A new approach to Mueller matrix reconstruction of skin cancer lesions using a dual rotating retarder polarimeter

The Mueller matrix is an elegant mathematical method to fully characterize the polarization properties of an object. If the Mueller matrix of an optical element is known as well as the polarization of an incident beam (and its Stokes vector) then the polarization state of the beam exiting the optical element can be uniquely determined. Over the last thirty years, several polarimeters have been proposed for reconstructing the Mueller matrix of any optical element through a set of measurements. One the most successful polarimeters is the dual rotating retarder polarimeter (DRR), invented by Azzam in 1978. This system is composed of two polarizer and retarder pairs, and is able to reconstruct the Mueller matrix of an object inserted in between the two polarizing pairs via an angular modulation of the retarders. Chenault et al in 1992 suggested that the Mueller matrix of a sample inserted in a DRR polarimeter could be calculated multiplying the pseudo-inverse of a data reduction matrix by the measurements vector. The pseudo-inverse of the data reduction matrix is calculated with a least-square approach. This method is now of common usage in the scientific community. In this paper we will show that the reconstruction of the Mueller matrix can be done with higher accuracy using singular value decomposition of the data reduction equation. Our method suggests that a vast range of retardations for the retarders of a DRR obtaining identical results and not only the 127° one as recently suggested by few authors.