Theoretical basis for MALLS instruments

The angular intensity distribution of scattered light l 9,n) at angle 6, for particles of diameter d and refractive index fi is given by Mie scattering theoiy. For a polydisperse distribution  

For a ring detector the scattered light arriving at the /th ring of the detector is given by  

Similar equations apply to each ring of the detector. This results in a linear set of / equations with k (discrete size classes) unknowns. The vector of scattered energy can be expressed as a matrix equation  

Alvares et. al. [141] successfully applied a method known as the Tikhonov Regularization method and L-curve criterion to generate data in close accord with the Malvern software. 

Information on the particle size distribution can be found by measuring the scattered light flux at several radial locations to characterize the series of annular rings from the particle s diffraction pattern. It is then necessary to invert the relationship between the scattering pattern and the particle size distribution. This can be done using iterative methods or analytical inversion techniques. 

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