1988/12/01 by J. A. Potton, G. J. Daniell, G.J. Daniell +2 · 82 citations
Chemistry · Engineering · Mathematics · Physics and Astronomy · #Astron #Chemistry #Computational physics #Data set #Geometry #Inverse #Ion-surface interactions and analysis #Materials science #Mathematics #Neutron scattering #Nuclear Physics and Applications #Nuclear physics #Nuclear reactor physics and engineering #Optics #Particle size #Physics #Principle of maximum entropy #Scattering #Small-angle scattering #Statistical physics #Statistics #Void (composites)
paper · doi:10.1107/s0021889888004595
published in Journal of Applied Crystallography 21(6), 891-897 (Wiley)
openalex publication_date 1988/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/25
The determination of a particle size distribution p(R) from small-angle scattering data is an example of a practical linear inverse problem for which there is no unique solution. It is shown (i) how the maximum entropy algorithm may be used to extract a unique solution which is the most uniform function compatible with the data set and is necessarily positive, and (ii) how the Backus–Gilbert [Geophys. J. R. Astron. Soc. (1968), 16, 169–205] method may be used to judge the significance of features in distributions derived from a data set of given statistical accuracy. As an illustration, void size distributions are presented for a sample of irradiated stainless steel which was successively annealed at increasing temperatures.