Abstract

This reflectometer measures the principal angle of incidence θ¯ and the principal azimuth ψ¯ of a reflecting surface. To determine θ¯, the polarizer and analyzer angles are modulated at different frequencies. The difference frequency appears in a component of the detector output, and the amplitude of this component is directly proportional to cosδ. Consequently, θ¯ is located by searching for a null in this component. Modulation is achieved by mechanically oscillating the polarizing elements. A simple alignment procedure is entirely adequate in making the effect of alignment errors negligible with respect to the sensitivity of the instrument (which is better than 10 sec of arc for θ¯). The method for observing ψ¯ involves the measuring of the polarizer and analyzer rotations required to maintain the transmitted irradiance at a constant value. This eliminates the need for linearity in the photodetector. The value of tan ψ¯ is accurate to 1 part in 1000. No corrections are necessary for source and detector polarization. Deliberately large polarizer and analyzer misaligmnents of 0.02 rad have no significant effect on the accuracy of the determination of tanψ. Although operation has been confined to visible wavelengths, the techniques should be capable of operating over a wider range of wavelengths.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Swindell, Appl. Opt. 7, 943 (1968).
    [CrossRef] [PubMed]
  2. C. Boeckner, J. Opt. Soc. Amer. 19, 7 (1935).
  3. R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
    [CrossRef]
  4. J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1945).
    [CrossRef]
  5. I. Simon, J. Opt. Soc. Amer. 41, 730 (1951).
    [CrossRef]
  6. D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).
  7. K. Ishiguro, T. Sasaki, Sci. Papers Coll. Gen. Educ. Univ. Tokyo 12, 19 (1962).
  8. R. E. Lindquist, A. W. Ewald, J. Opt. Soc. Amer. 53, 247 (1963).
    [CrossRef]
  9. D. W. Junkner, J. Opt. Soc. Amer. 55, 295 (1965).
    [CrossRef]
  10. H. B. Holl, Symposium on Thermal Radiation in Solids (NASA, Washington, D. C., 1965), p. 45.
  11. B. Dold, Opt. 22, 519 (1965).
  12. A. Englesrath, E. V. Loewenstein, Appl. Opt. 5, 565 (1966).
    [CrossRef]
  13. R. F. Potter, Appl. Opt. 4, 53 (1965).
    [CrossRef]
  14. R. F. Potter, J. Opt. Soc. Amer. 54, 904 (1964).
    [CrossRef]
  15. H. Damay, J. Opt. Soc. Amer. 55, 1558 (1965).
    [CrossRef]

1968

1966

1965

R. F. Potter, Appl. Opt. 4, 53 (1965).
[CrossRef]

D. W. Junkner, J. Opt. Soc. Amer. 55, 295 (1965).
[CrossRef]

B. Dold, Opt. 22, 519 (1965).

H. Damay, J. Opt. Soc. Amer. 55, 1558 (1965).
[CrossRef]

1964

R. F. Potter, J. Opt. Soc. Amer. 54, 904 (1964).
[CrossRef]

1963

R. E. Lindquist, A. W. Ewald, J. Opt. Soc. Amer. 53, 247 (1963).
[CrossRef]

1962

K. Ishiguro, T. Sasaki, Sci. Papers Coll. Gen. Educ. Univ. Tokyo 12, 19 (1962).

1952

D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).

1951

I. Simon, J. Opt. Soc. Amer. 41, 730 (1951).
[CrossRef]

1945

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1945).
[CrossRef]

1939

R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
[CrossRef]

1935

C. Boeckner, J. Opt. Soc. Amer. 19, 7 (1935).

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).

Bock, R. O.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1945).
[CrossRef]

Boeckner, C.

C. Boeckner, J. Opt. Soc. Amer. 19, 7 (1935).

Collins, J. R.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1945).
[CrossRef]

Damay, H.

H. Damay, J. Opt. Soc. Amer. 55, 1558 (1965).
[CrossRef]

Dold, B.

B. Dold, Opt. 22, 519 (1965).

Englesrath, A.

Ewald, A. W.

R. E. Lindquist, A. W. Ewald, J. Opt. Soc. Amer. 53, 247 (1963).
[CrossRef]

Holl, H. B.

H. B. Holl, Symposium on Thermal Radiation in Solids (NASA, Washington, D. C., 1965), p. 45.

Ishiguro, K.

K. Ishiguro, T. Sasaki, Sci. Papers Coll. Gen. Educ. Univ. Tokyo 12, 19 (1962).

Junkner, D. W.

D. W. Junkner, J. Opt. Soc. Amer. 55, 295 (1965).
[CrossRef]

Lindquist, R. E.

R. E. Lindquist, A. W. Ewald, J. Opt. Soc. Amer. 53, 247 (1963).
[CrossRef]

Loewenstein, E. V.

Potter, R. F.

R. F. Potter, Appl. Opt. 4, 53 (1965).
[CrossRef]

R. F. Potter, J. Opt. Soc. Amer. 54, 904 (1964).
[CrossRef]

Sasaki, T.

K. Ishiguro, T. Sasaki, Sci. Papers Coll. Gen. Educ. Univ. Tokyo 12, 19 (1962).

Simon, I.

I. Simon, J. Opt. Soc. Amer. 41, 730 (1951).
[CrossRef]

Swindell, W.

Tousey, R.

R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Amer.

R. F. Potter, J. Opt. Soc. Amer. 54, 904 (1964).
[CrossRef]

H. Damay, J. Opt. Soc. Amer. 55, 1558 (1965).
[CrossRef]

C. Boeckner, J. Opt. Soc. Amer. 19, 7 (1935).

R. Tousey, J. Opt. Soc. Amer. 29, 235 (1939).
[CrossRef]

I. Simon, J. Opt. Soc. Amer. 41, 730 (1951).
[CrossRef]

R. E. Lindquist, A. W. Ewald, J. Opt. Soc. Amer. 53, 247 (1963).
[CrossRef]

D. W. Junkner, J. Opt. Soc. Amer. 55, 295 (1965).
[CrossRef]

Opt.

B. Dold, Opt. 22, 519 (1965).

Proc. Phys. Soc.

D. G. Avery, Proc. Phys. Soc. B65, 425 (1952).

Rev. Sci. Instrum.

J. R. Collins, R. O. Bock, Rev. Sci. Instrum. 14, 135 (1945).
[CrossRef]

Sci. Papers Coll. Gen. Educ. Univ. Tokyo

K. Ishiguro, T. Sasaki, Sci. Papers Coll. Gen. Educ. Univ. Tokyo 12, 19 (1962).

Other

H. B. Holl, Symposium on Thermal Radiation in Solids (NASA, Washington, D. C., 1965), p. 45.

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 (7)

Fig. 1
Fig. 1

Schematic diagram of reflectometer components. A—tungsten filament light source; B—condensing lens; C—aperture; D—collimating lens; E—aperture; F—spectral filter; G—polarizer; H—specimen; I—analyzer; and J—photocathode.

Fig. 2
Fig. 2

The oscillating polarizer. The Polaroid sheet attached to the cantilever is electromagnetically vibrated.

Fig. 3
Fig. 3

Block diagram of the electronic apparatus used in the determination of θ ¯ : PA—power amplifier; TA—tuned amplifier; PSD—phase sensitive detector. The dotted line shows the connection to the cathode ray oscilloscope, which is used for aligning the instrument.

Fig. 4
Fig. 4

The oscillograms observed in the process of aligning the polarizing elements: (a) correctly aligned, (b) misaligned.

Fig. 5
Fig. 5

Showing how the output of the amplifier varies with the angle of incidence using (a) normal rectification, (b) phase sensitive detection.

Fig. 6
Fig. 6

Showing the sensitivity of the present technique. The error in assuming that either of the zero crossings is located at θ ¯ is 6 sec of arc.

Fig. 7
Fig. 7

The dotted line shows the theoretical variation of Δ θ ¯ when polarizer misalignment a0 and analyzer misalignment b0 = 0.08 rad are present. The open circles are experimental points.

Tables (2)

Tables Icon

Table I Results for tan ψ ¯ Obtained Over a Wide Range of Chosen Values of I(a1,a2,b1,b2)a

Tables Icon

Table II Effect cn tan ψ ¯ of Misalignments of Polarizer and Analyzer

Equations (2)

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

Δ θ ¯ = K ( 4 a 0 b 0 tan θ ¯ ) / ( 2 + tan 2 θ ¯ ) .
tan ψ ¯ = ( a 1 a 2 / b 1 b 2 ) 1 2 .

Metrics