Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices

Polar decomposition consists of representing an arbitrary Mueller matrix with a product of three simpler matrices, but, since these matrices do not commute, the result depends on the order in which they are multiplied. We show that the six possible decompositions can be classified into two families and that one of these families always leads to physical elementary matrices, whereas the other does not. (C) 2004 Optical Society of America.