  One of the most challenging open questions in physics today is discovering
the nature of dark matter. In this work we study the imaging formation in dark
matter (DM) halos due to an external light source using some DM profiles for
comparison with astronomical observations. Approaching these models on a small
scale, we analyze the images generated on the lens plane by obtaining the
analytical scaled surface mass densities $\Sigma_{*}(x)$ and their
corresponding deflection angles $\alpha_{*}(x)$, for later applying a method
for ray tracing using the gravitational refraction law. The method is able to
locate the positions of the images on the lens plane, by mapping fringes that
represent possible sources (such as other galaxies), placed on the source
plane. The regions where the strong lensing occurs for each profile, are
determined by fixing the $\lambda$ parameter that establishes the ray tracing
process. It is shown that the presence of Einstein rings generated by each
profile is directly related with the central branch of the caustic. This method
gives us a possible alternative way to distinguish between different DM
candidates by observing imaging from external sources.
