Abstract

Measurements and calculations have been made to investigate the effects due to the change in groove orientation on efficiencies of gratings ruled on a spherical surface. Typical efficiency maps across the surface are given for various angles of incidence and wavelengths in the VUV and UV regions. Computations based on electromagnetic theory show a good agreement with the experimental data over the 150-2500-Å wavelength range. A simple explanation is given to interpret and predict the shape of efficiency maps obtained from both theory and experiments.

© 1980 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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, 662 (1974).
    [CrossRef]
  4. D. J. Michels, T. L. Mkikes, W. R. Hunter, Appl. Opt. 13, 1223 (1974).
    [CrossRef] [PubMed]
  5. W. Liller, Appl. Opt. 2, 187 (1963).
    [CrossRef]
  6. P. Facq, these d'État, Limoges, France (1977).
  7. D. Maystre, J. Opt. Soc. Am. 68, 490 (1978).
    [CrossRef]
  8. M. Neviere, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
    [CrossRef]
  9. E. G. Loewen, M. Neviere, Appl. Opt. 17, 1087 (1978).
    [CrossRef] [PubMed]
  10. E. G. Loewen, M. Neviere, D. Maystre, J. Opt. Soc. Am. 68, 496 (1978).
    [CrossRef]
  11. M. Neviere, D. Maystre, W. R. Hunter, J. Opt. Soc. Am. 68, 1106 (1978).
    [CrossRef]
  12. D. Maystre, R. Petit, Nouv. Rev. Opt. 7, 165 (1976).
    [CrossRef]

1978 (4)

1976 (1)

D. Maystre, R. Petit, Nouv. Rev. Opt. 7, 165 (1976).
[CrossRef]

1974 (3)

1963 (1)

1962 (1)

Facq, P.

P. Facq, these d'État, Limoges, France (1977).

Hunter, W. R.

Liller, W.

Loewen, E. G.

Maystre, D.

Meltzer, R. J.

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

Michels, D. J.

Mkikes, T. L.

Neviere, M.

Petit, R.

D. Maystre, R. Petit, Nouv. Rev. Opt. 7, 165 (1976).
[CrossRef]

M. Neviere, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
[CrossRef]

Samson, J. A. R.

Vincent, P.

M. Neviere, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Orientation of grating during measurements. Angle of incidence is angle between incident beam and normal N to grating surface at its center. Efficiency maps are obtained by recording the signal as the grating is translated past the incident beam in direction of scan.

Fig. 2
Fig. 2

Efficiency maps of blazed grating at 2530 Å at different angles of incidence. Abscissa represents ruled area, which extends from B where blaze angle is smallest to A where it is largest, a distance of 50 mm. Grating coating is Al + MgF2, radius of curvature is nominally 1 m, and groove density is 600/mm.

Fig. 3
Fig. 3

Efficiency maps of grating of Fig. 2 at +30° angle of incidence for three different wavelengths: 2530,1608, and 1216 Å. For measurements at 584 Å, another replica grating from the same master was used with a gold coating.

Fig. 4
Fig. 4

Theoretical efficiency curves for grating of Fig. 2.

Fig. 5
Fig. 5

Theoretical efficiency curves for grating of Fig. 3.

Fig. 6
Fig. 6

RWF mounting for positive angles of incidence. Angles θ and θn are always positive.

Fig. 7
Fig. 7

RWF mounting for negative angles of incidence.

Fig. 8
Fig. 8

Measured efficiency vs wavelength for 0th, 1st, 2nd, and 3rd orders of a gold-coated holographic grating with sinusoidal groove profiles, 1-m radius of curvature, and 1200 grooves/mm. Depth of grooves is 520 Å, angle of incidence, 80°.

Fig. 9
Fig. 9

Theoretical efficiencies for 0th, 1st, and 2nd orders of holographic grating of Fig. 8.

Fig. 10
Fig. 10

Measured efficiency vs wavelength for 0th, 1st, and 2nd orders of a gold, conventionally ruled, blazed grating with a 1-m radius of curvature 1200 grooves/mm and a blaze angle of 2.6°. Angle of incidence is 80°. Dashed lines represent efficiencies of the holographic grating of Fig. 8.

Fig. 11
Fig. 11

Theoretical efficiencies for 0th, 1st, and 2nd orders of conventional grating of Fig. 10.

Tables (1)

Tables Icon

Table I Values of αn Computed for Concave Grating used in Experiments for Several Wavelengths, Angles of Incidence, and Spectral Orders Corresponding to Curves of Figs. 4 and 5

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

n = R ( φ ) min ( cos θ n cos θ , cos θ cos θ n ) .
θ n = θ + 2 α .
sin θ n = sin θ + n λ / d ,
sin ( φ + α ) = sin ( φ α ) + n λ / d , 2 sin α cos φ = + n λ / d , λ = ( 2 d / n ) sin α cos φ .
α = ( ½ ) [ arcsin n λ / d + sin θ ) θ ] ;
n = ( d / λ ) sin ( θ + 2 α ) sin θ ] .
λ = [ 2 d / ( + n ) ] sin α cos φ ,
sin ( 2 α + θ ) = sin θ + n λ / d , α = ( ½ ) [ arcsin ( sin θ + n λ / d ) θ ] .

Metrics