  The paper considers the stationary Poisson Boolean model with spherical
grains and proposes a family of nonparametric estimators for the radius
distribution. These estimators are based on observed distances and radii,
weighted in an appropriate way. They are ratio-unbiased and asymptotically
consistent for growing observation window. It is shown that the asymptotic
variance exists and is given by a fairly explicit integral expression.
Asymptotic normality is established under a suitable integrability assumption
on the weight function. The paper also provides a short discussion of related
estimators as well as a simulation study.
