The Stokes vector is a four-element vector containing real-valued polarization combinations and is an alternative form of representing a full (=quad) polarimetric dataset, besides the complex-valued scattering matrix. Stokes vectors can be measured as real quantities and are preferred over the complex-valued Jones vector formalism when a coherent (phase-preserving) measurement system is absent. Stokes vectors can be used to form the 4x4 Mueller matrix for target scattering analyses, mostly used in the field of optics. First component of the Stokes vector is the sum of the co-polar fields and represents the total energy of the wave. Second component is the difference of the co-polar fields. Thrid component is the real part of the cross-correlation of the fields and fourth component is the imaginary part of it. The different polarization states can be represented by the Stokes vector and an O(3) elliptical transformation can be used to change the polarization basis, similar to the Jones vector where the SU(2) elliptical transformation is used.