  We derive the leading-order correction to the proximity force approximation
(PFA) result for the electromagnetic Casimir interaction in the plane-sphere
geometry by developing the scattering approach in the plane-wave basis.
Expressing the Casimir energy as a sum over round trips between plane and
sphere, we find two distinct contributions to the correction. The first one
results from the variation of the Mie reflection operator, calculated within
the geometric optical WKB approximation, over the narrow Fourier interval
associated to specular reflection at the vicinity of the point of closest
approach on the spherical surface. The second contribution, accounting for
roughly 90% of the total correction, results from the modification of the
geometric optical WKB Mie scattering amplitude due to diffraction. Our
derivation provides a clear physical understanding of the nature of the PFA
correction for spherical surfaces.
