Bi-directional polarised light transport

While there has been considerable applied research in computer graphics on polarisation rendering, no principled investigation of how the inclusion of polarisation information affects the mathematical formalisms that are used to describe light transport algorithms has been conducted so far. Simple uni-directional rendering techniques do not necessarily require such considerations: but for modern bi-directional light transport simulation algorithms, an in-depth solution is needed. In this paper, we first define the transport equation for polarised light based on the Stokes Vector formalism. We then define a notion of polarised visual importance, and we show that it can be conveniently represented by a 4 x 4 matrix, similar to the Mueller matrices used to represent polarised surface reflectance. Based on this representation, we then define the adjoint transport equation for polarised importance. Additionally, we write down the path integral formulation for polarised light, and point out its salient differences from the usual formulation for light intensities. Based on the above formulations, we extend some recently proposed advanced light transport simulation algorithms to support polarised light, both in surface and volumetric transport. In doing that, we point out optimisation strategies that can be used to minimise the overhead incurred by including polarisation support into such algorithms.