## Abstract

A spectral analysis of the electrical signal from the detector in degree of polarization (DOP) measurements that use a rotating polarizer shows base band frequencies that create a noise floor. The noise floor arises from phase and intensity modulation of the optical field owing to the varying thickness and transmission of the rotating optical polarizer in the DOP apparatus. A physical model is presented for the noise floor arising from the phase and intensity modulation, and a calibration procedure including configuration guidelines is provided to minimize the effects of the unwanted modulations.

© 2009 Optical Society of America

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### Equations (8)

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(1)
$${\mathrm{DOP}}_{y}=\frac{\underset{0}{\overset{\infty}{\int}}[{L}_{x}(E)-{L}_{z}(E)]R(E)\mathrm{d}E}{\underset{0}{\overset{\infty}{\int}}[{L}_{x}(E)+{L}_{z}(E)]R(E)\mathrm{d}E},$$
(2)
$$P=\u3008\phantom{\rule{0.265em}{0ex}}|\phantom{\rule{0.265em}{0ex}}{\int}_{\mathrm{\Omega},k}m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta )+\varphi (k,t)]\mathrm{d}r\phantom{\rule{0.265em}{0ex}}r\mathrm{d}\theta \phantom{\rule{0.265em}{0ex}}\mathrm{d}k\phantom{\rule{0.265em}{0ex}}{|}^{2}\phantom{\rule{0.265em}{0ex}}\u3009\mathrm{.}$$
(3)
$$P=\u3008\phantom{\rule{0.265em}{0ex}}|\phantom{\rule{0.265em}{0ex}}{\int}_{\mathrm{\Omega}}m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta )]\mathrm{d}r\phantom{\rule{0.265em}{0ex}}r\mathrm{d}\theta \phantom{\rule{0.265em}{0ex}}{|}^{\hspace{0.17em}2}\phantom{\rule{0.265em}{0ex}}\u3009\mathrm{.}$$
(4)
$$P=\u3008\hspace{0.17em}|\phantom{\rule{0.265em}{0ex}}{\int}_{\mathrm{\Omega}}[1-\rho (r,\theta )]\times m(r,\theta )\mathrm{cos}(\omega t+kl)+\rho (r,\theta )\phantom{\rule{0ex}{0ex}}\times m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta )]\mathrm{d}r\phantom{\rule{0.265em}{0ex}}r\mathrm{d}\theta \phantom{\rule{0.265em}{0ex}}{|}^{\hspace{0.17em}2}\u3009\mathrm{.}$$
(5)
$$P=\u3008|(\overline{m(r,\theta )}\phantom{\rule{0.265em}{0ex}}-\overline{\rho (r,\theta )\times m(r,\theta )})\mathrm{cos}(\omega t+kl)+\overline{\rho (r,\theta )\times m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta )]\hspace{0.17em}}{|}^{2}\u3009=\u3008|\overline{({m}^{\prime}(r,\theta )}\phantom{\rule{0.265em}{0ex}}\mathrm{cos}(\omega t+kl)+\overline{\rho (r,\theta )\times m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta )]}{|}^{2}\u3009\mathrm{.}$$
(6)
$$P=\u3008{\phantom{\rule{0.265em}{0ex}}\overline{{m}^{\prime}(r,\theta )}}^{2}\phantom{\rule{0.265em}{0ex}}{\mathrm{cos}}^{2}(\omega t+kl)\u3009+\u30082\overline{{m}^{\prime}(r,\theta )}\mathrm{cos}(\omega t+kl)\times \overline{\rho (r,\theta )\times m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta )]}\u3009+\u3008\overline{\rho (r,\theta )\times m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta ){]}^{2}}\u3009,$$
(7)
$$\u30082\phantom{\rule{0.265em}{0ex}}\overline{{m}^{\prime}(r,\theta )}\phantom{\rule{0.265em}{0ex}}\mathrm{cos}[\omega t+kl]\times \overline{\rho (r,\theta )\times m(r,\theta )\mathrm{cos}[\omega t+kl(r,\theta )]}\u3009\approx \overline{{m}^{\prime}(r,\theta )}\times \overline{\rho (r,\theta )\times m(r,\theta )\mathrm{cos}[kl-kl(r,\theta )]}\approx \overline{\rho (r,\theta )\times \mathrm{cos}[kl-kl(r,\theta )]},$$
(8)
$$E(t)=\sum _{{n}_{1}=-\infty}^{\infty}\sum _{{n}_{2}=-\infty}^{\infty}\dots \sum _{{n}_{k}=-\infty}^{\infty}{J}_{{n}_{1}}({z}_{1}){J}_{{n}_{2}}({z}_{2})\dots {J}_{{n}_{k}}({z}_{k})\underset{}{\overset{}{}}\phantom{\rule{0ex}{0ex}}\times \mathrm{cos}\left[\right\{\omega (1+{a}_{o})+\sum _{i=1}^{k}{n}_{i}i{\omega}_{m}\}t+\sum _{i=1}^{k}{n}_{i}{\theta}_{i}],$$