## Abstract

Detecting objects in turbid media by use of just radiance signals has been a subject of study for many years. The use of Mueller matrix imaging methods has only recently been used as a tool for target detection. We will show not only that can targets still be detected by Mueller matrix methods even after their detection has escaped normal radiance schemes but also that their surface features can also still be distinguished. We will also show how the shape of the volume scattering function as well as the target and medium albedo strongly influences various elements of the Mueller matrix. One of the more interesting features of Mueller matrix imaging is that the diagonal elements are sensitive to perturbations in the environment surrounding the target. This implies that targets can be detected far beyond their geometric cross section. The methods presented here will have applications to submersible object detection, remote sensing in the atmosphere, and the detection of inhomogeneities in tissue.

© 2003 Optical Society of America

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### Equations (9)

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(1)
$${p}_{\mathrm{SH}}\left(\mathrm{\mu},\mathrm{\varphi};g\right)=\frac{1}{4\mathrm{\pi}}\frac{1-{g}^{2}}{{\left(1-2g\mathrm{\mu}+{g}^{2}\right)}^{3/2}};\mathrm{\mu}=cos\mathrm{\theta};g=\u3008cos\mathrm{\theta}\u3009.$$
(2)
$${p}_{\mathrm{TTH}}\left(\mathrm{\mu},\mathrm{\varphi};\mathrm{\alpha},{g}_{1},{g}_{2}\right)=\mathrm{\alpha}{p}_{\mathrm{SH}}\left(\mathrm{\mu},\mathrm{\varphi};{g}_{1}\right)+\left(1-\mathrm{\alpha}\right){p}_{\mathrm{SH}}\left(\mathrm{\mu},\mathrm{\varphi};{g}_{2}\right),$$
(3)
$${p}_{\mathrm{SH}}\left(1,\mathrm{\varphi};g\right)={p}_{\mathrm{TTH}}\left(1,\mathrm{\varphi};\mathrm{\alpha},{g}_{1},{g}_{2}\right);g=0.95;{g}_{2}=-0.95,$$
(4)
$$\frac{1+g}{{\left(1-g\right)}^{2}}=\mathrm{\alpha}\frac{1+{g}_{1}}{{\left(1-{g}_{1}\right)}^{2}}+\left(1-\mathrm{\alpha}\right)\frac{1+{g}_{2}}{{\left(1-{g}_{2}\right)}^{2}}.$$
(5)
$$\mathrm{\alpha}=\frac{\mathrm{\beta}-\mathrm{\delta}}{\mathrm{\gamma}-\mathrm{\delta}},$$
(6)
$$\mathrm{\beta}=\frac{1+g}{{\left(1-g\right)}^{2}};\mathrm{\gamma}=\frac{1+{g}_{1}}{{\left(1-{g}_{1}\right)}^{2}};\mathrm{\delta}=\frac{1+{g}_{2}}{{\left(1-{g}_{2}\right)}^{2}}.$$
(7)
$${\int}_{0}^{2\mathrm{\pi}}{\int}_{0}^{\mathrm{\pi}/2}\tilde{p}\left(\mathrm{\theta},\mathrm{\varphi}\right)\mathrm{d}\mathrm{\theta}\mathrm{d}\mathrm{\varphi}=\frac{1}{2},$$
(8)
$$1-{\tilde{M}}_{22}={\tilde{M}}_{44}-{\tilde{M}}_{33}.$$
(9)
$$\left[\begin{array}{cccc}1& \frac{{\mathrm{\mu}}^{2}-1}{{\mathrm{\mu}}^{2}+1}& 0& 0\\ \frac{{\mathrm{\mu}}^{2}-1}{{\mathrm{\mu}}^{2}+1}& 1& 0& 0\\ 0& 0& \frac{2\mathrm{\mu}}{{\mathrm{\mu}}^{2}+1}& 0\\ 0& 0& 0& \frac{2\mathrm{\mu}}{{\mathrm{\mu}}^{2}+1}\end{array}\right],$$