Abstract

The light traverses a rotating polarizer and the relative intensity behind this analyzer is measured photoelectrically as a function of the analyzer azimuth. A Fourier analysis is applied to the values obtained. The Fourier constants are practically equivalent to the Stokes parameters and their relations to other polarization parameters such as the phase difference, the azimuth, and the degree of polarization are given. The method may be applied to light of any wavelength. The theory is demonstrated by some measurements which were made with an especially constructed analyzer drive. For most practical cases a very satisfactory precision in the measurement of the polarization parameters is obtained.

© 1962 Optical Society of America

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References

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  1. G. G. Stokes, Trans. Cambridge Phil. Soc. 9, 399 (1852).
  2. F. Perrin, J. Chem. Phys. 10, 415 (1942).
    [CrossRef]
  3. H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
    [CrossRef]
  4. M. Richartz, H. Hsü, J. Opt. Soc. Am. 39, 136 (1949).
    [CrossRef]
  5. C. V. Kent, J. Lawson, J. Opt. Soc. Am. 27, 117 (1937).
    [CrossRef]
  6. H. Willie, Optik 9, 84 (1952).
  7. A. Kawski, A. Skwierz, Bull. Acad. Polon. Sci. Classe III 7, 361 (1959).
  8. R. Bauer, M. Rozwadowski, Optik 18, 37 (1961).
  9. M. Born, E. Wolf, Principles of Optics (Pergamon Press, London and New York, 1959), pp. 24–31.
  10. G. Szivessy, Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, Germany, 1928), Vol. 19, p. 920.
  11. Y. Beers, Introduction to the Theory of Error (Addison-Wesley, Reading, Mass., 1953).
  12. B. A. Brice, M. Halwer, R. Speiser, J. Opt. Soc. Am. 40, 768 (1950).
    [CrossRef]
  13. O. C. Jones, C. L. Sanders, J. Opt. Soc. Am. 51, 105 (1961).
    [CrossRef]

1961 (2)

R. Bauer, M. Rozwadowski, Optik 18, 37 (1961).

O. C. Jones, C. L. Sanders, J. Opt. Soc. Am. 51, 105 (1961).
[CrossRef]

1959 (1)

A. Kawski, A. Skwierz, Bull. Acad. Polon. Sci. Classe III 7, 361 (1959).

1952 (1)

H. Willie, Optik 9, 84 (1952).

1950 (1)

1949 (1)

1948 (1)

1942 (1)

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

1937 (1)

1852 (1)

G. G. Stokes, Trans. Cambridge Phil. Soc. 9, 399 (1852).

Bauer, R.

R. Bauer, M. Rozwadowski, Optik 18, 37 (1961).

Beers, Y.

Y. Beers, Introduction to the Theory of Error (Addison-Wesley, Reading, Mass., 1953).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London and New York, 1959), pp. 24–31.

Brice, B. A.

Halwer, M.

Hsü, H.

Jerrard, H. G.

Jones, O. C.

Kawski, A.

A. Kawski, A. Skwierz, Bull. Acad. Polon. Sci. Classe III 7, 361 (1959).

Kent, C. V.

Lawson, J.

Perrin, F.

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Richartz, M.

Rozwadowski, M.

R. Bauer, M. Rozwadowski, Optik 18, 37 (1961).

Sanders, C. L.

Skwierz, A.

A. Kawski, A. Skwierz, Bull. Acad. Polon. Sci. Classe III 7, 361 (1959).

Speiser, R.

Stokes, G. G.

G. G. Stokes, Trans. Cambridge Phil. Soc. 9, 399 (1852).

Szivessy, G.

G. Szivessy, Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, Germany, 1928), Vol. 19, p. 920.

Willie, H.

H. Willie, Optik 9, 84 (1952).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London and New York, 1959), pp. 24–31.

Bull. Acad. Polon. Sci. Classe III (1)

A. Kawski, A. Skwierz, Bull. Acad. Polon. Sci. Classe III 7, 361 (1959).

J. Chem. Phys. (1)

F. Perrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

J. Opt. Soc. Am. (5)

Optik (2)

H. Willie, Optik 9, 84 (1952).

R. Bauer, M. Rozwadowski, Optik 18, 37 (1961).

Trans. Cambridge Phil. Soc. (1)

G. G. Stokes, Trans. Cambridge Phil. Soc. 9, 399 (1852).

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London and New York, 1959), pp. 24–31.

G. Szivessy, Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, Germany, 1928), Vol. 19, p. 920.

Y. Beers, Introduction to the Theory of Error (Addison-Wesley, Reading, Mass., 1953).

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Figures (4)

Fig. 1
Fig. 1

Parameters of elliptically polarized light. Explanation of the symbols is given in the text.

Fig. 2
Fig. 2

Schematic diagram of analyzer drive. T1, T2—coaxial tubes carrying polarizer and protractor, respectively; W1—worm for relative adjustment of polarizer and protractor; W2, G1, G2—worm and gears for driving the polarizer–protractor combination by synchronous motor.

Fig. 3
Fig. 3

View of analyzer drive with front plate removed. P—polarizer; M—microswitch; D—disk with groove for contact closure every five degrees of protractor rotation; W2—worm on motor shaft. (Worm W1 is mounted behind the ball bearing and cannot be seen.)

Fig. 4
Fig. 4

Photomultiplier output as function of analyzer azimuth α. Curve 1: unpolarized light; curve 2: linearly polarized light; curve 3: elliptically polarized light. The analyzer azimuth is indicated by the marks from the marker pen at the upper edge of the graph.

Equations (25)

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E x = a 1 cos ( ν t δ 1 ) , E y = a 2 cos ( ν t δ 2 ) ,
δ = δ 1 δ 2
E x 2 a 1 2 + E y 2 a 2 2 E x E y a 1 a 2 cos δ = sin 2 δ ,
S 0 = a 1 2 + a 2 2 , S 1 = a 1 2 a 2 2 , S 2 = 2 a 1 a 2 cos δ , S 3 = 2 a 1 a 2 sin δ .
S 0 2 = S 1 2 + S 2 2 + S 3 2 .
a 2 + b 2 = a 1 2 + a 2 2 a 2 b 2 = ( a 1 2 a 2 2 ) cos 2 φ + 2 a 1 a 2 sin 2 φ cos δ a b = a 1 a 2 sin δ .
P = I max I min I max + I min ,
I = 1 2 ( a 1 2 cos 2 α + a 2 2 sin 2 α + a 1 a 2 sin 2 α cos δ ) ,
I = C 1 + C 2 cos 2 ( α φ ) ,
C 1 = 1 2 ( a 2 + b 2 ) and C 2 = 1 2 ( a 2 b 2 ) .
I = k 0 + k 1 cos 2 α + k 2 sin 2 α ,
k 0 = C 1 , k 1 = C 2 cos 2 φ , k 2 = C 2 sin 2 φ ,
C 1 = k 0 , C 2 = ( k 1 2 + k 2 2 ) 1 / 2 , tan 2 φ = k 2 / k 1 .
k 0 = 1 n i = 1 n I i , k 1 = 2 n i = 1 n I i cos 2 α i , k 2 = 2 n i = 1 n I i sin 2 α i .
S 0 = 2 C 1 , S 1 = 2 C 2 cos 2 φ , S 2 = 2 C 2 sin 2 φ , S 3 = 2 ( C 1 2 C 2 2 ) 1 / 2 ,
S 0 = 2 k 0 , S 1 = 2 k 1 , S 2 = 2 k 2 , S 3 = 2 ( k 0 2 k 1 2 k 2 2 ) 1 / 2 .
cos δ = k 2 k 0 2 k 1 2 .
P = C 2 C 1 = k 1 2 + k 2 2 k 0 .
tan 2 χ = k 2 k 1 2 + k 2 2 ,
tan β = k 0 + k 1 k 0 k 1 .
k 0 = C 1 = 50.12 , k 1 = 46.31 , k 2 = 19.13.
C 2 = 50.11 , tan 2 φ = 0.4130 , δ = 0.9980 , P = 1.000.
C 1 = k 0 = 71.97 , k 1 = 8.56 , k 2 = 27.09 ,
C 2 = 28.41 , tan 2 φ = 3.17 , cos δ = 0.3791 , P = 0.3948 .
C 0 = k 0 : ± 0.03 k 1 : ± 0.05 k 2 : ± 0.05 C 2 : ± 0.05 P : ± 0.001.

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