  We argue that relative to non-spherical planetary nebulae (PNs), spherical
PNs are about an order of magnitude less likely to be detected, at distances of
several kiloparsecs. Noting the structure similarity of halos around
non-spherical PNs to that of observed spherical PNs, we assume that most
unobserved spherical PNs are also similar in structure to the spherical halos
around non-spherical PNs. The fraction of non-spherical PNs with detected
spherical halos around them, taken from a recent study, leads us to the claim
of a large (relative to that of non-spherical PNs) hidden population of
spherical PNs in the visible band. Building a toy model for the luminosity
evolution of PNs, we show that the claimed detection fraction of spherical PNs
based on halos around non-spherical PNs, is compatible with observational
sensitivities. We use this result to update earlier studies on the different PN
shaping routes in the binary model. We estimate that ~30% of all PNs are
spherical, namely, their progenitors did not interact with any binary
companion. This fraction is to be compared with the ~3% fraction of observed
spherical PNs among all observed PNs. From all PNs, ~15% owe their moderate
elliptical shape to the interaction of their progenitors with planets, while
\~55% of all PNs owe their elliptical or bipolar shapes to the interaction of
their progenitors with stellar companions.
