Optical singularities indicate zero-intensity points in space where parameters, such as phase, polarization, are undetermined. Vortex beams such as the Laguerre–Gaussian modes are characterized by a phase factor e^ilθ, and contain a phase singularity in the middle of its beam. In the case of a transversal optical singularity (TOS), it occurs perpendicular to the propagation, and its phase integral is 2π in nature. Since it emerges within a nano-size range, one expects that TOSs could be sensitive in the light-matter interaction process and could provide a great possibility for accurate determination of certain parameters of nanostructure. Here, we propose to use TOSs generated by a three-wave interference to illuminate a step nanostructure. After interaction with the nanostructure, the TOS is scattered into the far field. The scattering direction can have a relation with the physical parameters of the nanostructure. We show that by monitoring the spatial coordinates of the scattered TOS, its propagation direction can be determined, and as consequence, certain physical parameters of the step nanostructure can be retrieved with high precision.