Particle Size Distributions from Fraunhofer Diffraction

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Abstract
Generalized concepts of information theory indicate that the numerical solution of the Fredholm equation of the first kind relating a particlesize distribution to its Fraunhofer diffraction pattern can be achieved without ill-conditioning by use of a truncated eigenfunction expansion. We give explicit analytic formulae for the eigenfunctions and eigenvalues of this problem and give numerical values of the latter of use for experimental reductions. The results show how many independent fractions of a particle-size distribution may be determined in the presence of quantified levels of noise.

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