Reciprocal polarization imaging of complex media

The vectorial evolution of polarized light interaction with a medium can reveal its microstructure and anisotropy beyond what can be obtained from scalar light interaction. Anisotropic properties (diattenuation, retardance, and depolarization) of a complex medium can be quantified by polarization imaging by measuring the Mueller matrix. However, polarization imaging in the reflection geometry, ubiquitous and often preferred in diverse applications, has suffered a poor recovery of the medium's anisotropic properties due to the lack of suitable decomposition of the Mueller matrices measured inside a backward geometry. Here, we present reciprocal polarization imaging of complex media after introducing reciprocal polar decomposition for backscattering Mueller matrices. Based on the reciprocity of the optical wave in its forward and backward scattering paths, the anisotropic diattenuation, retardance, and depolarization of a complex medium are determined by measuring the backscattering Mueller matrix. We demonstrate reciprocal polarization imaging in various applications for quantifying complex non-chiral and chiral media (birefringence resolution target, tissue sections, and glucose suspension), uncovering their anisotropic microstructures with remarkable clarity and accuracy. We also highlight types of complex media that Lu-Chipman and differential decompositions of backscattering Mueller matrices lead to erroneous medium polarization properties, whereas reciprocal polar decomposition recovers properly. Reciprocal polarization imaging will be instrumental in imaging complex media from remote sensing to biomedicine and will open new applications of polarization optics in reflection geometry.