  The Talbot effect is usually modeled using 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.
However, it is a heuristic approximation that is not mathematically well
justified, so K. I. Oskolkov raised the problem of "mathematizing" it. We show
that it holds exactly in the sense of distributions.
