ANALYTICAL INVERSIONS IN REMOTE-SENSING OF PARTICLE-SIZE DISTRIBUTIONS .4. COMPARISON OF FYMAT AND BOX-MCKELLAR SOLUTIONS IN THE ANOMALOUS DIFFRACTION APPROXIMATION

It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively.Sufficient conditions of validity of the two formulas are established.Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability.For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.© 1979 Optical Society of America.