Abstract

A null-type photoelectric universal polarimeter (or ellipsometer) utilizing Faraday cells and a quarter-wave plate is described and its precision evaluated. For elliptically polarized light of small circularity (i.e., almost linearly polarized), the azimuth could be determined with a precision of 10 sec and the circularity to within 20 sec of arc. For light of large circularity (on the order of 35 deg), the corresponding precisions were 7 min (0.12 deg) for azimuth and 14 min (0.24 deg) for circularity. Errors due to a nonexact quarter-wave plate and nonperfect alignment of the compensator with respect to the elliptically polarized light are discussed. The use of this instrument as a high-precision Sénarmont compensator for the measurement of birefringence is also described.

© 1964 Optical Society of America

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References

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  1. C. A. Skinner, J. Opt. Soc. Am. and Rev. Sci. Instr. 10, 491 (1925).
    [CrossRef]
  2. P. J. Fopiano and M. B. Trageser, S. B. thesis, Department of Physics, MIT (1951) (unpublished).
  3. A. C. Hardy, P. J. Fopiano, and M. B. Trageser, U. S. Patent No. 2,974,561, “Polarimeter” (1961).
  4. E. J. Gillham, Nature 179, 1412 (1956).
    [CrossRef]
  5. E. J. Gillham, J. Sci. Instr. 34, 435 (1957).
    [CrossRef]
  6. J. W. Gates, Chem. Ind. (London)1958, 190.
  7. M. Billardon and J. Badoz, Compt. Rend. 248, 2466 (1959).
  8. V. A. Kizel and V. I. Permogorov, Opt. i Spektroskopiya 10, 541 (1961) [Engl. Transl. Opt. Spectry. 10, 281 (1961)].
  9. H. Takasaki, J. Opt. Soc. Am. 51, 462, 1146 (1961); J. Opt. Soc. Am. 52, 718 (1962).
    [CrossRef]
  10. H. Wenking, Z. Instrumentenk. 66, 1 (1958).
  11. B. Zimm, Rev. Sci. Instr. 29, 360 (1958).
    [CrossRef]
  12. H. Wayland, Compt. Rend. 249, 1228 (1959).
  13. H. Wayland and J. Badoz, Compt. Rend. 250, 688 (1960).
  14. R. W. Goranson and L. H. Adams, J. Franklin Inst. 216, 475 (1933).
    [CrossRef]
  15. C. V. Kent and J. Lawson, J. Opt. Soc. Am. 27, 117 (1937).
    [CrossRef]
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    [PubMed]
  17. C. C. Robinson, J. Opt. Soc. Am. 53, 681 (1963).
    [CrossRef]
  18. A complete description of the apparatus developed here has been given in an MIT Plastics Research Laboratory report (15June1961) which is available from the present authors.
  19. E. F. Gurnee, L. T. Patterson, and R. D. Andrews, J. Appl. Phys. 26, 1106 (1955).
    [CrossRef]
  20. D. Bergman, J. Opt. Soc. Am. 52, 1080 (1962).
    [CrossRef]

1963 (1)

1962 (1)

1961 (2)

V. A. Kizel and V. I. Permogorov, Opt. i Spektroskopiya 10, 541 (1961) [Engl. Transl. Opt. Spectry. 10, 281 (1961)].

H. Takasaki, J. Opt. Soc. Am. 51, 462, 1146 (1961); J. Opt. Soc. Am. 52, 718 (1962).
[CrossRef]

1960 (1)

H. Wayland and J. Badoz, Compt. Rend. 250, 688 (1960).

1959 (2)

H. Wayland, Compt. Rend. 249, 1228 (1959).

M. Billardon and J. Badoz, Compt. Rend. 248, 2466 (1959).

1958 (2)

H. Wenking, Z. Instrumentenk. 66, 1 (1958).

B. Zimm, Rev. Sci. Instr. 29, 360 (1958).
[CrossRef]

1957 (1)

E. J. Gillham, J. Sci. Instr. 34, 435 (1957).
[CrossRef]

1956 (1)

E. J. Gillham, Nature 179, 1412 (1956).
[CrossRef]

1955 (1)

E. F. Gurnee, L. T. Patterson, and R. D. Andrews, J. Appl. Phys. 26, 1106 (1955).
[CrossRef]

1950 (1)

J. F. Archard, P. L. Clegg, and A. M. Taylor, Research 3, 339 (1950).
[PubMed]

1937 (1)

1933 (1)

R. W. Goranson and L. H. Adams, J. Franklin Inst. 216, 475 (1933).
[CrossRef]

1925 (1)

C. A. Skinner, J. Opt. Soc. Am. and Rev. Sci. Instr. 10, 491 (1925).
[CrossRef]

Adams, L. H.

R. W. Goranson and L. H. Adams, J. Franklin Inst. 216, 475 (1933).
[CrossRef]

Andrews, R. D.

E. F. Gurnee, L. T. Patterson, and R. D. Andrews, J. Appl. Phys. 26, 1106 (1955).
[CrossRef]

Archard, J. F.

J. F. Archard, P. L. Clegg, and A. M. Taylor, Research 3, 339 (1950).
[PubMed]

Badoz, J.

H. Wayland and J. Badoz, Compt. Rend. 250, 688 (1960).

M. Billardon and J. Badoz, Compt. Rend. 248, 2466 (1959).

Bergman, D.

Billardon, M.

M. Billardon and J. Badoz, Compt. Rend. 248, 2466 (1959).

Clegg, P. L.

J. F. Archard, P. L. Clegg, and A. M. Taylor, Research 3, 339 (1950).
[PubMed]

Fopiano, P. J.

P. J. Fopiano and M. B. Trageser, S. B. thesis, Department of Physics, MIT (1951) (unpublished).

A. C. Hardy, P. J. Fopiano, and M. B. Trageser, U. S. Patent No. 2,974,561, “Polarimeter” (1961).

Gates, J. W.

J. W. Gates, Chem. Ind. (London)1958, 190.

Gillham, E. J.

E. J. Gillham, J. Sci. Instr. 34, 435 (1957).
[CrossRef]

E. J. Gillham, Nature 179, 1412 (1956).
[CrossRef]

Goranson, R. W.

R. W. Goranson and L. H. Adams, J. Franklin Inst. 216, 475 (1933).
[CrossRef]

Gurnee, E. F.

E. F. Gurnee, L. T. Patterson, and R. D. Andrews, J. Appl. Phys. 26, 1106 (1955).
[CrossRef]

Hardy, A. C.

A. C. Hardy, P. J. Fopiano, and M. B. Trageser, U. S. Patent No. 2,974,561, “Polarimeter” (1961).

Kent, C. V.

Kizel, V. A.

V. A. Kizel and V. I. Permogorov, Opt. i Spektroskopiya 10, 541 (1961) [Engl. Transl. Opt. Spectry. 10, 281 (1961)].

Lawson, J.

Patterson, L. T.

E. F. Gurnee, L. T. Patterson, and R. D. Andrews, J. Appl. Phys. 26, 1106 (1955).
[CrossRef]

Permogorov, V. I.

V. A. Kizel and V. I. Permogorov, Opt. i Spektroskopiya 10, 541 (1961) [Engl. Transl. Opt. Spectry. 10, 281 (1961)].

Robinson, C. C.

Skinner, C. A.

C. A. Skinner, J. Opt. Soc. Am. and Rev. Sci. Instr. 10, 491 (1925).
[CrossRef]

Takasaki, H.

Taylor, A. M.

J. F. Archard, P. L. Clegg, and A. M. Taylor, Research 3, 339 (1950).
[PubMed]

Trageser, M. B.

P. J. Fopiano and M. B. Trageser, S. B. thesis, Department of Physics, MIT (1951) (unpublished).

A. C. Hardy, P. J. Fopiano, and M. B. Trageser, U. S. Patent No. 2,974,561, “Polarimeter” (1961).

Wayland, H.

H. Wayland and J. Badoz, Compt. Rend. 250, 688 (1960).

H. Wayland, Compt. Rend. 249, 1228 (1959).

Wenking, H.

H. Wenking, Z. Instrumentenk. 66, 1 (1958).

Zimm, B.

B. Zimm, Rev. Sci. Instr. 29, 360 (1958).
[CrossRef]

Compt. Rend. (3)

M. Billardon and J. Badoz, Compt. Rend. 248, 2466 (1959).

H. Wayland, Compt. Rend. 249, 1228 (1959).

H. Wayland and J. Badoz, Compt. Rend. 250, 688 (1960).

J. Appl. Phys. (1)

E. F. Gurnee, L. T. Patterson, and R. D. Andrews, J. Appl. Phys. 26, 1106 (1955).
[CrossRef]

J. Franklin Inst. (1)

R. W. Goranson and L. H. Adams, J. Franklin Inst. 216, 475 (1933).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. and Rev. Sci. Instr. (1)

C. A. Skinner, J. Opt. Soc. Am. and Rev. Sci. Instr. 10, 491 (1925).
[CrossRef]

J. Sci. Instr. (1)

E. J. Gillham, J. Sci. Instr. 34, 435 (1957).
[CrossRef]

Nature (1)

E. J. Gillham, Nature 179, 1412 (1956).
[CrossRef]

Opt. i Spektroskopiya (1)

V. A. Kizel and V. I. Permogorov, Opt. i Spektroskopiya 10, 541 (1961) [Engl. Transl. Opt. Spectry. 10, 281 (1961)].

Research (1)

J. F. Archard, P. L. Clegg, and A. M. Taylor, Research 3, 339 (1950).
[PubMed]

Rev. Sci. Instr. (1)

B. Zimm, Rev. Sci. Instr. 29, 360 (1958).
[CrossRef]

Z. Instrumentenk. (1)

H. Wenking, Z. Instrumentenk. 66, 1 (1958).

Other (4)

J. W. Gates, Chem. Ind. (London)1958, 190.

P. J. Fopiano and M. B. Trageser, S. B. thesis, Department of Physics, MIT (1951) (unpublished).

A. C. Hardy, P. J. Fopiano, and M. B. Trageser, U. S. Patent No. 2,974,561, “Polarimeter” (1961).

A complete description of the apparatus developed here has been given in an MIT Plastics Research Laboratory report (15June1961) which is available from the present authors.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of azimuth polarimeter showing optical and electrical systems.

Fig. 2
Fig. 2

Notation used to describe elliptically polarized light of azimuth ϕ and circularity ψ.

Fig. 3
Fig. 3

Optical system of universal polarimeter.

Fig. 4
Fig. 4

Experimental uncertainty in the measurement of azimuth (ϕ) and circularity (ψ) using the universal polarimeter described in text.

Tables (1)

Tables Icon

Table I (a) Error (=ψψ′) in seconds in the measurement of circularity (ψ) resulting from the use of a nonexact quarter-wave plate, with retardation π/2+ξ, but with axes correctly aligned. All values of are to be taken as positive in this case. (b) Error (=ψψ′) in seconds in the measurement of circularity (ψ), when the quarter-wave plate is exact in retardation, but has its axes misaligned by an angle ζ. All values of are to be taken as negative in this case.

Equations (5)

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I ( t ) = K cos 2 ( θ + α ) = ( K / 2 ) ( 1 + cos 2 θ cos 2 α - sin 2 θ sin 2 α ) ,
I ( t ) = K 2 { 1 + cos 2 θ [ ( 1 - α 0 2 + α 0 4 4 ) + ( α 0 2 - α 0 4 3 ) cos 4 π f 0 t + ] - sin 2 θ [ ( 2 α 0 - α 0 3 + α 0 5 6 ) sin 2 π f 0 t + ( α 0 3 3 - α 0 5 12 ) sin 6 π f 0 t + ] } .
ψ = tan - 1 b / a .
tan 2 ψ / tan 2 ψ 1 - ( ξ 2 / 2 ) .
tan 2 ψ / tan 2 ψ 1 + ( ζ 2 / 2 ) .