  In this paper we study the near-field refractor problem with point source at
the origin and prescribed target on the given receiver surface $\Sigma$. This
nonvariational problem can be studied in the framework of prescribed Jacobian
equations. We construct the corresponding generating function and show that the
Aleksandrov and the Brenier type solutions are equivalent. Our main result
establishes local smoothness of Aleksandrov's solutions when the data is smooth
and when the medium containing the source has smaller refractive index than the
medium containing the target. This is done by deriving the Monge-Ampere type
equation that smooth solutions satisfy and establishing the validity of the MTW
condition for a large class of receiver surfaces, which in turn implies the
local $C^2 $ regularity of the refactor.
