  We present a detailed analysis of a previously published realization of
Popper's experiment using entangled ghost imaging. Our analysis, which is based
on optical diffraction integrals, shows that, for the configuration previously
described, the transverse spread of an unmeasured particle (the signal photon
here) does not increase in inverse proportion to the width of its virtual
confinement when its entangled twin is confined in transverse dimension by a
physical slit. Rather we show that the spread of the unmeasured particle
carries no dependence on the width of its virtual confinement in the published
configuration. Instead, it spreads geometrically at a rate determined by the
numerical aperture of the ghost imaging system. We further propose an
alternative configuration for which the spread of the unmeasured particle does
increase in inverse proportion to the width of its virtual confinement. We
discuss the relation of these results to the predictions of Popper.
