  The horizontal impact parameter profile of synchrotron radiation, for fixed
vertical angle of the photon, is calculated. This profile is observed through
an astigmatic optical system, horizontally focused on the electron trajectory
and vertically focused at infinity. It is the product of the usual angular
distribution of synchrotron radiation, which depends on the vertical angle
$\psi$, and the profile function of a caustic staying at distance $\bcl =
(\gamma^{-2} + \psi^2) \RB/2 $ from the orbit circle, $\RB$ being the bending
radius and $\gamma$ the Lorentz factor. The {\it classical impact parameter}
$\bcl$ is connected to the Schott term of radiation damping theory. The caustic
profile function is an Airy function squared. Its fast oscillations allow a
precise determination of the horizontal beam width.
