Analytical inversion for laser diffraction spectrometry giving improved resolution and accuracy in size distribution

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Abstract
We formulate the Chin–Shifrin integral transform inversion for calculating the particle-size distribution from an observed forward-scattering pattern in a way that does not require knowledge of the derivative of the data. The resulting equations are suitable for use with a photodiode array of the type commonly used to record forward-scattering signatures. By attention to the range of integration in the inversion, and by suitable apodization of the input signal, we are able to reduce noise in the inversion to an acceptable level. Some sample analyses are presented.