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We motivate then formulate a novel variant of the near-field reflectorproblem 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 abounded open set $U$. Suppose that the light emitted from the source at $O$ indirections 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 inputaperture $D$, radiance $g$, `target' set $T$, and irradiance $f$. We focusentirely on the case where the target set $T$ is finite.

Weak solutions to the near-field reflector problem with spatial restrictions approached with generalized reflectors constructed from ellipsoids