Abstract

A design for a new plane grating monochromator is described. The system employs a symmetrical configuration of off-axis paraboloids for both the collimator and camera mirrors. The entrance and exit slits are mounted on the same side of the grating and are curved in order to eliminate wavelength errors due to spectral line curvature. There is, in fact, a remarkable coincidence between the curvature which is required to avoid wavelength errors and the curvature which is required to obtain equal curvatures in the object and image planes. Ray tracing calculations for a symmetrical configuration of off-axis paraboloids show that the image of a curved slit with a length equal to 0.05 times the focal length of an f/5 mirror is diffraction limited for wavelengths λ > 0.2 μ.

© 1969 Optical Society of America

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References

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  1. W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
    [CrossRef]
  2. M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
    [CrossRef]
  3. H. Ebert, Wied. Ann. 38, 489 (1889).
    [CrossRef]
  4. W. G. Fastie, J. Opt. Soc. Amer. 42, 647 (1952).
    [CrossRef]
  5. W. G. Fastie, J. Opt. Soc. Amer. 43, 1174 (1953).
    [CrossRef]
  6. R. A. Hill, Appl. Opt. 7, 2184 (1968).
    [CrossRef] [PubMed]
  7. C. A. Lehman, LASL Lens Design Program for the IBM 7090, Los Alamos Scientific Laboratory Rep. LA–2837 (1963).
    [PubMed]

1968 (1)

1953 (1)

W. G. Fastie, J. Opt. Soc. Amer. 43, 1174 (1953).
[CrossRef]

1952 (2)

W. G. Fastie, J. Opt. Soc. Amer. 42, 647 (1952).
[CrossRef]

W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
[CrossRef]

1930 (1)

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

1889 (1)

H. Ebert, Wied. Ann. 38, 489 (1889).
[CrossRef]

Czerny, M.

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

Ebert, H.

H. Ebert, Wied. Ann. 38, 489 (1889).
[CrossRef]

Fastie, W. G.

W. G. Fastie, J. Opt. Soc. Amer. 43, 1174 (1953).
[CrossRef]

W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
[CrossRef]

W. G. Fastie, J. Opt. Soc. Amer. 42, 647 (1952).
[CrossRef]

Hill, R. A.

Lehman, C. A.

C. A. Lehman, LASL Lens Design Program for the IBM 7090, Los Alamos Scientific Laboratory Rep. LA–2837 (1963).
[PubMed]

Turner, A. F.

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Amer. (3)

W. G. Fastie, J. Opt. Soc. Amer. 42, 641 (1952).
[CrossRef]

W. G. Fastie, J. Opt. Soc. Amer. 42, 647 (1952).
[CrossRef]

W. G. Fastie, J. Opt. Soc. Amer. 43, 1174 (1953).
[CrossRef]

Wied. Ann. (1)

H. Ebert, Wied. Ann. 38, 489 (1889).
[CrossRef]

Z. Phys. (1)

M. Czerny, A. F. Turner, Z. Phys. 61, 792 (1930).
[CrossRef]

Other (1)

C. A. Lehman, LASL Lens Design Program for the IBM 7090, Los Alamos Scientific Laboratory Rep. LA–2837 (1963).
[PubMed]

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Figures (11)

Fig. 1
Fig. 1

(a) A symmetrical system of off-axis paraboloids; (b) an unsymmetrical system of off-axis paraboloids; (c) definition of coordinates and parameters for the ray tracing calculations.

Fig. 2
Fig. 2

rms Δy image widths as a function of the image plane coordinate z for points on a straight slit at x = 0 mm, 5 mm, and 10 mm.

Fig. 3
Fig. 3

Images of a 20-mm straight slit as photographed for both symmetrical (a) and unsymmetrical (b) configurations of 381-mm focal length, 13.308° off-axis paraboloids at f/5.

Fig. 4
Fig. 4

Ray diagram showing the object and image planes for a symmetrical configuration of off-axis paraboloids. The slit curvature is toward the collimated light in (a).

Fig. 5
Fig. 5

rms Δy image widths as a function of the image plane coordinate z for points on a curved slit at x = 0 mm, 5 mm, 10 mm, and 15 mm for a symmetrical configuration of 381-mm focal length, 13.308° off-axis paraboloids. The vertical dashed lines represent the z coordinates of the four points in the object plane while the solid lines represent the z coordinates of the four points in the image plane at best focus.

Fig. 6
Fig. 6

rms Δy image widths as a function of the image plane coordinate z for points on a curved slit at x = 0 mm, 5 mm, …25 mm for a symmetrical configuration of 1016-mm focal length, 8.578° off-axis paraboloids. The vertical dashed lines represent the z coordinates of the six points in the object plane.

Fig. 7
Fig. 7

The grating cone defines a surface along which both central rays (a, b, and c) of the incident collimated light and the central rays (a′, b′, and c′) of the diffracted light must travel if wavelength errors due to spectral line curvature are to be avoided at all grating positions. The intersection of the grating cone with the collimator and camera mirrors defines the radius of curvature of the entrance and exit slits, respectively.

Fig. 8
Fig. 8

Design for a monochromator using a symmetrical configuration of off-axis paraboloids. The grating cone has an apex angle 2α, where α is the off-axis angle of the paraboloids. The length of one side of the grating cone is (f + y02/4f), a distance equal to that from the slit to the paraboloid surface as measured along the central ray. The slits lie in planes parallel to the base of the grating cone and have radii of curvature equal to that of the cone base.

Fig. 9
Fig. 9

Light path through the monochromator. G is a plane grating; P1 and P2 are off-axis paraboloids, S1 and S2 are the slits, and M is a flat pick-off mirror. A larger separation of the paraboloids and the slits can be obtained with paraboloids having a larger off-axis angle α.

Fig. 10
Fig. 10

Errors in the x and y image plane coordinates resulting from the use of curved slits having r0y0. For r0 < y0, the radius of curvature in the image plane ri < r0. For r0 > y0, the radius of curvature in the image plane ri < r0. To within the accuracy of the calculations, ± 0.0001 mm, the radii of curvature in the object and image planes are equal only if r0 = y0.

Fig. 11
Fig. 11

The resolving power as a function of the off-axis distance x along the curved slit. The resolving power is calculated from R = (tanΔα)−1, where Δα is the rms angular spread in the rays from the collimator mirror.

Tables (2)

Tables Icon

Table I Object and Image Coordinates for a Symmetrical System of 13.308° Off-Axis, 381-mm Focal Length Paraboloids

Tables Icon

Table II Object and Image Coordinates for a Symmetrical System of 8.5780 Off-Axis, 1016-mm Focal Length Paraboloids

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