Abstract

The change in blaze wavelength as a function of position on a blazed concave diffraction grating surface is discussed. An experimental study of ruled and interferometric blazed concave gratings showed that the change in blaze across the grating surface is much less for an interferometric grating than for a ruled grating. Thus interferometric gratings can be expected to have a more uniform distribution of efficiency across their surfaces.

© 1981 Optical Society of America

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References

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  1. J. A. R. Samson, J. Opt. Soc. Am. 52, 525 (1962).
    [CrossRef]
  2. R. J. Meltzer, in Applied Optics and Optical Engineering, Vol. 5, R. Kingslake, Ed. (Academic, New York, 1969), pp. 65–67.
    [CrossRef]
  3. D. J. Michels, J. Opt. Soc. Am. 64, 622 (1974).
  4. M. Neviere, W. R. Hunter, Appl. Opt. 19, 2059 (1980).
    [CrossRef] [PubMed]
  5. D. J. Michels, T. L. Mikes, W. R. Hunter, Appl. Opt. 13, 1223 (1974).
    [CrossRef] [PubMed]

1980 (1)

1974 (2)

1962 (1)

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

J. A. R. Samson, J. Opt. Soc. Am. 52, 525 (1962).
[CrossRef]

D. J. Michels, J. Opt. Soc. Am. 64, 622 (1974).

Other (1)

R. J. Meltzer, in Applied Optics and Optical Engineering, Vol. 5, R. Kingslake, Ed. (Academic, New York, 1969), pp. 65–67.
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Grating in autocollimation for (a) ideal blazing and (b) actual blazing.

Fig. 2
Fig. 2

Diagram showing how to calculate the change in blaze angle for a ruled grating.

Fig. 3
Fig. 3

Idealized efficiency curve for a blazed grating.

Fig. 4
Fig. 4

Illustration of how measuring a concave blazed grating across its surface is equivalent to measuring a plane grating at different wavelengths. As the idealized efficiency curve is translated along the wavelength axis, the nonuniform efficiency curve for the concave grating can be constructed.

Fig. 5
Fig. 5

Efficiency measurements from a concave tripartite grating at three wavelengths in the VUV. Radius of curvature is 40 cm.3

Fig. 6
Fig. 6

Optical arrangement for recording an interference grating that will become blazed during the etching process.

Fig. 7
Fig. 7

Illustration of how the index of refraction of photoresist modifies the blaze characteristics of an interference grating.

Fig. 8
Fig. 8

Comparison of calculated efficiency maps, at a single wavelength, of ruled and interference gratings that are blazed.

Fig. 9
Fig. 9

Measured efficiency map of a conventional concave gold-coated grating at 562 Å. Angle of incidence was 10°, 1200 grooves/mm, and a 1-m radius of curvature.

Fig. 10
Fig. 10

Measured efficiency map of a blazed concave gold-coated interference grating at 412 Å. Angle of incidence was 10°, 1200 grooves/mm, and a 1-m radius of curvature.

Fig. 11
Fig. 11

Superimposition of the negative first-order efficiency maps of Figs. 9 and 10 to show how the change in blaze of an interference grating across its surface is less than that of a ruled grating.

Equations (8)

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sin θ = m λ B / 2 d .
cos θ θ = m λ B / 2 d ,
cot θ θ = λ B / λ B , or Δ λ B = λ B cot θ Δ θ ,
tan P S P = P Q / Q S Δ ω cos θ R cos θ - Δ ω sin θ = Δ ω / R - tan ( d θ ) ,
Δ λ B = λ B cot ( Δ ω / R ) .
sin θ = sin θ / n = λ 0 / 2 d n .
2 d sin R S O = λ 0 / n , that is , sin R S O = λ 0 / 2 d n , so that R S O = θ ,
sin - 1 ( 0.21 2 × 0.833 ) = sin - 1 ( 0.126 ) = 7 ° 1 4 ,

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