  Polarimetric sensing by orthogonality breaking has been recently proposed as
an alternative technique for performing direct and fast polarimetric
measurements using a specific dual-frequency dual-polarization (DFDP) source.
Based on the instantaneous Stokes-Mueller formalism to describe the
high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the
interaction of such a beam with birefringent, dichroic and depolarizing
samples. This allows us to confirm that orthogonality breaking is produced by
the sample diattenuation, whereas this technique is immune to both
birefringence and diagonal depolarization. We further analyze the robustness of
this technique when polarimetric sensing is performed through a birefringent
waveguide, and the optimal DFDP source configuration for fiber-based endoscopic
measurements is subsequently identified. Finally, we consider a stochastic
depolarization model based on an ensemble of random linear diattenuators, which
makes it possible to understand the progressive vanishing of the detected
orthogonality breaking signal as the spatial heterogeneity of the sample
increases, thus confirming the insensitivity of this method to diagonal
depolarization. The fact that the orthogonality breaking signal is exclusively
due to the sample dichroism is an advantageous feature for the precise
decoupled characterization of such an anisotropic parameter in samples showing
several simultaneous effects.
