Cartesian coordinates transformation for backscattering computational polarimetry

Computational Mueller matrix polarimetry holds great promise in biomedical studies and clinical applications, providing comprehensive polarization-related vectorial information within the sample. For backscattering polarization imaging systems aimed at in vivo tissue polarimetry, the measurement results can be affected by the Cartesian coordinates transformation due to the vectorial properties of polarized light and the non-collinear characteristics of the measurement system. It can influence the reliability of polarization information decoding and extraction. In this study, we elucidate the coupling effects of the photon and space coordinate systems on the backscattering computational polarimetry and provide complete solutions regarding the Cartesian coordinates transformation. We systematically derive the specific forms of the Mueller matrix elements under all combinations of Cartesian coordinates and demonstrate their interconversion relationships. From anisotropic modulus and direction perspectives, we further investigate the influence mechanism of Cartesian coordinates transformation on different polarization effects. Particularly, polarimetric parameters characterizing anisotropic direction exhibit sensitivity features of true negatives or false positives. Based on theoretical analysis and experimental results, we finally propose correction strategies based on photon and space coordinate system markers. Our study will provide significant insights and references for in vivo research and applications of biomedical optics and biophotonics involving coordinate system selection and transformation such as polarimetric endoscopes, full polarization biosensors, and polarization-sensitive optical coherence tomography.