  Aperture based scanning near field optical microscopes are important
instruments to study light at the nanoscale and to understand the optical
functionality of photonic nanostructures. In general, a detected image is
affected by both, the transverse electric and magnetic field components of
light. The discrimination of the individual field components is challenging, as
these four field components are contained within two signals in the case of a
polarization-resolved measurement. Here, we develop a methodology to solve the
inverse imaging problem and to retrieve the vectorial field components from
polarization- and phase-resolved measurements. Our methodology relies on the
discussion of the image formation process in aperture based scanning near field
optical microscopes. On this basis, we are also able to explain how the
relative contributions of the electric and magnetic field components within
detected images depend on the probe geometry, its material composition, and the
illumination wavelength. This allows to design probes that are dominantly
sensitive either to the electric or magnetic field components of light.
