The classification of high-resolution and fully polarimetric SAR/ISAR data has gained a lot of attention in remote sensing and surveillance problems and is addressed by decomposing the radar target Sinclair matrix. In this paper, the Sinclair matrix has been projected onto the circular polarization basis and is decomposed into five parameters that are invariant to the relative phase Φ, the Faraday rotation Ω, and the target orientation Ψ without any information loss. The physical interpretation of these parameters, useful for target classification studies, is found in the wave-particle nature of radar scattering phenomenon given the circular polarization of elemental packets of energy. The proposed deterministic target decomposition is based on the left-orthogonal special unitary SU(2) basis, decomposing the signal backscattered by point targets, represented by the target vector, via six special unitary SU(4) rotation matrices, and by providing full resolution and lossless analysis. Comparisons between the proposed deterministic target decomposition and the Cameron, Kennaugh, Krogager, and Touzi decompositions are also pointed out. Generally, the proposed decomposition provides simpler interpretation, faster parameter extraction, and better generalization properties for the analysis of nonreciprocal or random targets. Several polarimetric SAR/ISAR data sets of UWB data, airborne fully polarimetric EMISAR data, and spaceborne RADARSAT2 are used for illustrating the effectiveness and the usefulness of this decomposition for the classification of point targets. Results are very promising for application use in the next generation of high-resolution spaceborne and airborne Pol-SAR and Pol-ISAR systems.