## Abstract

The basic compensator–nalyzer–olarimeter is automated by inserting
two modulated optical rotators, one in front of the compensator and the other between
the compensator and the analyzer. The modulated optical rotators (e.g., two
series-connected Faraday cells) are excited by the same ac source to produce
sinusoidal optical rotations of the same frequency, generally of different
amplitudes, that are mutally in or 180° out of phase. We show that, when the
radiation leaving this generalized polarimeter (which is of constant polarization) is
linearly detected, limited Fourier analysis of the resulting signal yields the four
Stokes parameters of the incident radiation.

© 1977 Optical Society of America

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### Equations (11)

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(1)
$$i={S}_{0}+({S}_{1}cos2C+{S}_{2}sin2C)\times cos(2A-2C)+{S}_{3}sin(2A-2C),$$
(2)
$$i={S}_{0}+{S}_{1}cos(2C+2{r}_{1})cos(2A-2C+2{r}_{2})+{S}_{2}sin(2C+2{r}_{1})cos(2A-2C+2{r}_{2})+{S}_{3}sin(2A-2C+2{r}_{2})\phantom{\rule{0.2em}{0ex}}.$$
(3)
$$i={S}_{0}+\xbd{S}_{1}[cos4Ccos(2{r}_{1}-2{r}_{2})-sin4Csin(2{r}_{1}-2{r}_{2})+cos(2{r}_{1}+2{r}_{2})]+\xbd{S}_{2}\phantom{\rule{0.2em}{0ex}}[sin4Ccos(2{r}_{1}-2{r}_{2})+cos4Csin(2{r}_{1}-2{r}_{2})+sin(2{r}_{1}+2{r}_{2})]-{S}_{3}\phantom{\rule{0.2em}{0ex}}(sin2Ccos2{r}_{2}-cos2Csin2{r}_{2})\phantom{\rule{0.2em}{0ex}}.$$
(4)
$${r}_{1}={\widehat{r}}_{1}sin\omega t,{r}_{2}={\widehat{r}}_{2}sin\omega t,$$
(5)
$$\widehat{\mathbf{\text{i}}}=\mathbf{\text{M}}{\mathbf{\text{S}}}^{\prime},$$
(6)
$$\begin{array}{cc}\widehat{\mathbf{\text{i}}}=\left(\begin{array}{c}{\widehat{i}}_{\omega}\\ {\widehat{i}}_{2\omega}\\ {\widehat{i}}_{3\omega}\end{array}\right)& {\mathbf{\text{S}}}^{\prime}=\left(\begin{array}{c}{S}_{1}\\ {S}_{2}\\ {S}_{3}\end{array}\right)\end{array},$$
(7)
$$\mathbf{\text{M}}=\left[\begin{array}{ccc}\hfill -sin4C{J}_{1}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})& \hfill cos4C{J}_{1}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})+{J}_{1}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})\hfill & \hfill 2cos2C{J}_{1}(2{\widehat{r}}_{2})\\ \hfill cos4C{J}_{2}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})+{J}_{2}(2{\widehat{r}}_{1}+2{\widehat{r}}_{2})\hfill & \hfill sin4C{J}_{2}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})\hfill & \hfill -2sin2C{J}_{2}(2{\widehat{r}}_{2})\\ -sin4C{J}_{3}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})\hfill & \hfill cos4C{J}_{3}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})+{J}_{3}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})\hfill & \hfill 2cos2C{J}_{3}(2{\widehat{r}}_{2})\hfill \end{array}\right]\phantom{\rule{0.2em}{0ex}}.$$
(8)
$${i}_{\text{dc}}={S}_{0}+\xbd{S}_{1}[cos4C{J}_{0}((2{\widehat{r}}_{1}-2{\widehat{r}}_{2}){J}_{0}(2{\widehat{r}}_{1}+2{\widehat{r}}_{2})]+\xbd{S}_{2}\phantom{\rule{0.2em}{0ex}}[sin4C{J}_{0}(2{\widehat{r}}_{1}-2{\widehat{r}}_{2})]-{S}_{3}\phantom{\rule{0.2em}{0ex}}[sin2C{J}_{0}(2{\widehat{r}}_{2})]\phantom{\rule{0.2em}{0ex}}.$$
(9)
$${\mathbf{\text{S}}}^{\prime}={\mathbf{\text{M}}}^{-1}\widehat{\mathbf{\text{i}}}.$$
(10)
$$det\mathbf{\text{M}}\ne 0,$$
(11)
$$det\mathbf{\text{M}}=0,$$