Abstract

It is possible by modern methods to shape the grooves of a grating in such a manner that a major portion of the incident flux is reflected into the desired order and wavelength region; but this wavelength region of high efficiency is small for gratings used in conventional mounts. By solving, simultaneously, the law of specular reflection and the grating diffraction law, it is possible to determine the conditions for working on the blaze, that wavelength region for which the direction of diffracted flux coincides with that of specularly reflected flux. It can be shown that by rotation of the grating in combination with rotation and translation of a plane mirror from which the diffracted flux is reflected, the grating may be used on the blaze over wide wavelength regions in a particular order. Design equations are derived and examples of visible and infrared applications are given. The system is particularly applicable to infrared spectrometry where ordinarily several gratings are required to cover the desired wavelength range.

© 1951 Optical Society of America

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References

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  1. R. W. Wood, Phil. Mag. 20, 770 (1910).
    [CrossRef]
  2. Richardson, Wiley, and Sheldon, J. Opt. Soc. Am. 40, 259 (1950).
  3. J. H. Greig and W. F. C. Ferguson, J. Opt. Soc. Am. 40, 504 (1950).
    [CrossRef]

1950 (2)

Richardson, Wiley, and Sheldon, J. Opt. Soc. Am. 40, 259 (1950).

J. H. Greig and W. F. C. Ferguson, J. Opt. Soc. Am. 40, 504 (1950).
[CrossRef]

1910 (1)

R. W. Wood, Phil. Mag. 20, 770 (1910).
[CrossRef]

Ferguson, W. F. C.

Greig, J. H.

Richardson,

Richardson, Wiley, and Sheldon, J. Opt. Soc. Am. 40, 259 (1950).

Sheldon,

Richardson, Wiley, and Sheldon, J. Opt. Soc. Am. 40, 259 (1950).

Wiley,

Richardson, Wiley, and Sheldon, J. Opt. Soc. Am. 40, 259 (1950).

Wood, R. W.

R. W. Wood, Phil. Mag. 20, 770 (1910).
[CrossRef]

J. Opt. Soc. Am. (2)

Richardson, Wiley, and Sheldon, J. Opt. Soc. Am. 40, 259 (1950).

J. H. Greig and W. F. C. Ferguson, J. Opt. Soc. Am. 40, 504 (1950).
[CrossRef]

Phil. Mag. (1)

R. W. Wood, Phil. Mag. 20, 770 (1910).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic defining the relative positions of the grating and plane mirror. i=central ray of incident beam, d=central ray of diffracted beam, r=central ray of beam reflected from plane mirror, D=separation (perpendicular) of incident and reflected beams, N=normal to grating surface, α=angle of incidence measured from grating normal, β=angle of diffraction measured from grating normal, ϕ=angle between incident and diffracted beams, n=normal to illuminated groove faces, ψ=angle to which the grooves are cut relative to the grating surface, γ=angle between the plane mirror surface and the central ray of the reflected beam, and x=translation of the plane mirror along the direction of the reflected beam.

Fig. 2
Fig. 2

Angles of incidence and diffraction and motions of grating and plane mirror as functions of wavelength. 600 grooves/mm; a=1.67μ, 1850A to 6430A: ψ=11°20′; and 4225A to 10,000A: ψ=18°30′. (The λ at the top of the right-hand abscissa should be X).

Fig. 3
Fig. 3

Mechanical linkage for rotating the grating and translating and rotating the plane mirror as functions of wavelength. The displacement y is linearly proportional to the wavelength setting.

Fig. 4a
Fig. 4a

Schematic showing parabolic mirrors as collimating and focusing elements.

Fig. 4b
Fig. 4b

Positions of the grating and plane mirror for two different wavelengths.

Equations (35)

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ψ = ( α ± β ) / 2 ,
m λ = a ( sin α ± sin β ) ,
ψ = ( α - β ) / 2 ,
m λ = a ( sin α - sin β ) .
β = cos - 1 ( m λ / 2 a sin ψ ) - ψ ,
α = cos - 1 ( m λ / 2 a sin ψ ) + ψ ,
ϕ = α + β = 2 cos - 1 ( m λ / 2 a sin ψ ) .
α = cos - 1 ( m λ / 2 a sin ψ ) + ψ ,
γ = ϕ / 2 = cos - 1 ( m λ / 2 a sin ψ ) ,
X = D tan ( ϕ - 90 ° ) ,
[ cos - 1 ( m λ / 2 a sin ψ ) + ψ ] 85 ° .
β 0.
cos - 1 ( m λ / 2 a sin ψ ) - ψ 0 ,             cos ψ ( m λ / 2 a sin ψ ) .
α = 2 ψ + β ,
m λ / 2 a sin ψ 1.
sin ψ cos ( 85 ° - ψ ) m λ / 2 a sin ψ cos ψ .
2 sin ψ cos ( 85 ° - ψ ) m λ / a sin 2 ψ ,
sin ψ cos ( 85 ° - ψ ) = m λ min / 2 a .
λ max = a sin 2 ψ / m .
sin 2 ψ = m λ max / a .
λ min = 2 a sin ψ cos ( 85 ° - ψ ) / m .
m = 1 , a = 1.67 microns .
sin ψ cos ( 85 ° - ψ ) = m λ min / 2 a = 0.055.
ψ = 11 ° 20 .
λ max = a sin 2 ψ / m = 6430 A .
sin 2 ψ = m λ max / a = 0.600 , ψ = 18 ° 30 .
λ min = 2 a sin ψ cos ( 85 ° - ψ ) m = 4225 A .
m = 1 , a = 3.34 microns .
ψ = 7 ° 30 , λ max = 8650 A .
ψ = 8 ° 40 , λ min = 2380 A .
m = 1 , a = 6.67 microns .
ψ = 4 ° 40 , λ max = 10 , 800 A .
ψ = 4 ° 20 , λ min = 1640 A .
m = 1 , a = 16.7 microns , ψ = 7 ° 50 : 1.0 microns - 4.5 microns range of operation , and ψ = 18 ° 30 : 4.2 microns - 10.0 microns range of operation .
m = 1 , a = 62.5 microns , ψ = 3 ° 10 : 1.0 microns - 7.0 microns range of operation , and ψ = 11 ° 35 : 7.2 microns - 25.0 microns range of operation .