Abstract

The previous paper ( Wm. G. FastieJ. Opt. Soc. Am. 42, 641 ( 1952)) described a plane grating monochromator optical system which apparently has not been used since Ebert described it in 1889. The high resolution obtained has inspired the design of an f/6 spectrometer of that type for the infrared region. This paper describes the results of preliminary tests and calculations which show that the Ebert system is capable of near theoretical resolution at f/6 even when very long slits are used. Both slits must be curved in order to remove the effect of astigmatism and to avoid wavelength errors at the exit slit which arise from curvature of spectrum when a plane grating is employed. That the same curvature of slits simultaneously corrects these two image errors is a fortunate coincidence which makes the Ebert system appear to be superior to currently employed spectrometer optical systems. Comparison with other systems and discussion of the limitations of the Ebert system are presented.

© 1952 Optical Society of America

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References

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  1. Wm. G. Fastie, J. Opt. Soc. Am. 42, 641 (1952).
    [CrossRef]
  2. H. Ebert, Wied. Ann. 38, 489 (1889).
    [CrossRef]
  3. W. Benesch and J. Strong, J. Opt. Soc. Am. 41, 252 (1951).
    [CrossRef]
  4. M. Czerny and A. F. Turner, Zeits. Physik 61, 792 (1930).
    [CrossRef]

1952 (1)

1951 (1)

1930 (1)

M. Czerny and A. F. Turner, Zeits. Physik 61, 792 (1930).
[CrossRef]

1889 (1)

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

Benesch, W.

Czerny, M.

M. Czerny and A. F. Turner, Zeits. Physik 61, 792 (1930).
[CrossRef]

Ebert, H.

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

Fastie, Wm. G.

Strong, J.

Turner, A. F.

M. Czerny and A. F. Turner, Zeits. Physik 61, 792 (1930).
[CrossRef]

J. Opt. Soc. Am. (2)

Wied. Ann. (1)

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

Zeits. Physik (1)

M. Czerny and A. F. Turner, Zeits. Physik 61, 792 (1930).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Optical diagram of f/6 spectrometer.

Fig. 2
Fig. 2

Geometrical relationship between exit slit and line image of a point at the end of the entrance slit.

Fig. 3
Fig. 3

Geometrical relationship between line image dL of point a on circular exit slit.

Fig. 4
Fig. 4

Skew ray diagram to describe interference relationship between adjacent facets.

Fig. 5
Fig. 5

Limitation on l value imposed by curvature of the spectrum when straight slits are used. Crosses indicate best resolving power obtained in various wavelength regions by five different spectroscopists using straight slits.

Fig. 6
Fig. 6

Geometrical relationship between extreme and central rays. The extreme rays R1 and R3 are parallel after reflecting from the concave mirror. The central ray R2 is not parallel to R1 and R3 after reflecting from the concave mirror. The point A is the center of curvature of the concave mirror.

Fig. 7
Fig. 7

Relationship between f number of Ebert spectrometer and resolving power. When the f number is small the resolution is limited because of curvature of the wave front incident on the grating.

Equations (15)

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E ~ L d A / F 2 ,
E ~ L A / F ~ A l .
d F = 0.4 F φ 2 ,
d L = d F / f = 0.4 W φ 2 = 0.1 W / f 2 .
w d = F λ / W = f λ .
w a = L d L / W = f λ = W d .
L = 10 λ f 3 .
w a = d L 2 / 8 W .
n λ = 2 t cos φ .
n λ = 2 a sin θ cos φ .
n λ = 2 a sin θ [ 1 - W 2 + L 2 8 F 2 ] ,
d λ = a L 2 sin θ / 4 n F 2 ,
d λ = λ L 2 / 8 F 2 = λ l 2 / 8.
l = ( 8 / R ) 1 2 .
1 / R = cos tan - 1 ( 1 / 2 f ) - cos 2 sin - 1 ( 1 / 4 f ) .