Abstract

In this work we present the design of a Czerny-Turner spectrograph with practically constant images over a wide spectral range (3500–7500 Å). The plate diagram method is used to determine the parameters and the resulting design is evaluated by ray tracing.

© 1988 Optical Society of America

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References

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  1. J. M. Simon, M. A. Gil, A. N. Fantino, “Use of the Plate Diagram in the Fast Evaluation of Monochromators and Spectrographs,” Appl. Opt. 27, 0000 (1988), same issue.
    [CrossRef]
  2. A. B. Shafer, L. R. Megill, L. Droppleman, “Optimization of the Czerny-Turner Spectrometer,” J. Opt. Soc. Am. 54, 879 (1964).
    [CrossRef]
  3. G. G. Chandler, “Optimization of a 4-m Asymmetric Czerny-Turner Spectrograph,” J. Opt. Soc. Am. 58, 895 (1968).
    [CrossRef]
  4. C. D. Allemand, “Coma Correction in Czerny-Turner Spectrographs,” J. Opt. Soc. Am. 58, 159 (1968).
    [CrossRef]
  5. P. E. Rouse, B. Brixner, J. V. Kline, “Optimization of a 4-m Asymmetric Czerny-Turner Spectrograph,” J. Opt. Soc. Am. 59, 955 (1969).
  6. J. Reader, “Optimization Czerny-Turner Spectrographs: a Comparison Between Analytical Theory and Ray Tracing,” J. Opt. Soc. Am. 59, 1189 (1969).
    [CrossRef]
  7. Peter Lindblom, “Theory of the Two Mirrors Plane Grating Spectrograph,” J. Opt. Soc. Am. 62, 756 (1972).
    [CrossRef]
  8. H. G. Beutler, “The Theory of Concave Grating,” J. Opt. Soc. Am. 35, 311 (1945).
    [CrossRef]
  9. T. Namioka, “Theory of the Concave Grating. I,” J. Opt. Soc. Am. 49, 446 (1959).
    [CrossRef]
  10. M. V. R. K. Murty, “Cary Principle in Monochromator Design,” Appl. Opt. 12, 2018 (1973).
    [CrossRef] [PubMed]
  11. J. K. Pribram, C. M. Penchina, “Stray Light in Czerny-Turner and Ebert Spectrometers,” Appl. Opt. 7, 2005 (1968).
    [CrossRef] [PubMed]
  12. W. G. Fastie, U.S. Patent3,011,391 (1961).

1988

J. M. Simon, M. A. Gil, A. N. Fantino, “Use of the Plate Diagram in the Fast Evaluation of Monochromators and Spectrographs,” Appl. Opt. 27, 0000 (1988), same issue.
[CrossRef]

1973

1972

1969

1968

1964

1959

1945

Allemand, C. D.

Beutler, H. G.

Brixner, B.

Chandler, G. G.

Droppleman, L.

Fantino, A. N.

J. M. Simon, M. A. Gil, A. N. Fantino, “Use of the Plate Diagram in the Fast Evaluation of Monochromators and Spectrographs,” Appl. Opt. 27, 0000 (1988), same issue.
[CrossRef]

Fastie, W. G.

W. G. Fastie, U.S. Patent3,011,391 (1961).

Gil, M. A.

J. M. Simon, M. A. Gil, A. N. Fantino, “Use of the Plate Diagram in the Fast Evaluation of Monochromators and Spectrographs,” Appl. Opt. 27, 0000 (1988), same issue.
[CrossRef]

Kline, J. V.

Lindblom, Peter

Megill, L. R.

Murty, M. V. R. K.

Namioka, T.

Penchina, C. M.

Pribram, J. K.

Reader, J.

Rouse, P. E.

Shafer, A. B.

Simon, J. M.

J. M. Simon, M. A. Gil, A. N. Fantino, “Use of the Plate Diagram in the Fast Evaluation of Monochromators and Spectrographs,” Appl. Opt. 27, 0000 (1988), same issue.
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Other

W. G. Fastie, U.S. Patent3,011,391 (1961).

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Figures (3)

Fig. 1
Fig. 1

Schematic representation of a Czerny-Turner spectrograph. Diagrams correspond to the collimator and camera.

Fig. 2
Fig. 2

Representation of the width of the image of coma (shaded area) as a function of k. Symmetrical image [ k s = ( 3 ρ x 2 + t r ρ y 2 ) / [ ( 3 ρ x 2 + ρ y 2 ) t r 3 ] and minimum width image [ k m = ( 1 / t r 3 )].

Fig. 3
Fig. 3

Images obtained by ray tracing corresponding to the origin and border of the object field and different wavelengths. The symbols blank, ●, +, *, and ao-27-19-4069-i001 denote the number of rays passing through a given point of the image and correspond to 0, 1,2, or 3; 4,5, 6, or 7; and 8 or more rays, respectively.

Equations (17)

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t λ = cos ϕ 0 cos ϕ 0 λ = cos ϕ 0 cos Δ ϕ λ = t r + φ ( Δ ϕ λ 2 ) ,
D x = θ r 4 f [ 3 x 2 t r ( k - 1 t r 3 ) + y 2 t r ( k - 1 t r ) ] , D y = θ r 4 f [ 2 x y ( k - 1 t r ) ] .
D x 1 = θ r 4 f 3 ρ x 2 ( k t r - 1 t r 2 ) ,
D x 2 = θ r 4 f ρ y 2 ( k t r - 1 ) ,
D x 3 = 0 ,
D y 1 , 2 = ± θ r 2 f ρ x ρ y ( k - 1 t r ) .
[ - Δ f 2 f 2 ( x 2 + y 2 ) ]
[ - Δ f ( λ ) 2 f 2 ( x 2 + y 2 ) ]
Δ f = - θ 2 f 2 ( t r 2 - 1 ) ( 3 t r 2 - 1 + 2 θ r 2 θ 2 ) ,
Δ f ( λ ) = θ 2 f 2 [ 2 t r 2 + θ r 2 θ 2 ( 3 - t r 2 ) 1 - t r 2 - 4 θ r θ 2 Δ ϕ λ - Δ ϕ λ 2 θ 2 ] .
- 1 32 f 3 [ x 4 ( 1 + 1 t r 4 ) + 2 x 2 y 2 ( 1 + 1 t r 2 ) + 2 y 4 ] .
θ 4 f 2 [ x 3 ( 1 - θ r θ t r 3 ) + x y 2 ( 1 - θ r θ t r ) ] .
- θ 2 2 f x 2 ( 1 + θ r 2 θ 2 t r 2 ) .
- θ 2 4 f { x 2 [ 1 + θ r 2 θ 2 t r 2 - ( β 0 θ ) 2 ( 1 + 1 t r 2 ) - Δ ϕ λ - α 0 λ θ t r 2 ( 4 θ r θ + Δ ϕ λ - α 0 λ θ ) ] + y 2 [ 1 + θ r 2 θ 2 - 2 ( β 0 θ ) 2 - Δ ϕ λ - α 0 λ θ ( 4 θ r θ + Δ ϕ λ - α 0 λ θ ) ] } .
δ x p + δ x c = θ 3 [ 1 - ( β θ ) 2 ] , δ y p + δ y c = 0 ,
δ x p + δ x c = - θ r 3 [ 1 - ( β θ r ) 2 - ( Δ ϕ λ - α 0 λ θ r ) 2 ] , δ y r + δ y r = 0 ,
α 0 λ = - 1 2 β 0 2 ( sin ϕ 0 + sin ϕ 0 λ ) cos ϕ 0 λ .

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