  We revisit the isocurvature density perturbations induced by quantum
fluctuations of the axion field by extending a recently developed analytic
method and approximations to a time-dependent scalar potential, which enables
us to follow the evolution of the axion until it starts to oscillate. We find
that, as the initial misalignment angle approaches the hilltop of the
potential, the isocurvature perturbations become significantly enhanced, while
the non-Gaussianity parameter increases slowly but surely. As a result, the
isocurvature constraint on the inflation scale is tightened as Hinf < O(100)
GeV for the axion decay constant fa < 10^10 GeV, near the smaller end of the
axion dark matter window. We also derive useful formulae for the power spectrum
and non-Gaussianity of the isocurvature perturbations.
