Energy-redistribution signatures in transmission microscopy of Rayleigh and Mie particles

We describe the transmission characteristics for the interaction of an arbitrary beam with (possibly multilayered) spherical particles of arbitrary size and electric permeability. Within the generalized Lorenz-Mie theory, expressions that generalize the total cross sections to their fractional counterparts are presented, which allow for an analytic quantification of transmission signals, both on-axis and off-axis. For Gaussian (Davis) beams, the relative angular domain of collection as compared to the beam's angle of divergence determines sensitively the shape and magnitude of the interference signal. Depending on the particle's position within the beam, the transmission signatures related to a pure energy redistribution as well as to accompanying absorption are discussed for Rayleigh particles in terms of their complex-valued polarizability. Implications for positioning, temperature control, spectroscopy, and optimized extinction measurements are discussed.