Abstract

A new photopolarimeter for the simultaneous measurement of all four Stokes parameters of light is described. The light beam, whose state of polarization is to be determined, strikes at oblique incidence three photodetector surfaces in succession, each of which is partially specularly reflecting and each of which generates an electrical signal proportional to the fraction of the radiation that it absorbs. A fourth photodetector captures the remainder of the light. The four outputs thus developed form a 4 × 1 signal vector I, which is linearly related, I = AS, to the input Stokes vector S. Consequently, S is obtained by S = A−1I. The 4 × 4 instrument matrix A must be nonsingular, and this requires that the light beam not remain in one plane. For a given arrangement of four detectors, A can be either computed or determined by calibration. The advantages of this polarimeter are enumerated.

© 1985 Optical Society of America

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References

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  1. See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 554.
  2. An excellent review is given by P. S. Hauge, Surface Sci. 96, 108 (1980). See also K. Serkowski, in Planet, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1977), pp. 135–174.
    [CrossRef]
  3. R. M. A. Azzam, Optik 52, 253 (1979).
  4. E. Collett, Surface Sci. 96, 156 (1980).
    [CrossRef]
  5. R. M. A. Azzam, Opt. Acta 29, 685 (1982).
    [CrossRef]
  6. For a discussion of the Mueller-matrix calculus see, for example, W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), Chap. 8.
  7. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 491–492.
  8. R. M. A. Azzam, A.-R. M. Zaghloul, J. Opt. Soc. Am. 67, 1058 (1977); R. M. A. Azzam, J. Opt. Soc. Am. 71, 1523 (1981).
    [CrossRef]
  9. D. E. Aspnes, P. S. Hauge, J. Opt. Soc. Am. 66, 949 (1976).
    [CrossRef]
  10. See, for example, R. J. Perry, A. H. Hunt, D. R. Huffman, Appl. Opt. 17, 2700 (1978).
    [CrossRef] [PubMed]

1982 (1)

R. M. A. Azzam, Opt. Acta 29, 685 (1982).
[CrossRef]

1980 (2)

An excellent review is given by P. S. Hauge, Surface Sci. 96, 108 (1980). See also K. Serkowski, in Planet, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1977), pp. 135–174.
[CrossRef]

E. Collett, Surface Sci. 96, 156 (1980).
[CrossRef]

1979 (1)

R. M. A. Azzam, Optik 52, 253 (1979).

1978 (1)

1977 (1)

1976 (1)

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, Opt. Acta 29, 685 (1982).
[CrossRef]

R. M. A. Azzam, Optik 52, 253 (1979).

R. M. A. Azzam, A.-R. M. Zaghloul, J. Opt. Soc. Am. 67, 1058 (1977); R. M. A. Azzam, J. Opt. Soc. Am. 71, 1523 (1981).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 491–492.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 491–492.

Born, M.

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 554.

Collett, E.

E. Collett, Surface Sci. 96, 156 (1980).
[CrossRef]

Hauge, P. S.

An excellent review is given by P. S. Hauge, Surface Sci. 96, 108 (1980). See also K. Serkowski, in Planet, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1977), pp. 135–174.
[CrossRef]

D. E. Aspnes, P. S. Hauge, J. Opt. Soc. Am. 66, 949 (1976).
[CrossRef]

Huffman, D. R.

Hunt, A. H.

Perry, R. J.

Shurcliff, W. A.

For a discussion of the Mueller-matrix calculus see, for example, W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), Chap. 8.

Wolf, E.

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 554.

Zaghloul, A.-R. M.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Opt. Acta (1)

R. M. A. Azzam, Opt. Acta 29, 685 (1982).
[CrossRef]

Optik (1)

R. M. A. Azzam, Optik 52, 253 (1979).

Surface Sci. (2)

E. Collett, Surface Sci. 96, 156 (1980).
[CrossRef]

An excellent review is given by P. S. Hauge, Surface Sci. 96, 108 (1980). See also K. Serkowski, in Planet, Stars and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1977), pp. 135–174.
[CrossRef]

Other (3)

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 554.

For a discussion of the Mueller-matrix calculus see, for example, W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), Chap. 8.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), pp. 491–492.

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Figures (1)

Fig. 1
Fig. 1

The four-detector photopolarimeter. The surfaces of photodetectors D0, D1, and D2 are partially specularly reflecting, whereas that of D3 is totally absorbing. The four output electrical signals i0, i2, and i3 determine the input Stokes vector S. The light beam does not remain in one plane. α1 is the angle between the planes of incidence for the successive reflections from D0 and D1, and α2 is the corresponding angle for the reflections from D1 and D2. pn is the reference polarization direction parallel to the nth plane of incidence.

Equations (11)

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S = [ S 0 S 1 S 2 S 3 ] ,
S 0 = M 0 S , S 1 = M 1 R 1 ( α 1 ) M 0 S , S 2 = M 2 R 2 ( α 2 ) M 1 R 1 ( α 1 ) M 0 S ,
i 0 = k 0 ( S 0 - S 0 0 ) , i 1 = k 1 ( S 0 0 - S 1 0 ) , i 2 = k 2 ( S 1 0 - S 2 0 ) , i 3 = k 3 S 2 0 .
[ i 0 i 1 i 2 i 3 ] = [ a 00 a 01 a 02 a 03 a 10 a 11 a 12 a 13 a 20 a 21 a 22 a 23 a 30 a 31 a 32 a 33 ] [ S 0 S 1 S 2 S 3 ] ,
I = AS .
S = A - 1 I ,
M = r [ 1 - cos 2 ψ 0 0 - cos 2 ψ 1 0 0 0 0 sin 2 ψ cos Δ sin 2 ψ sin Δ 0 0 - sin 2 ψ sin Δ sin 2 ψ cos Δ ] ,
R ( α ) = [ 1 0 0 0 0 cos 2 α sin 2 α 0 0 - sin 2 α cos 2 α 0 0 0 0 1 ] .
A = [ k 0 t - k 0 r b 0 0 k 1 r t k 1 r t b 0 - k 1 r 2 a b k 2 r 2 t k 2 r 2 t b k 2 r 3 a 2 b k 2 r 2 t a b k 3 r 3 k 3 r 3 b - k 3 r 3 a 2 b k 3 r 3 a b ] ,
t = 1 - r ,             a = sin 2 ψ , b = - cos 2 ψ = - ( 1 - a 2 ) 1 / 2 .
det A = ( k 0 k 1 k 2 k 3 ) r 4 a 3 b ( 1 - a 2 r ) ,

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