Analysis and investigation of photon coordinate system transformation invariants in backscattering Mueller matrix computational polarimetry

Polarization imaging and computational polarimetric methods based on backscattering Mueller matrix measurement have shown great potential as a powerful information probing tool in the field of in vivo biomedical detection. However, for the backscattering polarization measurement system, the calculation and analysis of the Mueller matrix derived parameters are often related to the photon coordinate system, which can produce distinct responses with different selection and transformation of coordinate. Here, for the backscattering polarization measurement system with nearly the normal incidence, we first explore the representation of Mueller matrix elements in right-handed-nonunitary and non-right-handed-unitary systems, and further deduce and prove the photon coordinate system transformation invariants in the Mueller matrix decoding methods prevalently used in backscattering tissue polarimetry. Finally, we validate the theoretical derivation results experimentally, which can be helpful for providing a crucial criterion of parameters selection for backscattering Mueller matrix imaging under different photon coordinate systems.