  A photon surface $S$ is defined as a three-dimensional timelike hypersurface
such that any null geodesic initially tangent to $S$ continues to be included
in $S$, like $r=3M$ of the Schwarzschild spacetime. Using analytic solutions to
static perturbations of a Schwarzschild spacetime, we examine whether a
nonspherical spacetime can possess a distorted static photon surface. It is
shown that if the region outside of $r=3M$ is vacuum, no distorted photon
surface can be present. Therefore, we establish the perturbative uniqueness for
an asymptotically flat vacuum spacetime with a static photon surface. It is
also pointed out that if matter is present in the outside region, there is a
possibility that a distorted photon surface could form.
