NORMAL-FORM FOR MUELLER MATRICES IN POLARIZATION OPTICS

The normal (canonical) form for Mueller matrices in polarization optic s is derived: it is shown that a non-singular real 4 x 4 matrix M qual ifies to be the bona fide Mueller matrix of some physical system if an d only if it has the canonical form M = L'LAMBDAL, where L and L' are elements of the proper orthochronous Lorentz group L+up, and where LAM BDA = diag (lambda0, lambda1, lambda2, lambda3) with lambda0 greater-t han-or-equal-to \lambda(j)\ > 0. It is further shown that lambda1 and lambda2 can be taken to be positive so that the signature of lambda3 i s the same as that of det M. Several experimentally measured Mueller m atrices are analysed in the light of the normal form. The case of sing ular Mueller matrices is briefly discussed as a limiting case.