Abstract

The aberration formulas derived in paper II are checked against the well-known behavior of the Wadsworth and Eagle Mountings. A quantitative analysis of the Czerny-Turner arrangement of two mirrors and the Ebert-Fastie spectrograph is given. The compensation of the residual astigmatism for the Czerny-Turner arrangement is treated. It is found that a plane grating produces coma and astigmatism in a homocentric, converging light bundle.

© 1962 Optical Society of America

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References

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  1. G. Rosendahl, J. Opt. Soc. Am. 51, 1 (1961).
    [Crossref]
  2. G. Rosendahl, J. Opt. Soc. Am. 52, 407 (1962), preceding paper.
  3. The first numeral of hyphenated formula numbers refer to part I and II; see references 1 and 2.
  4. G. Harrison, R. Lord, and J. Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948).
  5. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
    [Crossref]
  6. T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).
    [Crossref]
  7. T. Namioka, J. Opt. Soc. Am. 49, 460 (1959).
    [Crossref]
  8. W. A. Rense and T. Violett, J. Opt. Soc. Am. 49, 139 (1959).
    [Crossref]
  9. M. Czerny and A. Turner, Z. Phys. 61, 792 (1930).
    [Crossref]
  10. M. Czerny and V. Plettig, Z. Phys. 63, 590 (1930).
    [Crossref]
  11. W. G. Fastie, J. Opt. Soc. Am. 42, 641 (1952); J. Opt. Soc. Am. 42, 647 (1952); J. Opt. Soc. Am. 43, 1174 (1953).
    [Crossref]
  12. From still unpublished investigations by Dr. Fastie. Without his kind advance information of his results, the following would have been overlooked.

1962 (1)

G. Rosendahl, J. Opt. Soc. Am. 52, 407 (1962), preceding paper.

1961 (1)

1959 (3)

1952 (1)

1945 (1)

1930 (2)

M. Czerny and A. Turner, Z. Phys. 61, 792 (1930).
[Crossref]

M. Czerny and V. Plettig, Z. Phys. 63, 590 (1930).
[Crossref]

Beutler, H. G.

Czerny, M.

M. Czerny and A. Turner, Z. Phys. 61, 792 (1930).
[Crossref]

M. Czerny and V. Plettig, Z. Phys. 63, 590 (1930).
[Crossref]

Fastie, W. G.

Harrison, G.

G. Harrison, R. Lord, and J. Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948).

Loofbourow, J.

G. Harrison, R. Lord, and J. Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948).

Lord, R.

G. Harrison, R. Lord, and J. Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948).

Namioka, T.

Plettig, V.

M. Czerny and V. Plettig, Z. Phys. 63, 590 (1930).
[Crossref]

Rense, W. A.

Rosendahl, G.

G. Rosendahl, J. Opt. Soc. Am. 52, 407 (1962), preceding paper.

G. Rosendahl, J. Opt. Soc. Am. 51, 1 (1961).
[Crossref]

Turner, A.

M. Czerny and A. Turner, Z. Phys. 61, 792 (1930).
[Crossref]

Violett, T.

J. Opt. Soc. Am. (7)

Z. Phys. (2)

M. Czerny and A. Turner, Z. Phys. 61, 792 (1930).
[Crossref]

M. Czerny and V. Plettig, Z. Phys. 63, 590 (1930).
[Crossref]

Other (3)

The first numeral of hyphenated formula numbers refer to part I and II; see references 1 and 2.

G. Harrison, R. Lord, and J. Loofbourow, Practical Spectroscopy (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1948).

From still unpublished investigations by Dr. Fastie. Without his kind advance information of his results, the following would have been overlooked.

Cited By

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Figures (3)

Fig. 1
Fig. 1

Two-mirror arrangement: (a) antisymmetrical, Czerny-Turner case; (b) symmetrical case.

Fig. 2
Fig. 2

Calculation of coma for the two-mirror arrangement: (a) Czerny-Turner case, (b) symmetrical case. The optical scheme is folded apart around tangent at apex of mirror surfaces in agreement with the sign convention for reflection as explained in part I.

Fig. 3
Fig. 3

Czerny-Turner arrangement with compensation for astigmatism.

Equations (48)

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y ¯ c = - h ¯ 2 sin σ 0 / r cos 2 σ 0 .
1 / s ¯ s = - ( 2 cos σ 0 ) / r + 1 / s ¯ s .
r = - R
1 / s ¯ ( 1 ) = - ( 2 / R ) ( 1 + Δ ) ;             s ¯ ( 1 ) = - R / 2 ( 1 + Δ ) ,
1 / s ¯ s ( 1 ) = ( 2 / R ) [ cos σ 0 - ( 1 + Δ ) ] .
s ¯ s ( 2 ) = s ¯ s ( 1 ) - d ;             1 / [ s ¯ s ( 2 ) ] = 1 / [ s ¯ s ( 1 ) - d ] ,
d = - 2 s ¯ s ( 1 ) = + R / ( 1 + Δ ) .
1 s ¯ s ( 2 ) = 2 R [ cos σ 0 + cos σ 0 - ( 1 + Δ ) 3 ( 1 + Δ ) - 2 cos σ 0 ( 1 + Δ ) ] ,
1 s ¯ m ( 1 ) = 2 R [ 1 cos σ 0 - ( 1 + Δ ) ] .
1 s ¯ m ( 2 ) = 2 R [ 1 cos σ 0 + 1 / cos σ 0 - ( 1 + Δ ) 3 ( 1 + Δ ) - 2 / cos σ 0 ( 1 + Δ ) ] .
1 + Δ = cos σ 0 ,
1 s ¯ m ( 2 ) - 1 s ¯ s ( 2 ) = 2 R [ T + T cos σ 0 cos σ 0 - 2 T ] ; T = 1 / cos σ 0 - cos σ 0 .
1 / s ¯ m ( 2 ) - 1 / s ¯ s ( 2 ) = ( 4 / R ) σ 0 2 .
δ = - h ¯ / s ¯ m .
1 / s ¯ m ( 1 ) = 0 ;             d = R ;             h ¯ ( 1 ) = h ¯ ( 2 ) .
s ¯ m ( 1 ) = - ( R / 2 ) cos σ 0 ( 1 ) = - ( R / 2 ) cos σ 0 ( 2 ) = - s ¯ m ( 2 ) ,
δ ( 1 ) = 2 h ¯ ( 1 ) R cos σ 0 ( 1 ) = 2 h ¯ ( 2 ) R cos σ 0 ( 2 ) = δ ( 2 ) .
y ¯ c ( 1 ) = s ¯ m ( 2 ) s ¯ m ( 2 ) y ¯ c ( 1 ) .
y ¯ c ( 1 ) = 3 h ¯ 2 ( 1 ) 2 R cos σ 0 ( 1 ) tan σ 0 ( 1 ) ,
1 / s ¯ m ( 1 ) = 1 / s ¯ m ( 2 ) = 0 ,
s ¯ m ( 1 ) / s ¯ m ( 2 ) = 1.
y ¯ c ( 2 ) = - 3 h ¯ 2 ( 2 ) 2 R cos σ 0 ( 2 ) tan σ 0 ( 2 ) .
σ 0 ( 1 ) = + σ 0 ( 2 ) .
y ¯ c = y ¯ c ( 1 ) + y ¯ c ( 2 ) = 0.
σ 0 ( 2 ) = - σ 0 ( 1 ) ,
y ¯ c = + 3 4 R · δ 2 ( 1 ) · sin σ 0 ( 1 ) .
1 / s ¯ m - C 2 / s ¯ m = - M m / r ;
C 2 = cos 2 σ 0 / cos 2 σ 0 ;
M m = ( cos σ 0 + cos σ 0 ) / cos 2 σ 0 ;
1 / s ¯ s - 1 / s ¯ s = - M s / r ;
M s = cos σ 0 + cos σ 0 .
- s ¯ m ( 1 ) = - s ¯ s ( 1 ) = s ¯ m ( 4 ) = s ¯ s ( 4 ) ,
s ¯ m ( 2 ) = s ¯ s ( 2 ) = - s ¯ m ( 3 ) = - s ¯ s ( 3 ) = .
C 2 ( 4 ) s ¯ m ( 4 ) - M m ( 4 ) r ( 4 ) = 1 s ¯ s ( 4 ) - M s ( 4 ) r ( 4 )
r ( 4 ) = M m ( 4 ) - M s ( 4 ) C 2 ( 4 ) / s ¯ m ( 4 ) - 1 / s ¯ s ( 4 ) = r ( 1 ) .
1 / s ¯ m = 1 / s ¯ m = 1 / s ¯ s = 1 / s ¯ s = 0.
y ¯ c ( G r ) = 0.
y ¯ c ( 1 ) = 3 2 h ¯ 2 ( 1 ) R cos 2 σ 0 ( 1 ) cos σ 0 ( G r ) cos σ 0 ( G r ) cos σ 0 ( 2 ) tan σ 0 ( 1 ) ,
y ¯ c ( G r ) = 0 ,
y ¯ c ( 2 ) = - 3 2 h ¯ 2 ( 1 ) R cos σ 0 ( 2 ) cos 2 σ 0 ( G r ) cos 2 σ 0 ( G r ) tan σ 0 ( 2 ) ,
h ¯ ( 2 ) = h ¯ ( G r ) = h ¯ ( G r ) cos σ 0 ( G r ) cos σ 0 ( G r ) ,
sin σ 0 ( 2 ) cos 3 σ 0 ( 2 ) = [ cos σ 0 ( G r ) cos σ 0 ( G r ) ] 3 sin σ 0 ( 1 ) cos 3 σ ( 1 ) ,
s ¯ m = s ¯ ( δ / δ ) ( k / k ) .
1 / r = 0 ;             φ = h ¯ / r = 0 ;
k k = cos σ 0 + δ sin σ 0 cos σ 0 + δ sin σ 0 = cos σ 0 cos σ 0 ( 1 + δ tan σ 0 - δ tan σ 0 ) ,
δ = δ cos σ 0 cos σ 0 .
s ¯ m ( δ ) = s ¯ m cos 2 σ 0 cos 2 σ 0 [ 1 + δ ( cos σ 0 cos σ 0 tan σ 0 - tan σ 0 ) ] .
s ¯ s = s ¯ s .