Huynen has already provided a method to decompose a Mueller matrix in order to retrieve detailed target information in a polarimetric radar system. However, this decomposition sometimes fails in the presence of small error or noise in the elements of a Mueller matrix. This paper attempts to improve Huynen's decomposition method. First, we give the definition of stable decomposition and present an example, showing a problem of Huynen's approach. Then two methods are proposed to carry out stable decompositions, based on the nonlinear least square method and the Newton's method. Stability means the decomposition is not sensitive to noise. The proposed methods overcomes the problems on the unstable decomposition of Mueller matrix, and provides correct information of a target.

For the completely polarized wave case, this paper presents the explicit formulae of the characteristic polarization states in the co-polarized radar channel, from which one can obtain the CO-POL Max, the CO-POL Saddle and the CO-POL Nulls in the Stokes vector form. Then the problem on the polarimetric contrast optimization is discussed, and the explicit formula of the optimal polarization state for contrast enhancement is presented in the Stokes vector form for the first time. To verify these formulae, we give some numerical examples. The results are completely identical with other authors', which shows the validity of the presented method.