Abstract

Methods are discussed for finding the optimum configuration of an inplane Czerny–Turner-type spectrograph. An asymmetry parameter is used which involves a lateral movement of the grating, perpendicular to the rulings. This displacement improves image quality at the center of a fixed photographic plate, and we find that the grating position for best imaging varies with angle. The optimum relationship between grating angle and position is derived by ray tracing for a specific 4-m instrument and the image widths are found to be superior to those calculated for configurations based on analytical expressions. Ray tracing is used to derive a compromise configuration with a fixed plate and a fixed grating for which the image quality is maximized at the photographic plate-center for all useful grating angles, and falls off symmetrically toward each end of the plate. For this configuration, it is necessary only to refocus the entrance slit as the grating is rotated to scan wavelengths.

© 1968 Optical Society of America

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References

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  1. A. B. Shafer, L. R. Megill, and L. Droppleman, J. Opt. Soc. Am. 54, 879 (1964).
    [Crossref]
  2. The only other instrument with this movement appears to be the Jarrell–Ash 5-m spectrograph in which the grating shift is linked mechanically to the rotation. However, the linkage is based on the imaging condition derived by Rosendahl,3 the cos3 relationship, which, as is shown later, may not produce the best configuration.
  3. G. Rosendahl, J. Opt. Soc. Am. 52, 412 (1962).
    [Crossref]
  4. W. G. Fastie, J. Opt. Soc. Am. 42, 647 (1952).
    [Crossref]
  5. W. T. Welford, in Progress in Optics 4, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), p. 243.
  6. W. G. Fastie, in Symposium on Interferometry, Natl. Phys. Lab. 1960 (H. M. Stationery Office1961), p. 243.
  7. A. S. Filler, J. Opt. Soc. Am. 54, 424 (1964).
  8. L. R. Megill (private communication, 1966).

1964 (2)

1962 (1)

1952 (1)

Droppleman, L.

Fastie, W. G.

W. G. Fastie, J. Opt. Soc. Am. 42, 647 (1952).
[Crossref]

W. G. Fastie, in Symposium on Interferometry, Natl. Phys. Lab. 1960 (H. M. Stationery Office1961), p. 243.

Filler, A. S.

Megill, L. R.

Rosendahl, G.

Shafer, A. B.

Welford, W. T.

W. T. Welford, in Progress in Optics 4, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), p. 243.

J. Opt. Soc. Am. (4)

Other (4)

L. R. Megill (private communication, 1966).

The only other instrument with this movement appears to be the Jarrell–Ash 5-m spectrograph in which the grating shift is linked mechanically to the rotation. However, the linkage is based on the imaging condition derived by Rosendahl,3 the cos3 relationship, which, as is shown later, may not produce the best configuration.

W. T. Welford, in Progress in Optics 4, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), p. 243.

W. G. Fastie, in Symposium on Interferometry, Natl. Phys. Lab. 1960 (H. M. Stationery Office1961), p. 243.

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Figures (11)

Fig. 1
Fig. 1

General configuration for an asymmetric Czerny–Turner spectrograph. M1 and M2 are collimator and camera mirrors respectively, G is the grating, S is the entrance slit, P is the plate holder.

Fig. 2
Fig. 2

Two configurations of the instrument. Unprimed angles are for the position of the grating corresponding to Rosendahl correction at the blaze wavelength 5948 Å. Primed angles are for some other grating position, shifted by ΔZ. PC, is the plate-center, α and β are the angles of incidence and diffraction, respectively.

Fig. 3
Fig. 3

Coordinate system for ray tracing in the plane of the instrument (Y = 0).

Fig. 4
Fig. 4

Minimum image width (W in μ) plotted against grating shift (ΔZ in cm) for three wavelengths at the plate center, representing the blaze angle and two extremes of grating angle. The varying focus shift needed to minimize the image widths is not shown. ○ λc = 6249 Å, θ ~ 68° ● λc = 5948 Å, θ ~ 63° Δ λc = 5448 Å, θ ~ 54°.

Fig. 5
Fig. 5

Minimum image width (W in μ) and corresponding focal plane coordinate (Xe in cm) plotted against wavelength (λ in Å) over a 50-cm plate, for the three grating angles and positions optimized in Fig. 4. ○ θ = 68.500°, ΔZ = +4.0 cm, Xo = 399.75 cm. ● θ = 62.467°, ΔZ = +7.0 cm, Xo = 399.68 cm. Δ θ = 54.737°, ΔZ = + 11.0 cm, Xo = 399.66 cm. The dotted line represents the compromise flat, tilted plate discussed in the text.

Fig. 6
Fig. 6

Minimum image width (W in μ) plotted against wavelength (λ in Å) over two compromise types of plate, each optimized for the blaze configuration. —curved, tilted plate (corresponding to — in Fig. 5); - - - - flat, tilted plate (corresponding to - - - - in Fig. 5). θ, ΔZ, and Xo values are the same as in Fig. 5.

Fig. 7
Fig. 7

Minimum image width (W in μ) plotted against wavelength (λ in Å) over the fiat, tilted plate, with and without grating shifts. - - - - variable ΔZ, values as in Figs. 5 and 6. — ΔZ = +7.0 cm with ○ θ = 69.033°, Xo = 399.80 cm; ● θ = 62.4670, Xo = 399.68 cm; Δ θ = 54.0230. Xo = 399.55 cm.

Fig. 8
Fig. 8

Image width(W in μ) plotted against wavelength (λ in Å) over the flat, tilted plate for fixed slit (Xo = 399.68 cm) and fixed grating (ΔZ = +7.0 cm). The grating angles are the same as in Fig. 7 (solid lines).

Fig. 9
Fig. 9

Minimizing the image width (W in μ) at the plate-center (Xe = 400.0 cm) for a fixed grating (ΔZ = +7.0 cm), by varying the entrance slit focus (Xo in cm). ○ θ = 69.033°; ● θ = 62.467°; △ θ = 54.023°.

Fig. 10
Fig. 10

Computed spot diagrams at five positions on the plate represented by their wavelengths, for the optimized blaze angle of the grating (θ = 62.467°, ΔZ = +7.0 cm, Xo = 399.68 cm). The numerical scale is microns.

Fig. 11
Fig. 11

Image widths (W in μ), for two symmetrical Czerny–Turner configurations, plotted against grating angle (θ in deg). — slit-to-image separation 62.45 cm, entrance slit focused for each angle; - - - - slit-to-image separation 55.92 cm, entrance slit focused for each angle; – - – - – slit-to-image separation 55.92 cm, fixed entrance slit focus at Xo = 400.00 cm.

Tables (2)

Tables Icon

Table I Values of the grating shifts (ΔZ) required to minimize coma for wavelengths at the plate center (λc) corresponding to grating angles (θ), calculated by Rosendahl’s cos3 relationship.

Tables Icon

Table II Minimum image widths (W) and corresponding best-focus position (Xo) calculated by the ray-tracing method for different values of the grating shift (ΔZ), for a wavelength in the 10th order of 5948 Å. The varying values of grating angle (θ) and mirror tilts (γ1 and γ2) required to keep this wavelength at the plate center are also given.