  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.
