  The transmission characteristics of a spherical (possibly multilayered)
particle of arbitrary size under focused illumination are discussed within the
generalized Lorenz-Mie theory. Expressions generalizing the total extinction
and scattering cross-sections to their fractional counterparts are presented
which allow for a convenient modeling of transmission signals, both on-axis and
off-axis. The strong dependence of the signal on the collection angle and the
complex polarizability are readily included in this minimal, yet accurate
model. The precise signature of the energy redistribution and absorption are
found for particles of arbitrary complex-valued polarizability. For perfect
dielectrics, a transition from sensitive extinction to insensitive scattering
signals is observed and quantified for apertures including angles larger than
twice the beam's angle of divergence. Implications for positioning, temperature
control, spectroscopy and optimized extinction measurements are discussed.
