## Abstract

We have built a new camera system to measure the downwelling polarized radiance distribution in the ocean. This system uses 4 fisheye lenses and coherent fiber bundles behind each image to transmit all 4 fisheye images onto a single camera image. This allows simultaneous images to be collected with 4 unique polarization states, and thus the full Stokes vector of the rapidly changing downwelling light field.

© 2011 OSA

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### Equations (5)

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(1)
$${M}_{LP}=\left[\begin{array}{cccc}1& \mathrm{cos}2\theta & \mathrm{sin}2\theta & 0\\ \mathrm{cos}2\theta & {\mathrm{cos}}^{2}2\theta & \mathrm{cos}2\theta \mathrm{sin}2\theta & 0\\ \mathrm{sin}2\theta & \mathrm{cos}2\theta \mathrm{sin}2\theta & {\mathrm{sin}}^{2}2\theta & 0\\ 0& 0& 0& 0\end{array}\right]\text{.}$$
(2)
$${M}_{ret}({\theta}_{f},\varphi )=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& co{s}^{2}2{\theta}_{f}+cos\varphi si{n}^{2}2{\theta}_{f}& (1-cos\varphi )sin2{\theta}_{f}cos2{\theta}_{f}& -sin\varphi sin2{\theta}_{f}\\ 0& (1-cos\varphi )sin2{\theta}_{f}cos2{\theta}_{f}& si{n}^{2}2{\theta}_{f}+cos\varphi co{s}^{2}2{\theta}_{f}& sin\varphi cos2{\theta}_{f}\\ 0& sin\varphi sin2{\theta}_{f}& -sin\varphi cos2{\theta}_{f}& cos\varphi \end{array}\right].$$
(3)
$$S\text{'}={M}_{LP}(\theta ){M}_{\mathrm{Re}t}({\theta}_{f},\varphi ){M}_{LP}({\theta}_{p})S,$$
(4)
$$\begin{array}{c}I\text{'}(\theta )=1+cos2\theta \left[cos2{\theta}_{p}{}_{}\left(co{s}^{2}{}^{}2{\theta}_{f}{}_{}+cos\varphi si{n}^{2}2{\theta}_{f}\right)+sin2{\theta}_{p}\left(1-cos\varphi \right)sin2{\theta}_{f}cos2{\theta}_{f}\right]\\ +sin2\theta \left[cos2{\theta}_{p}\left(1-cos\varphi \right)sin2{\theta}_{f}cos2{\theta}_{f}+sin2{\theta}_{p}\left(si{n}^{2}2{\theta}_{f}+cos\varphi co{s}^{2}2{\theta}_{f}\right)\right].\end{array}$$
(5)
$$\left[\begin{array}{c}1\\ Q/I\\ U/I\\ V/I\end{array}\right]=\left[\begin{array}{cccc}{T}_{11}& {T}_{12}& {T}_{13}& {T}_{14}\\ {T}_{21}& {T}_{22}& {T}_{23}& {T}_{24}\\ {T}_{31}& {T}_{32}& {T}_{33}& {T}_{34}\\ {T}_{41}& {T}_{42}& {T}_{43}& {T}_{44}\end{array}\right]\left[\begin{array}{c}{I}_{1}\left(\theta \right)\\ {I}_{2}\left(\theta \right)\\ {I}_{3}\left(\theta \right)\\ {I}_{4}\left(\theta \right)\end{array}\right].$$