ cos θ cos 2 β 0 ( 2 Γ - 1 ) cos 2 α 0 .
l = ( 2 r 0 / Φ ) sec cos 2 α 0 sin ( α 0 - β 0 )
tan = ( 1 / 3 ) ( tan α 0 + tan β 0 ) [ 1 + ( 2 / Φ ) ( cos 3 α 0 + cos 3 β 0 ) ] 2 + ( 6 / Φ 2 ) cos 2 β 0 { cos 4 α 0 tan α 0 sin 2 ( α 0 - β 0 ) - tan β 0 [ cos 4 α 0 + cos 4 β 0 + 2 cos 2 α 0 cos 2 β 0 cos ( α 0 - β 0 ) ] } ,
Φ = cos 3 β 0 + 3 cos 2 α 0 cos β 0 cos ( α 0 - β 0 ) - 2 cos 3 α 0 .
Δ r = r 0 [ 1 + 2 Δ q r 0 cos ( α 0 - β 0 ) + Δ q 2 r 0 2 ] 1 2 × { 1 - ( cos 2 α 0 cos 2 β 0 - Δ q r 0 ) [ cos ( β 0 + δ ) cos ( α 0 + δ ) + Δ q r 0 ] 2 × [ 1 + 2 Δ q r 0 cos ( α 0 - β 0 ) + Δ q 2 r 0 2 ] - 3 2 } ,
Δ q = l sec ( α 0 + δ ) [ sin ( + δ ) - sin ] .
m λ σ A = sin ( α 0 + δ ) + [ sin ( β 0 + δ ) + Δ q r 0 sin ( α 0 + δ ) ] × [ 1 + 2 Δ q r 0 cos ( α 0 - β 0 ) + Δ q 2 r 0 2 ] - 1 2 .
sec γ = [ 1 + 2 Δ q r 0 cos ( α 0 - β 0 ) + Δ q 2 r 0 2 ] 1 2 × [ 1 + Δ q r 0 cos ( α 0 - β 0 ) ] - 1 .
cos γ d λ G B d β = σ m r 0 [ cos ( β 0 + δ ) + Δ q r 0 cos ( α 0 + δ ) ] × [ 1 + Δ q r 0 cos ( α 0 - β 0 ) ] × [ 1 + 2 Δ q r 0 cos ( α 0 - β 0 ) + Δ q 2 r 0 2 ] - 3 2 .
Δ p = 3 s 2 2 r 0 [ 1 + Δ q r 0 cos ( α 0 - β 0 ) ] - 1 × [ 1 + 2 Δ q r 0 cos ( α 0 - β 0 ) + Δ q 2 r 0 2 ] 3 2 × [ cos ( β 0 + δ ) + Δ q r 0 cos ( α 0 + δ ) ] - 1 × { cos 3 ( α 0 + δ ) cos 4 β 0 cos 4 α 0 ( 1 - Δ q cos 2 β 0 r 0 cos 2 α 0 ) - 2 × [ tan ( α 0 + δ ) - ( tan α 0 + tan β 0 cos α 0 cos β 0 ) × ( 1 - Δ q cos 2 β 0 r 0 cos 2 α 0 ) - 1 ] + [ 1 + 2 Δ q r 0 cos ( α 0 - β 0 ) + Δ q 2 r 0 2 ] - 5 2 × [ ( sin ( β 0 + δ ) + Δ q r 0 sin ( α 0 + δ ) ] × [ cos ( β 0 + δ ) + Δ q r 0 cos ( α 0 + δ ) ] 2 } .
and             0.30 A 0 - 0.30 , 50° α 0 , 45° θ > . }
n = 2
tan θ > A 0 ( 1 - sin α 0 sin β 0 ) cos α 0 cos 2 β 0 .
1 + ( sin θ Λ ) 1 2 ( 1 + sin θ - Λ 2 Λ sin 2 θ ) = 0.
sin 3 θ ( 1 + sin 2 θ ) cos θ ( 1 + 2 sin 2 θ ) 2 = 1 4 ( tan α 0 + tan β 0 cos α 0 cos β 0 ) .

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