Abstract

Measurement of optical properties in the VUV depends on photometric data rather than a mixture of photometric and relative phase data. Generally the measurement technique is that of measuring the reflected intensity at a number of angles of incidence and fitting these data to a calculated reflectance curve. The actual measured reflectance values need not always be known but are helpful in the final analysis of the data. Other more specialized methods include a critical angle method and the determination of extinction coefficients from transmittance measurements. The accuracy of the reflectance methods depends on the optical properties of the material being measured and the angles of incidence at which reflectance measurements are made. Instrumental errors and the condition of the surface being measured can also cause appreciable errors in the results. Accurate values of the optical constants can be used to characterize the electronic structure of a material and to design special reflecting and transmitting coatings for use in EUV astronomy and laboratory applications and possibly for use with excimer lasers in the VUV.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Shea, Wied. Ann. 47, 177 (1892).
    [CrossRef]
  2. C. Boeckner, J. Opt. Soc. Am. 19, 7 (1919).
    [CrossRef]
  3. R. Tousey, J. Opt. Soc. Am. 29, 235 (1939).
    [CrossRef]
  4. J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
    [CrossRef]
  5. I. Simon, J. Opt. Soc. Am. 41, 336 (1951).
    [CrossRef]
  6. D. G. Avery, Proc. Phys. Soc. London 65, 425 (1952).
    [CrossRef]
  7. S. P. F. Humphreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
    [CrossRef]
  8. T. Sasaki, K. Ishiguro, Jpn. J. Appl. Phys. 2, 289 (1963).
    [CrossRef]
  9. A. P. Prishivalko, Reflection of Light from Absorbing Media (Akad. Nauk SSR, Minsk, 1963).
  10. A. Vasicek, Tables of Determination of Optical Constants from the Intensities of Reflected Light (Nakladatelstvi Ceskoslovenske Akad. Vec, Prague, 1964).
  11. D. W. Juenker, J. Opt. Soc. Am. 55, 295 (1965).
    [CrossRef]
  12. W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
    [CrossRef]
  13. G. Hass, U.S. Army Electronics and Development Command, Night Vision and Electro-Optics Laboratory, Fort Belvoir, Va.; private communication.
  14. G. Hass, in Applied Optics and Optical Engineering, Vol. 3, Optical Components, R. Kingslake, Ed. (Academic, New York, 1965), pp. 319–320.
  15. W. R. Hunter, Appl. Opt. 6, 2140 (1967).
    [CrossRef] [PubMed]
  16. G. R. Field, E. Murphy, Appl. Opt. 10, 1402 (1971).
    [CrossRef] [PubMed]
  17. W. R. Hunter, G. Hass, J. Opt. Soc. Am. 64, 429 (1974).
    [CrossRef]
  18. D. Pines, Rev. Mod. Phys. 28, 184 (1956).
    [CrossRef]
  19. C. Zener, Nature London 132, 968 (1933).
    [CrossRef]
  20. W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964).
    [CrossRef]
  21. U. S. Whang, R. N. Hamm, E. T. Arakawa, M. W. Williams, J. Opt. Soc. Am. 63, 305 (1973).
    [CrossRef]
  22. M. W. Williams, E. T. Arakawa, Appl. Opt. 18, 1477 (1979).
    [CrossRef] [PubMed]
  23. W. R. Hunter, J. Phys. Paris 25, 154 (1964).
  24. G. Hass, W. R. Hunter, R. Tousey, J. Opt. Soc. Am. 47, 120A (1957).
  25. W. R. Hunter, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 136.
  26. W. R. Hunter, R. Tousey, J. Phys. Paris 25, 148 (1964).
  27. W. R. Hunter, in Physics of Thin Films, Vol. 7, G. Hass, M. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1973), p. 43.
  28. G. N. Steele, Luxel Corp., 515 Tucker Ave., Friday Harbor, Wash.; private communication.
  29. C. Kunz, DESY HASYLAB, Notkestieg 1, Hamburg 52, Germany; private communication.
  30. L. R. Canfield, G. Hass, J. E. Waylonis, Appl. Opt. 5, 45 (1966).
    [CrossRef] [PubMed]
  31. J. T. Cox, G. Hass, J. E. Waylonis, Appl. Opt. 7, 1535 (1968).
    [CrossRef] [PubMed]
  32. G. Hass, W. R. Hunter, in Space Optics, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, D.C., 1974), p. 525.
  33. W. R. Hunter, T. L. Mikes, G. Hass, Appl. Opt. 11, 1594 (1972).
    [CrossRef] [PubMed]
  34. G. Hass, W. R. Hunter, Appl. Opt. 17, 76 (1978).
    [CrossRef] [PubMed]
  35. W. R. Hunter, Naval Research Laboratory, Washington, D.C.; unpublished data.
  36. J. F. Osantowski, Goddard Space Flight Center, Greenbelt, Md.; private communication.
  37. D. Fabre, J. Romand, B. Vodar, J. Phys. Rad. 21, 263 (1960).
    [CrossRef]
  38. D. Fabre, J. Romand, J. Phys. Rad. 22, 324 (1961).
    [CrossRef]
  39. A. Daude, A. Savary, A. Seignac, S. Robin, Opt. Acta 20, 353 (1973).
    [CrossRef]
  40. G. Hass, R. Tousey, J. Opt. Soc. Am. 49, 593 (1959).
    [CrossRef]
  41. D. W. Angel, W. R. Hunter, R. Tousey, G. Hass, J. Opt. Soc. Am. 51, 913 (1961).
    [CrossRef]
  42. W. R. Hunter, Opt. Acta 9, 255 (1962).
    [CrossRef]
  43. E. Spiller, in Space Optics, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, D.C., 1974), p. 581.
  44. E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
    [CrossRef]
  45. G. Hass, G. F. Jacobus, W. R. Hunter, J. Opt. Soc. Am. 57, 758 (1967).
    [CrossRef]
  46. A. Malherbe, Nouv. Rev. Opt. Appl. 2, 337 (1971).
    [CrossRef]
  47. B. Flint, Acton Research Corp., Acton, Mass.; private communication.
  48. D. J. Schroeder, J. Opt. Soc. Am. 52, 1380 (1962).
    [CrossRef]
  49. B. Bates, D. J. Bradley, Appl. Opt. 5, 971 (1966).
    [CrossRef] [PubMed]
  50. D. H. Harrison, Appl. Opt. 7, 210 (1968).
    [CrossRef] [PubMed]
  51. A. Malherbe, M. Guillard, Nouv. Rev. Opt. Appl. 1, 410 (1970).
    [CrossRef]
  52. G. Rosenbaum, B. Feuerbacher, R. P. Godwin, M. Skibowski, Appl. Opt. 7, 1917 (1968).
    [CrossRef] [PubMed]
  53. D. W. Lynch, J. Phys. [Colloque C5, supplement to 38 (11), C5-21], 1977.

1980

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

1979

1978

1977

D. W. Lynch, J. Phys. [Colloque C5, supplement to 38 (11), C5-21], 1977.

1974

1973

1972

1971

1970

A. Malherbe, M. Guillard, Nouv. Rev. Opt. Appl. 1, 410 (1970).
[CrossRef]

1968

1967

1966

1965

1964

W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964).
[CrossRef]

W. R. Hunter, R. Tousey, J. Phys. Paris 25, 148 (1964).

W. R. Hunter, J. Phys. Paris 25, 154 (1964).

1963

T. Sasaki, K. Ishiguro, Jpn. J. Appl. Phys. 2, 289 (1963).
[CrossRef]

1962

1961

D. Fabre, J. Romand, J. Phys. Rad. 22, 324 (1961).
[CrossRef]

S. P. F. Humphreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

D. W. Angel, W. R. Hunter, R. Tousey, G. Hass, J. Opt. Soc. Am. 51, 913 (1961).
[CrossRef]

1960

D. Fabre, J. Romand, B. Vodar, J. Phys. Rad. 21, 263 (1960).
[CrossRef]

1959

1957

G. Hass, W. R. Hunter, R. Tousey, J. Opt. Soc. Am. 47, 120A (1957).

1956

D. Pines, Rev. Mod. Phys. 28, 184 (1956).
[CrossRef]

1952

D. G. Avery, Proc. Phys. Soc. London 65, 425 (1952).
[CrossRef]

1951

1943

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

1939

1933

C. Zener, Nature London 132, 968 (1933).
[CrossRef]

1919

1892

D. Shea, Wied. Ann. 47, 177 (1892).
[CrossRef]

Angel, D. W.

Arakawa, E. T.

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. London 65, 425 (1952).
[CrossRef]

Bates, B.

Bock, R. O.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

Boeckner, C.

Bradley, D. J.

Canfield, L. R.

Collins, J. R.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

Cox, J. T.

Daude, A.

A. Daude, A. Savary, A. Seignac, S. Robin, Opt. Acta 20, 353 (1973).
[CrossRef]

Fabre, D.

D. Fabre, J. Romand, J. Phys. Rad. 22, 324 (1961).
[CrossRef]

D. Fabre, J. Romand, B. Vodar, J. Phys. Rad. 21, 263 (1960).
[CrossRef]

Feuerbacher, B.

Field, G. R.

Flint, B.

B. Flint, Acton Research Corp., Acton, Mass.; private communication.

Godwin, R. P.

Guillard, M.

A. Malherbe, M. Guillard, Nouv. Rev. Opt. Appl. 1, 410 (1970).
[CrossRef]

Haelbich, R-P.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

Hamm, R. N.

Harrison, D. H.

Hass, G.

G. Hass, W. R. Hunter, Appl. Opt. 17, 76 (1978).
[CrossRef] [PubMed]

W. R. Hunter, G. Hass, J. Opt. Soc. Am. 64, 429 (1974).
[CrossRef]

W. R. Hunter, T. L. Mikes, G. Hass, Appl. Opt. 11, 1594 (1972).
[CrossRef] [PubMed]

J. T. Cox, G. Hass, J. E. Waylonis, Appl. Opt. 7, 1535 (1968).
[CrossRef] [PubMed]

G. Hass, G. F. Jacobus, W. R. Hunter, J. Opt. Soc. Am. 57, 758 (1967).
[CrossRef]

L. R. Canfield, G. Hass, J. E. Waylonis, Appl. Opt. 5, 45 (1966).
[CrossRef] [PubMed]

D. W. Angel, W. R. Hunter, R. Tousey, G. Hass, J. Opt. Soc. Am. 51, 913 (1961).
[CrossRef]

G. Hass, R. Tousey, J. Opt. Soc. Am. 49, 593 (1959).
[CrossRef]

G. Hass, W. R. Hunter, R. Tousey, J. Opt. Soc. Am. 47, 120A (1957).

G. Hass, U.S. Army Electronics and Development Command, Night Vision and Electro-Optics Laboratory, Fort Belvoir, Va.; private communication.

G. Hass, in Applied Optics and Optical Engineering, Vol. 3, Optical Components, R. Kingslake, Ed. (Academic, New York, 1965), pp. 319–320.

G. Hass, W. R. Hunter, in Space Optics, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, D.C., 1974), p. 525.

Humphreys-Owen, S. P. F.

S. P. F. Humphreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

Hunter, W. R.

G. Hass, W. R. Hunter, Appl. Opt. 17, 76 (1978).
[CrossRef] [PubMed]

W. R. Hunter, G. Hass, J. Opt. Soc. Am. 64, 429 (1974).
[CrossRef]

W. R. Hunter, T. L. Mikes, G. Hass, Appl. Opt. 11, 1594 (1972).
[CrossRef] [PubMed]

G. Hass, G. F. Jacobus, W. R. Hunter, J. Opt. Soc. Am. 57, 758 (1967).
[CrossRef]

W. R. Hunter, Appl. Opt. 6, 2140 (1967).
[CrossRef] [PubMed]

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
[CrossRef]

W. R. Hunter, J. Phys. Paris 25, 154 (1964).

W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964).
[CrossRef]

W. R. Hunter, R. Tousey, J. Phys. Paris 25, 148 (1964).

W. R. Hunter, Opt. Acta 9, 255 (1962).
[CrossRef]

D. W. Angel, W. R. Hunter, R. Tousey, G. Hass, J. Opt. Soc. Am. 51, 913 (1961).
[CrossRef]

G. Hass, W. R. Hunter, R. Tousey, J. Opt. Soc. Am. 47, 120A (1957).

W. R. Hunter, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 136.

W. R. Hunter, in Physics of Thin Films, Vol. 7, G. Hass, M. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1973), p. 43.

W. R. Hunter, Naval Research Laboratory, Washington, D.C.; unpublished data.

G. Hass, W. R. Hunter, in Space Optics, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, D.C., 1974), p. 525.

Ishiguro, K.

T. Sasaki, K. Ishiguro, Jpn. J. Appl. Phys. 2, 289 (1963).
[CrossRef]

Jacobus, G. F.

Juenker, D. W.

Kunz, C.

C. Kunz, DESY HASYLAB, Notkestieg 1, Hamburg 52, Germany; private communication.

Lynch, D. W.

D. W. Lynch, J. Phys. [Colloque C5, supplement to 38 (11), C5-21], 1977.

Malherbe, A.

A. Malherbe, Nouv. Rev. Opt. Appl. 2, 337 (1971).
[CrossRef]

A. Malherbe, M. Guillard, Nouv. Rev. Opt. Appl. 1, 410 (1970).
[CrossRef]

Mikes, T. L.

Murphy, E.

Osantowski, J. F.

J. F. Osantowski, Goddard Space Flight Center, Greenbelt, Md.; private communication.

Pines, D.

D. Pines, Rev. Mod. Phys. 28, 184 (1956).
[CrossRef]

Prishivalko, A. P.

A. P. Prishivalko, Reflection of Light from Absorbing Media (Akad. Nauk SSR, Minsk, 1963).

Rife, J.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

Robin, S.

A. Daude, A. Savary, A. Seignac, S. Robin, Opt. Acta 20, 353 (1973).
[CrossRef]

Romand, J.

D. Fabre, J. Romand, J. Phys. Rad. 22, 324 (1961).
[CrossRef]

D. Fabre, J. Romand, B. Vodar, J. Phys. Rad. 21, 263 (1960).
[CrossRef]

Rosenbaum, G.

Sasaki, T.

T. Sasaki, K. Ishiguro, Jpn. J. Appl. Phys. 2, 289 (1963).
[CrossRef]

Savary, A.

A. Daude, A. Savary, A. Seignac, S. Robin, Opt. Acta 20, 353 (1973).
[CrossRef]

Schroeder, D. J.

Segmuller, A.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

Seignac, A.

A. Daude, A. Savary, A. Seignac, S. Robin, Opt. Acta 20, 353 (1973).
[CrossRef]

Shea, D.

D. Shea, Wied. Ann. 47, 177 (1892).
[CrossRef]

Simon, I.

Skibowski, M.

Spiller, E.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

E. Spiller, in Space Optics, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, D.C., 1974), p. 581.

Steele, G. N.

G. N. Steele, Luxel Corp., 515 Tucker Ave., Friday Harbor, Wash.; private communication.

Tousey, R.

Vasicek, A.

A. Vasicek, Tables of Determination of Optical Constants from the Intensities of Reflected Light (Nakladatelstvi Ceskoslovenske Akad. Vec, Prague, 1964).

Vodar, B.

D. Fabre, J. Romand, B. Vodar, J. Phys. Rad. 21, 263 (1960).
[CrossRef]

Waylonis, J. E.

Whang, U. S.

Williams, M. W.

Zener, C.

C. Zener, Nature London 132, 968 (1933).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

E. Spiller, A. Segmuller, J. Rife, R-P. Haelbich, Appl. Phys. Lett. 37, 1048 (1980).
[CrossRef]

J. Opt. Soc. Am.

J. Phys.

D. W. Lynch, J. Phys. [Colloque C5, supplement to 38 (11), C5-21], 1977.

J. Phys. Paris

W. R. Hunter, J. Phys. Paris 25, 154 (1964).

W. R. Hunter, R. Tousey, J. Phys. Paris 25, 148 (1964).

J. Phys. Rad.

D. Fabre, J. Romand, B. Vodar, J. Phys. Rad. 21, 263 (1960).
[CrossRef]

D. Fabre, J. Romand, J. Phys. Rad. 22, 324 (1961).
[CrossRef]

Jpn. J. Appl. Phys.

T. Sasaki, K. Ishiguro, Jpn. J. Appl. Phys. 2, 289 (1963).
[CrossRef]

Nature London

C. Zener, Nature London 132, 968 (1933).
[CrossRef]

Nouv. Rev. Opt. Appl.

A. Malherbe, Nouv. Rev. Opt. Appl. 2, 337 (1971).
[CrossRef]

A. Malherbe, M. Guillard, Nouv. Rev. Opt. Appl. 1, 410 (1970).
[CrossRef]

Opt. Acta

A. Daude, A. Savary, A. Seignac, S. Robin, Opt. Acta 20, 353 (1973).
[CrossRef]

W. R. Hunter, Opt. Acta 9, 255 (1962).
[CrossRef]

Proc. Phys. Soc. London

D. G. Avery, Proc. Phys. Soc. London 65, 425 (1952).
[CrossRef]

S. P. F. Humphreys-Owen, Proc. Phys. Soc. London 77, 949 (1961).
[CrossRef]

Rev. Mod. Phys.

D. Pines, Rev. Mod. Phys. 28, 184 (1956).
[CrossRef]

Rev. Sci. Instrum.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1943).
[CrossRef]

Wied. Ann.

D. Shea, Wied. Ann. 47, 177 (1892).
[CrossRef]

Other

A. P. Prishivalko, Reflection of Light from Absorbing Media (Akad. Nauk SSR, Minsk, 1963).

A. Vasicek, Tables of Determination of Optical Constants from the Intensities of Reflected Light (Nakladatelstvi Ceskoslovenske Akad. Vec, Prague, 1964).

G. Hass, U.S. Army Electronics and Development Command, Night Vision and Electro-Optics Laboratory, Fort Belvoir, Va.; private communication.

G. Hass, in Applied Optics and Optical Engineering, Vol. 3, Optical Components, R. Kingslake, Ed. (Academic, New York, 1965), pp. 319–320.

W. R. Hunter, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966), p. 136.

W. R. Hunter, in Physics of Thin Films, Vol. 7, G. Hass, M. Francombe, R. W. Hoffman, Eds. (Academic, New York, 1973), p. 43.

G. N. Steele, Luxel Corp., 515 Tucker Ave., Friday Harbor, Wash.; private communication.

C. Kunz, DESY HASYLAB, Notkestieg 1, Hamburg 52, Germany; private communication.

W. R. Hunter, Naval Research Laboratory, Washington, D.C.; unpublished data.

J. F. Osantowski, Goddard Space Flight Center, Greenbelt, Md.; private communication.

E. Spiller, in Space Optics, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, D.C., 1974), p. 581.

B. Flint, Acton Research Corp., Acton, Mass.; private communication.

G. Hass, W. R. Hunter, in Space Optics, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, D.C., 1974), p. 525.

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 (17)

Fig. 1
Fig. 1

Reflectance-vs-angle of incidence curves calculated using the optical constants shown by the large numbers. Small numbers shown on the abscissa and ordinate are the values of the angle of incidence and reflectance, respectively.

Fig. 2
Fig. 2

Isoreflectance curves for Rp calculated using the optical constants shown by the large numbers. Small numbers used for the abscissa and ordinate show the scale in the n-k plane. Numeral 8 designates the isoreflectance curve corresponding to 80°. The other curves are for angles of incidence 70, 60, etc. through 10°. The curves usually occur in descending order. When not, each curve is labeled with a single digit to avoid confusion (method 1).

Fig. 3
Fig. 3

Effect of ± 1% error in the measurement of reflectance on the determination of n and k using method 1. Angles of incidence are 20 and 70°.

Fig. 4
Fig. 4

Curves of constant n and k as a function of Rp/Rs for small (30−20°) and large (70−50°) angles of incidence. Δn and Δk are each 0.2. Curves for integer n and k values are dashed (method 2).

Fig. 5
Fig. 5

Curves of constant n and k as a function of Rp and Rs for small (20°) and large (70°) angles of incidence. For the left-hand figure, Δk is 0.01 for 0 ≤ k ≤ 0.1. Otherwise Δk is 0.2. Δn is 0.1, and the curve for n = 0.5 is dashed. The dotted line corresponds to the value of n for the Brewster angle, n = 0.364. For the right-hand figure, Δk = Δn = 0.2. Curves for integer n and k values are dashed (method 3).

Fig. 6
Fig. 6

Curves of constant n and k as a function of Rp/Rs and the pB angle and of Rs and the pB angle (methods 4 and 5, respectively). Δn = Δk = 0.1 and curves for integer, and half-integer, n and k values are dashed.

Fig. 7
Fig. 7

Calculated R-vs-ϕ curves for n = 0.707, ϕc = 45°, and different values of k showing the behavior of the reflectance for nonpolarized light in the vicinity of the critical angle.

Fig. 8
Fig. 8

Curve at the top shows n values for Al obtained using the critical angle method. The curve at the bottom shows the extinction coefficient of Al deduced from transmittance measurements. Scatter of points indicates that the critical angle method gives fairly accurate values for n but that the transmittance method for finding k can give quite variable results.

Fig. 9
Fig. 9

Calculated transmittance vs thickness at 584 Å and at normal incidence for an unbacked Al film with 40 Å of oxide on both surfaces. The curve shows how interference effects alter the transmittance as the Al thickness changes.

Fig. 10
Fig. 10

Measured transmittance of an unbacked Al film 800 Å thick as a function of wavelength. Included for comparison are calculated curves for Al with and without 40-Å oxide layers on both surfaces. Interference effects cause the fluctuations in transmittance which are accentuated by the presence of the oxide layers.

Fig. 11
Fig. 11

Measured reflectance of evaporated Al films before and after 1-h, 1-day, and 1-month exposure to air in the 1000–2000-Å wavelength region. Curves show the effect of oxidation on the reflectance of Al.

Fig. 12
Fig. 12

Illustration of the procedure for obtaining isoreflectance curves for determining n and k using two media. Upper left shows reflectance vs thickness at normal incidence. Choosing t/λ = 0.13 (arrow), R-vs-ϕ curves are calculated as shown at bottom left. Using the parallel component, isoreflectance curves are obtained for the layer assuming the substrate is known (top right) and for the substrate assuming the layer is known (bottom right).

Fig. 13
Fig. 13

Reflectance of Al + MgF2 for different thicknesses of MgF2 using polarized and nonpolarized radiation at 1216 Å. The solid curves are measured values, and the dashed curves are calculated. The large difference between the two sets of curves is assumed to be due to changes in n and k in the MgF2 layer.

Fig. 14
Fig. 14

Measured R vs λ of two multilayer reflecting filters designed for maximum reflectance at 1216 Å.

Fig. 15
Fig. 15

Measured Rs of a 27-layer AuPd–C multilayer coating on glass as a function of wavelength for different angles of incidence.

Fig. 16
Fig. 16

Calculated R vs λ of a multilayer reflecting filter with the first-order interference at 575 Å. The layer materials are Al,Al203, and Au, and the substrate is glass. The order of occurrence of the materials is glass, Al,Al2O3, Au(Al2O3,Al,Al2O3,Au). The four-layer group in parentheses is repeated four times. The dashed line shows the reflectance of Ir for comparison.

Fig. 17
Fig. 17

Calculated R vs λ for the multilayer coating of Fig. 16 at different angles of incidence.

Equations (4)

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

R s = [ ( a cos ϕ 2 + b 2 ] / [ ( a + cos ϕ ) 2 + b 2 ] , R p = R s [ ( a sin ϕ tan ϕ ) 2 + b 2 ] / [ ( a + sin ϕ tan ϕ ) 2 + b 2 ] , R a = ½ [ R p ( 1 + p ) + R s ( 1 p ) ] ,
p = ( I p I s ) / ( I p + I s ) ,
a 2 = ½ { [ ( n 2 k 2 sin 2 ϕ ) + 4 n 2 k 2 ] 1 / 2 + ( n 2 k 2 sin 2 ϕ ) } , b 2 = ½ { [ ( n 2 k 2 sin 2 ϕ ) + 4 n 2 k 2 ] 1 / 2 ( n 2 k 2 sin 2 ϕ ) } .
2 ( p 2 + q ) υ 3 + p 2 ( p 2 3 ) υ 2 2 p 4 υ + p 4 = 0 ,

Metrics