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Advances in vectorial polarisation-resolved imaging are bringing newcapabilities to applications ranging from fundamental physics through toclinical diagnosis. Imaging polarimetry requires determination of the Muellermatrix (MM) at every point, providing a complete description of an object'svectorial properties. Despite forming a comprehensive representation, the MMdoes not usually provide easily-interpretable information about the object'sinternal structure. Certain simpler vectorial metrics are derived from subsetsof the MM elements. These metrics permit extraction of signatures that providedirect indicators of hidden optical properties of complex systems, whilefeaturing an intriguing asymmetry about what information can or cannot beinferred via these metrics. We harness such characteristics to reveal thespin-Hall effect of light, infer microscopic structure within laser-writtenphotonic waveguides, and conduct rapid pathological diagnosis through analysisof healthy and cancerous tissue. This provides new insight for the broaderusage of such asymmetric inferred vectorial information.

Revealing complex optical phenomena through vectorial metrics