  Minimizing the number of probes is one of the main challenges in
reconstructing geometric objects with probing devices. In this paper, we
investigate the problem of using an $\omega$-wedge probing tool to determine
the exact shape and orientation of a convex polygon. An $\omega$-wedge consists
of two rays emanating from a point called the apex of the wedge and the two
rays forming an angle $\omega$. To probe with an $\omega$-wedge, we set the
direction that the apex of the probe has to follow, the line $\overrightarrow
L$, and the initial orientation of the two rays. A valid $\omega$-probe of a
convex polygon $O$ contains $O$ within the $\omega$-wedge and its outcome
consists of the coordinates of the apex, the orientation of both rays and the
coordinates of the closest (to the apex) points of contact between $O$ and each
of the rays.
  We present algorithms minimizing the number of probes and prove their
optimality. In particular, we show how to reconstruct a convex $n$-gon (with
all internal angles of size larger than $\omega$) using $2n-2$ $\omega$-probes;
if $\omega = \pi/2$, the reconstruction uses $2n-3$ $\omega$-probes. We show
that both results are optimal. Let $N_B$ be the number of vertices of $O$ whose
internal angle is at most $\omega$, (we show that $0 \leq N_B \leq 3$). We
determine the shape and orientation of a general convex $n$-gon with $N_B=1$
(respectively $N_B=2$, $N_B=3$) using $2n-1$ (respectively $2n+3$, $2n+5$)
$\omega$-probes. We prove optimality for the first case. Assuming the algorithm
knows the value of $N_B$ in advance, the reconstruction of $O$ with $N_B=2$ or
$N_B=3$ can be achieved with $2n+2$ probes,- which is optimal.
