  Scattering-type scanning near-field optical microscope (s-SNOM) has become an
essential tool to study polaritons - quasiparticles of light coupled to
collective charge oscillations - via direct probing of their near field with a
spatial resolution far beyond the diffraction limit. However, extraction of the
polariton complex propagation constant from the near-field images requires
subtle considerations that have not received necessary attention so far. In
this study, we discuss important yet overlooked aspects of the near-field
analysis. First, we experimentally demonstrate that the sample orientation
inside the s-SNOM may significantly affect the near-field interference pattern
of mid-infrared polaritons, leading to an error in momentum measurement up to
7.7% even for the modes with effective index of 12.5. Second, we establish a
methodology to correctly extract the polariton damping rate from the
interference fringes depending on their origin - the s-SNOM nano-tip or the
material edge. Overall, our work provides a unified framework for the accurate
extraction of the polariton momentum and damping from the near-field
interference fringes.
