The inverse-scattering problem for a polydispersion f(a) of Mie partic
les is discussed. A new approach based on the mean value theorem and t
he method of employing Lagrange multipliers is developed. We show that
the mean value theorem enables us to obtain easily the key parameters
associated with the distribution function f(a). The method of Lagrang
e multipliers may then be used to construct f(a), the formal solution
to the inverse-scattering problem. The workability and the effectivene
ss of this approach are also demonstrated. (C) 1997 Optical Society of
America.