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Numerical studies on the Chin–Shifrin inversion method for particle sizing

The Chin–Shifrin (C-S) inversion method based on Fraunhofer diffraction is an inversion method for recovering size distribution from an optical pattern. The truncation error of the diffraction approximation limits the application of the C-S inversion method. In order to give a quantitative description of the truncation error, a new approximation error, ε, is defined by considering the characteristic of the integrand ECShCS . The inversions show that the true peak does not shift along with the variation of upper limit of integral angle when the corresponding ε is small. As the larger upper limit of integral angle can recover a more accurate size distribution, estimation of maximum approximation angle, θ max, for different sets of ε and refractive index, m, is made. The direct results for θ max are the minimum size parameter and new criterion for maximum angular resolution with which the C-S integral inversion can work. They are investigated using sampling theory.