Since the genesis of radiative transfer, polarization has in large part been ignored due to the complexity it introduced into the equation of transfer. It was often felt that no significant errors were introduced by neglecting it.. We will present a brief introduction of the Stokes vector-Mueller matrix approach and show why one should include it into the radiative transfer calculations. In addition to the fact that it is the only correct way to do radiative transfer, we will present cases to show the errors that will be incurred by neglecting it. We will also show the many new and exciting things that have evolved using this approach. The virtues of having this new information have led to applications ranging from better target detection both on-land and in the ocean to detection of precancerous skin lesions. There is also a possibility that Mueller matrix imaging may be used for remote detection of anthrax spores. Both linear and circular polarization convey different pieces of information about a target and we will show how each can be used to enhance the surface features of targets. Emphasis will be placed on how a Monte Carlo calculation can be used to compute the “effective” multiple scattering Mueller matrix (MSMM) ; however, often times a forward scheme will not be realistic and thus to improve statistics, a backward Monte Carlo scheme has to be used. This scheme requires using biased sampling to perform the calculation. We will show how effective this scheme is in calculating the MSMM and discuss future applications.
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