On the one-to-one correspondence of Mueller and Jones matrix formalisms under natural conditions

It is known that there is a reciprocal correspondence between deterministic Mueller and Jones matrices for nondepolarizing objects. However, in practice, there is a failure to define a Jones matrix corresponding to an experimental Mueller matrix of a deterministic object. The reason of such situation is the presence of experimental errors in the Mueller matrix measurements. A method of finding a deterministic Mueller matrix closest to the initial experimental matrix is offered for which the correspondent Jones matrix can be found. The measurement error influence on the possibility of transforming the measured Mueller matrix to a Jones one for consequent detail analysis is investigated. The corresponding analytical expressions for the transfer of the experimental Mueller matrix to a Jones matrix are presented