Abstract

We show how to correct polarization measurements performed with non-ideal polarizers. The formulas presented in this note can be used to perform precise polarization measurements using inexpensive polarizing sheets.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. G. N. Ramachandran, S. Ramaseshan, “Cristal Optics,” Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), XXV/1, pp. 1–217.
  2. M. Born, E. Wolf, Principles of Optics, sixth ed. (Pergamon Press, Oxford, U.K., 1989). Section 10.8.

Born, M.

M. Born, E. Wolf, Principles of Optics, sixth ed. (Pergamon Press, Oxford, U.K., 1989). Section 10.8.

Flügge, S.

G. N. Ramachandran, S. Ramaseshan, “Cristal Optics,” Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), XXV/1, pp. 1–217.

Ramachandran, G. N.

G. N. Ramachandran, S. Ramaseshan, “Cristal Optics,” Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), XXV/1, pp. 1–217.

Ramaseshan, S.

G. N. Ramachandran, S. Ramaseshan, “Cristal Optics,” Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), XXV/1, pp. 1–217.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, sixth ed. (Pergamon Press, Oxford, U.K., 1989). Section 10.8.

Other (2)

G. N. Ramachandran, S. Ramaseshan, “Cristal Optics,” Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), XXV/1, pp. 1–217.

M. Born, E. Wolf, Principles of Optics, sixth ed. (Pergamon Press, Oxford, U.K., 1989). Section 10.8.

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 (2)

Figure 1
Figure 1

Measuring the polarization state of light with a rotatable polarizer.

Figure 2
Figure 2

Polarimeter design proposed in this note. The arrows over the polarizers indicate the direction of maximum polarizer transmission.

Equations (24)

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

ω = arctan   ( [ I m i n / I m a x ] 1 / 2 ) .
P x = ( t + 0 0 t ) ,
P θ =   [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] [ t + 0 0 t ] [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] =   [ t + cos 2 ( θ ) + t sin 2 ( θ ) ( t + t ) cos ( θ )   sin ( θ ) ( t + t )   cos ( θ )   sin ( θ ) t + sin 2 ( θ ) + t cos 2 ( θ ) ] .
( E x E y ) = P θ   ( E 0 x E 0 y )
I ( θ ) = | P θ   E 0 | 2 = | E 0 x   [ t + cos 2 ( θ ) + t sin 2 ( θ ) ] + E 0 y [ ( t + t )       cos   ( θ )   sin   ( θ ) ] | 2 + E 0 x   [ ( t + t )   cos   ( θ )   sin   ( θ ) ] |   +             E 0 y   [ ( t + sin 2 ( θ ) + t cos 2 ( θ ) ] | 2
I ( θ ) = I 0 x   [ t + 2 cos 2 ( θ ) + t 2 sin 2   ( θ ) ] + I 0 y   [ t + 2 sin 2 ( θ )   + t 2 cos 2   ( θ ) ] + 2 R e   ( E o x E o y ) ( t + 2 t 2 ) cos ( θ ) sin ( θ )
I m a x = I 0 x t + 2 + I 0 y t 2
I m i n = I 0 x t 2 + I 0 y t + 2
I 0 x = ( I m a x t + 2 I m i n t 2 ) / ( t + 4 t 4 ) ,
I 0 y = ( I m i n t + 2 I m a x t 2 ) / ( t + 4 t 4 ) .
I m a x = I 0 x t + 2 , I m i n = I 0 x t 2 .
ω = arctan   [ ( I m i n / I m a x ) 1 / 2 ] = arctan   ( t / t + )
S 0 = I 0 + I 90
S 1 = I 0 I 90
S 2 = I 45 I 45
S 3 = ± ( S 0 2 S 1 2 S 2 2 ) 1 / 2 ,
I 0 = [ I ( 0 0 ) t + 2 I ( 90 0 ) t 2 ] / ( t + 4 t 4 ) , I 90 = [ I ( 90 ° ) t + 2 I ( 0 0 ) t 2 ] / ( t + 4 t 4 ) , I 45 = [ I ( 45 0 ) t + 2 I ( 45 0 ) t 2 ] / ( t + 4 t 4 ) , I 45 = [ I ( 45 0 ) t + 2 I ( 45 0 ) t 2 ] / ( t + 4 t 4 ) ,
S 0 = [ I ( 0 0 ) + I ( 90 0 ) ] / ( t + 2 + t 2 )
S 1 = [ I ( 0 0 ) I ( 90 0 ) ] / ( t + 2 t 2 )
S 2 = [ I ( 45 0 ) I ( 45 0 ) ] / ( t + 2 t 2 ) .
S ¯ 1     S 1 S 0 = I ( 0 0 ) I ( 90 0 ) I ( 0 0 ) I ( 90 0 ) ( t + 2 + t 2 t + 2 t 2 )
S ¯ 2     S 2 S 0 = I ( 45 0 ) I ( 45 0 ) I ( 0 0 ) + I ( 90 0 ) ( t + 2 + t 2 t + 2 t 2 )
S 0 2     S 1 2 + S 21 2 + S 3 2 .
S ¯ 3     S 3 S 0 = I ( L ) I ( R ) I ( 0 0 ) + I ( 90 0 ) ( t + 2 + t 2 t + 2 t 2 )

Metrics