Particle size distributions from SANS data using the maximum entropy method

The extraction of particle size distributions from small-angle neutron scattering data is an example of a practical linear inverse problem. Additional assumptions are necessary to obtain a unique solution. The application of the maximum entropy method to select a realistic size distribution is discussed. Principal features of the method include a proper treatment of experimental errors, no interpolation or smoothing of data, no fitting to empirical models, and guaranteed positivity of the solution everywhere in spite of statistical noise in the data. The resulting solution is the most uniform consistent with the data. Model data results are presented to show that the maximum entropy criterion proves very useful in problems of this type.