  We motivate then formulate a novel variant of the near-field reflector
problem and call it the near-field reflector problem with spatial restrictions.
Let $O$ be an anisotropic point source of light and assume that we are given a
bounded open set $U$. Suppose that the light emitted from the source at $O$ in
directions defined by the aperture $D\subseteq S^2$, of radiance $g(m)$ for
$m\in D$, is reflected off $R\subset \overline{U}$, creating the irradiance
$f(x)$ for $x\in T$. The inverse problem consists of constructing the reflector
$R\subseteq \overline{U}$ from the given position of the source $O$, the input
aperture $D$, radiance $g$, `target' set $T$, and irradiance $f$. We focus
entirely on the case where the target set $T$ is finite.
