A dielectric columnar thin film (CTF), characterized macroscopically by a relative permittivity dyadic, was investigated theoretically. The CTF was assumed, on the nanoscale, to be an assembly of parallel, identical, elongated ellipsoidal inclusions made of an isotropic dielectric material that has a different refractive index from the bulk material that was evaporated to fabricate the CTF. The inverse Bruggeman homogenization formalism was developed in order to estimate the refractive index of the deposited material, one of the two shape factors of the ellipsoidal inclusions, and the volume fraction occupied by the deposited material, from a knowledge of relative permittivity dyadic of the CTF. A modified Newton-Raphson technique was implemented to solve the inverse Bruggeman equations. Numerical studies revealed how the three nanoscale parameters of CTFs vary as functions of the vapor incidence angle.