Abstract

The properties of a 4-m plane-grating Czerny–Turner spectrograph have been analyzed by tracing rays through the spectrograph. Contrary to results recently reported by Chandler in this journal, it was found that the optimum position of the grating is near that predicted by the Fastie–Rosendahl analytical expression. It is also shown that the image width can be made small all the way across a 50-cm plate, that the focal curve can be made straight, and that a position of the entrance slit can be found that makes it unnecessary to refocus the spectrograph when the grating is rotated.

© 1969 Optical Society of America

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References

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  1. G. G. Chandler, J. Opt. Soc. Am. 58, 895 (1968).
    [Crossref]
  2. W. G. Fastie, U. S. Patent3,011,391.
  3. G. Rosendahl, J. Opt. Soc. Am. 52, 412 (1962).
    [Crossref]
  4. B. Brixner, Appl. Opt. 2, 1281 (1963).
    [Crossref]
  5. G. G. Chandler, private communication.
  6. P. E. Rouse, unpublished work.

1968 (1)

1963 (1)

1962 (1)

Brixner, B.

Chandler, G. G.

G. G. Chandler, J. Opt. Soc. Am. 58, 895 (1968).
[Crossref]

G. G. Chandler, private communication.

Fastie, W. G.

W. G. Fastie, U. S. Patent3,011,391.

Rosendahl, G.

Rouse, P. E.

P. E. Rouse, unpublished work.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Other (3)

W. G. Fastie, U. S. Patent3,011,391.

G. G. Chandler, private communication.

P. E. Rouse, unpublished work.

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Figures (1)

Fig. 1
Fig. 1

Schematic diagram of asymmetrical Czerny–Turner spectrograph. M1 and M2 are collimator and camera mirrors respectively, G is the grating, S is the entrance slit, and P is the plate holder.

Tables (6)

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Table I Calculated line widths at the image as a function of distance of the entrance slit from the tangential focal point of the collimator (Δt).

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Table II Values of the grating angle, θ, required to bring the tenth order of the given wavelength to the center of the plate.

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Table III Calculated line widths at the image as a function of ΔZ, the displacement of the grating from the position required by the Fastie–Rosendahl equation. Positive ΔZ corresponds to displacement away from the entrance slit. Calculations are for a wavelength of 5948 Å in the tenth order at the center of the focal curve.

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Table IV Calculated line image widths at the plate center as a function of ΔZ, the displacement of the grating from the position required by the Fastie–Rosendahl equation. Calculation is based on tracing rays lying in the central plane of the spectrograph. The wavelength is 5948 Å and the order is the tenth.

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Table V The sagitta of the focal curve as a function of Δt, the displacement of the entrance slit from the tangential focal point of the collimator. Sagitta is negative if the curve is concave toward the camera mirror. (Rg) is the longitudinal distance of the grating from the vertices of the spherical mirrors.

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Table VI Change of focus with change of grating angle for various positions of entrance slit. When Δt = 0.0 the slit is at the tangential focal point of the collimator. (Rg) = 335 cm.

Equations (23)

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z m = 2 ( R - g ) ( z s - z 0 ) / R .
x m = [ R 2 - ( z m - z 0 ) 2 ] 1 2 .
a = [ ( x m - g ) 2 + z m 2 ] 1 2 .
cos α = ( R a ) - 1 [ x m ( x m - g ) + ( z m - z 0 ) z m ] .
sin α = ( R a ) - 1 [ x m z m - ( x m - g ) ( z m - z 0 ) ] .
l = R - 1 [ x m cos α + ( z m - z 0 ) sin α ]
m = R - 1 [ ( z m - z 0 ) cos α - x m sin α ] ,
x e = x m - t l
z e = z m - t m .
t = R cos α / 2.
z m = z m + 2 a R ( z s - z e ) .
z ¯ 0 = z ¯ p - R 2 z ¯ m R - g .
t ¯ m = ( R cos α ¯ m ) / 2 ;
z ¯ 0 = z ¯ 0 + z ¯ p - z ¯ e .
b = tan - 1 [ z m / ( x m - g ) ] .
c = tan - 1 [ z ¯ m / ( x ¯ m - g ) ] .
φ = ( b + c ) / 2.
sin γ = n λ m 2 d cos φ ,
i = γ - φ ,
r = γ + φ .
θ = i + b .
d g = - ( d k c ) R 2 2 3 h 2 ,
g = R / 3 .