## Abstract

The water-leaving radiance field above a sea surface polluted by an oil film has been modelled using a Monte Carlo radiative transfer technique with large numbers of photons incident at a selected zenith angle. The calculated radiance was recorded for each of the 240 sectors of equal solid angle the upper hemisphere had been divided into. The results are presented in the form of a bi-directional reflectance distribution function (BRDF) and as a contrast function parameterised by observation angle for various angles of incident sunlight and for various states of the sea surface roughness. The conditions for observing maximal and minimal contrast are described.

©2001 Optical Society of America

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### Equations (5)

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(1)
$$r({\theta}_{r},{\phi}_{r},{\theta}_{i},{\phi}_{i})=\frac{L({\theta}_{r},{\phi}_{r})}{E({\theta}_{i},{\phi}_{i})}$$
(2)
$$L({\theta}_{r},{\phi}_{r})=\underset{0}{\overset{\pi \u20442}{\int}}\underset{0}{\overset{2\pi}{\int}}r({\theta}_{i},{\phi}_{i},{\theta}_{r},{\phi}_{r})L({\theta}_{i},{\phi}_{i})\mathrm{sin}{\theta}_{i}\phantom{\rule{.2em}{0ex}}d{\phi}_{i}\phantom{\rule{.2em}{0ex}}d{\theta}_{i}$$
(3)
$$c({\theta}_{r},{\phi}_{r},\lambda )=\frac{{L}_{p}({\theta}_{r},{\phi}_{r},\lambda )-{L}_{c}({\theta}_{r},{\phi}_{r},\lambda )}{{L}_{c}({\theta}_{r},{\phi}_{r},\lambda )}$$
(4)
$$c({\theta}_{r},{\phi}_{r},{\theta}_{i},{\phi}_{i},\lambda )=\frac{{r}_{p}({\theta}_{r},{\phi}_{r},{\theta}_{i},{\phi}_{i},\lambda )-{r}_{c}({\theta}_{r},{\phi}_{r},{\theta}_{i},{\phi}_{i},\lambda )}{{r}_{c}({\theta}_{r},{\phi}_{r},{\theta}_{i},{\phi}_{i},\lambda )}$$
(5)
$$c({\theta}_{r},{\theta}_{i})=\frac{{N}_{p}({\theta}_{r},{\theta}_{i})-{N}_{c}({\theta}_{r},{\theta}_{i})}{{N}_{c}({\theta}_{r},{\theta}_{i})}$$