Scattering-type scanning near-field optical microscopy provides access to super-resolution spectroscopic imaging of the surfaces of a variety of materials and nanostructures. In addition to chemical identification, it enables observations of nano-optical phenomena, such as mid-infrared plasmons in graphene and phonon polaritons in boron nitride. Despite the high lateral spatial resolution, scattering-type near-field optical microscopy is not able to provide characteristics of near-field responses in the vertical dimension, normal to the sample surface. Here, we present an accurate and fast reconstruction method to obtain vertical characteristics of near-field interactions. For its first application, we investigated the bound electromagnetic field component of surface phonon polaritons on the surface of boron nitride nanotubes and found that it decays within 20 nm with a considerable phase change in the near-field signal. The method is expected to provide characterization of the vertical field distribution of a wide range of nano-optical materials and structures.