  We revisit the image charge method for the Green's function problem of the
Poisson-Boltzmann equation for a dielectric sphere immersed in ionic solutions.
Using finite Mellin transformation, we represent the reaction potential due to
a source charge inside the sphere in terms of one dimensional distribution of
image charges. The image charges are generically composed of a point image at
the Kelvin point and a line image extending from the Kelvin point to infinity
with an oscillatory line charge strength. We further develop an efficient and
accurate algorithm for discretization of the line image using Pad\'e
approximation and finite fraction expansion. Finally we illustrate the power of
our method by applying it in a multiscale reaction-field Monte Carlo simulation
of monovalent electrolytes.
