Abstract

This paper presents measurements of astigmatism for a typical Czerny-Turner spectrograph and shows two ways of correcting astigmatism in this instrument by using lenses. For an f/6.3 instrument having a 0.75-m focal length collimating and camera mirror, the meridional and sagittal focal planes were separated approximately 15 mm at 60 mm left of the center of the film plane and approximately 43 mm at 70 mm to the right of the center of the plane, when the grating was set to put 5000 Å in the center of the film plane. Measurements of astigmatism for different lines of the Hg spectrum with 5000 Å in the center of the film plane showed the astigmatism to be determined primarily, if not entirely, by the angle at which the radiation left the grating and collimating mirror. The experimental results compared favorably with the theory given by Rosendahl. Two methods of correcting astigmatism by lenses were investigated: one experimental, the other theoretical. Both appear to be practical.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. R. Rosendahl, J. Opt. Soc. Amer. 51, 1 (1961).
    [CrossRef]
  2. G. R. Rosendahl, J. Opt. Soc. Amer. 52, 408 (1962).
    [CrossRef]
  3. A. B. Shafer, Appl. Opt. 6, 159 (1967).
    [CrossRef] [PubMed]
  4. M. L. Dalton, Appl. Opt. 5, 1121 (1966).
    [CrossRef] [PubMed]
  5. Edward L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Reading, Massachusetts, 1963), Chap. 3.
  6. W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, Inc., New York, 1964), Chaps. 3 and 4.
  7. A. Cox, A System of Optical Design (Focal Press, New York, 1964), p. 33 and Appendix G.

1967

1966

1962

G. R. Rosendahl, J. Opt. Soc. Amer. 52, 408 (1962).
[CrossRef]

1961

G. R. Rosendahl, J. Opt. Soc. Amer. 51, 1 (1961).
[CrossRef]

Brouwer, W.

W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, Inc., New York, 1964), Chaps. 3 and 4.

Cox, A.

A. Cox, A System of Optical Design (Focal Press, New York, 1964), p. 33 and Appendix G.

Dalton, M. L.

O’Neill, Edward L.

Edward L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Reading, Massachusetts, 1963), Chap. 3.

Rosendahl, G. R.

G. R. Rosendahl, J. Opt. Soc. Amer. 52, 408 (1962).
[CrossRef]

G. R. Rosendahl, J. Opt. Soc. Amer. 51, 1 (1961).
[CrossRef]

Shafer, A. B.

Appl. Opt.

J. Opt. Soc. Amer.

G. R. Rosendahl, J. Opt. Soc. Amer. 51, 1 (1961).
[CrossRef]

G. R. Rosendahl, J. Opt. Soc. Amer. 52, 408 (1962).
[CrossRef]

Other

Edward L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Reading, Massachusetts, 1963), Chap. 3.

W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, Inc., New York, 1964), Chaps. 3 and 4.

A. Cox, A System of Optical Design (Focal Press, New York, 1964), p. 33 and Appendix G.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Optical schematic of spectrograph and light source with the locations of proposed astigmatism correctors.

Fig. 2
Fig. 2

Astigmatic difference at the film plane for white light reflected from the grating in zero order.

Fig. 3
Fig. 3

Astigmatic difference as a function of the power of the correcting lens for various wavelengths.

Fig. 4
Fig. 4

Focal power as a function of wavelength of a near slit correcting lens required to eliminate astigmatism in the film plane.

Fig. 5
Fig. 5

Refractive index as a function of wavelength for ophthalmic crown glass.

Fig. 6
Fig. 6

Refractive index as a function of wavelength for the glasses comprising the correcting lens.

Fig. 7
Fig. 7

Ray-tracing diagram for a two-element overcorrected cylindraceous lens.

Tables (2)

Tables Icon

Table I Calculated Values of θ3 and θa

Tables Icon

Table II Calculated Values of Xa and Xs

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

( S s ¯ ) - 1 - ( S s ¯ ) - 1 = ( cos σ 0 + cos σ 0 ) / r
cos 2 σ 0 S m ¯ - cos 2 σ 0 S m ¯ = - r - 1 ( cos σ 0 + cos σ 0 ) ,
( S m ¯ ) - 1 - ( S s ¯ ) - 1 = ( 4 / R ) σ 0 ( 1 ) σ 0 ( 2 )
( b - a - d c ) = ( 1 - a 5 0 1 ) ( 1 0 t 4 1 ) ( 1 - a 3 0 1 ) × ( 1 0 t 2 1 ) ( 1 - a 1 0 1 ) ,
s = f - 1 = ( n 2 - n 1 ) / r 12
t = T / n ,
( b - a - d c ) = [ { 1 - a 3 T 2 - a 5 [ T 4 ( 1 - a 3 T 2 ) + T 2 ] } - a 3 - a 5 ( 1 - a 3 T 4 ) T 4 ( 1 - a 3 T 2 ) + T 2 ( 1 - a 3 T 4 ) ] .
a = a 3 + a 5 = ( n 2 - n 4 ) / r 3 + ( n 4 - n a ) / r 5 ,
sin θ 5 = n 2 n a sin θ 3 cos ( θ a - θ 3 ) + n 4 n a [ 1 - sin 2 θ 3 ( n 2 n 4 ) 2 ] 1 2 sin ( θ a - θ 3 )
θ 5 = θ 6 + θ a , θ 6 = tan - 1 ( h / focal length ) , h = r 5 sin θ s = r 3 sin θ 3 ,
X a = 0 h tan θ a d h ,
X s = 0 h tan θ s d h ,
h = r 5 sin θ s
( θ 3 / θ s ) = ( r 5 / r 3 ) = 3.45596 ,
θ 6 + θ a = [ ( n 2 - n 4 ) / n a ] θ 3 + n 4 n a θ a
θ 6 = [ ( n 2 - n 4 ) n a ] θ 3 + [ ( n 4 - n a ) n a ] θ a .
θ 3 tan θ 3 = h / r 3
θ a tan θ a θ s = h / r 5 .
h = l a tan θ a = l 6 tan θ 6 ,
l a = r a sin θ a = r a ( 0 ) - X a ,
l 6 = r 6 ( 0 ) + X a .
tan θ 6 / tan θ a = l a / l 6 = ( r a ( 0 ) - X a ) ( r 6 ( 0 ) + X a ) = r a ( 0 ) r 6 ( 0 ) + { [ 1 + r a ( 0 ) r 6 ( 0 ) ] n = 1 ( - X r 6 ( 0 ) ) n } .
tan θ 6 / tan θ a = r a ( 0 ) / r 6 ( 0 ) .
( θ 6 / θ a ) = r a ( 0 ) / r 6 ( 0 ) ,
sin ( 1 + k ) θ a = n 2 n a sin θ 3 cos ( θ a - θ 3 ) + n 4 n a [ 1 - sin 2 θ 3 ( n 2 n 4 ) 2 ] 1 2 sin ( θ a - θ 3 ) .
n 2 sin θ 3 = n 4 sin θ 4 ,
n 4 sin Δ θ = n a sin θ 5 .
Δ θ = θ a + θ 4 - θ 3 .
n a sin θ 5 = [ n 4 sin θ 4 cos ( θ a - θ 3 ) + cos θ 4 sin ( θ a - θ 3 ) ] .
sin θ 5 = n 2 n a sin θ 3 cos ( θ a - θ 3 ) + n 4 n a [ 1 - sin 2 θ 3 ( n 2 n 4 ) 2 ] 1 2 sin ( θ a - θ 3 ) .

Metrics