Abstract

A new formula has been developed and verified to account for the location of possible anomalous behavior of a plane diffraction grating when illuminated at skew incidence as in the Grieg and Ferguson mounting. It is shown that for their mounting, in contrast to both Littrow and Ebert mountings, blaze angles can be chosen which eliminate possible anomalous behavior in the observed spectra.

© 1968 Optical Society of America

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References

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  1. J. H. Greig, W. F. C. Ferguson, J. Opt. Soc. Am. 40, 504 (1950).
    [CrossRef]
  2. C. H. Palmer, J. Opt. Soc. Am. 42, 269 (1952).
    [CrossRef]
  3. C. H. Palmer, J. Opt. Soc. Am. 53, 1005 (1963).
    [CrossRef]

1963 (1)

1952 (1)

1950 (1)

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Figures (2)

Fig. 1
Fig. 1

Terminology. The incident ray makes angles a1, b1, and c1 with the x, y, and z axes, respectively; the diffracted ray makes angles a2, b2, and c2 with these axes. For clarity these angles have been omitted in the figure.

Fig. 2
Fig. 2

Angular relations between the direction angles a1, b1, and c1 and the measured angles θ, ϕ1. The angles are indicated as arcs on part of a unit sphere.

Tables (3)

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Table I Possible Anomalous Angles, Any Grating

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Table II Anomalies for Grating C

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Table III Comparison of Theory and Experiment

Equations (8)

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n λ = - d ( cos c 1 + cos c 2 ) ,
cos a 1 = - cos a 2 ,
N λ = - d [ cos c 1 ± ( 1 - cos 2 a 1 ) 1 2 ] .             General equation for anomalies
n λ = - 2 d cos ϕ sin θ .             Grating equation
N λ = - d { cos ϕ 1 sin θ ± [ 1 - cos 2 ( 90° - ϕ 1 ) ] 1 2 }
N λ = - d cos ϕ 1 ( sin θ ± 1 ) .             Anomaly equation
sin θ = ± n / ( 2 N - n ) .             Possible anomalous angles
- 2 d / λ n + 2 d / λ .             Possible number of orders

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