  The Talbot effect is usually modeled with the Helmholtz equation, but its
main experimental features are captured by the solution to the free
Schr\"odinger equation with the Dirac comb as initial datum. This simplified
description is a consequence of the paraxial approximation in geometric optics,
a heuristic procedure that is not mathematically well justified, so K. I.
Oskolkov raised the problem of "mathematizing" this approximation. As a first
approach to this question, the purpose of this article is to show that it holds
exactly in the sense of distributions.
