Home | Survey | Topics | Index | References | Dictionary | Contributing | Gallery | Community
| Equivalence of definitions of the degree of linear polarization | Parent topic |
Assume that a light beam is polarized elliptically with the major axis of the polarization ellipse making an arbitrary angle with a reference plane. According to the operational definition of the degree of linear polarization, the maximum irradiance, Imax = Il (Eq. 2a in Measures of polarization) of light measured following a linear polarizer will be noted when that polarizer axis is oriented parallel to the major axis of the polarization ellipse. The minimum irradiance, Imin = Ir will be measured when the polarizer axis in aligned with the minor axis of the ellipse (notation Il and Ir is explained in Stokes vector: Measurements).
Let us now rotate the reference plane so that it is parallel to the major axis of the polarization ellipse. In the reference frame tied to the new reference plane the element Q of the Stokes vector of the beam equals Il - Ir = Imax - Imin > 0, the element U equals 0, and the element I equals Il + Ir = Imax + Imin. Hence, according to Eq. 2 in Measures of polarization, we have:
| PL | = √( Q 2 + U 2 ) / I | |
| = | Q | / I | ||
| = ( Il - Ir ) / ( Il + Ir ) | ||
| = ( Imax - Imin ) / ( Imax + Imin ) | (1) |
However, both I and Q 2 + U 2 are invariant under a rotation of the reference frame about the beam axis (see Stokes vector). Hence PL is also invariant under such rotation, which completes the derivation.
| CITATION: Jonasz M. 2006. Measures of polarization (www.tpdsci.com/Tpc/StoVecDegPol.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 13-Apr-2006 Modified: 13-Apr-2006 Peer-reviewed: 11-Mar-2008 |
| Copyright 2005-2008 MJC Optical Technology. All rights reserved. | Terms of use | Menu |