  Uncertainty in physical parameters can make the solution of forward or
inverse light scattering problems in astrophysical, biological, and atmospheric
sensing applications, cost prohibitive for real-time applications. For example,
given a probability density in the parametric space of dimensions, refractive
index and wavelength, the number of required evaluations for the expected
scattering increases dramatically. In the case of dielectric and weakly
absorbing spherical particles (both homogeneous and layered), we begin with a
Fraunhofer approximation of the scattering coefficients consisting of
Riccati-Bessel functions, and reduce it into simpler nested trigonometric
approximations. They provide further computational advantages when
parameterized on lines of constant optical path lengths. This can reduce the
cost of evaluations by large factors $\approx$ 50, without a loss of accuracy
in the integrals of these scattering coefficients. We analyze the errors of the
proposed approximation, and present numerical results for a set of forward
problems as a demonstration.
