How to get R-R distribution from free distribution by laser particle size analyzer

How to get R-R distribution from free distribution by Winner Laser Particle Size Analyzer?

α is D50, representing the particle size characteristics, and β is D84 as the width parameter of particle size distribution.

The free distribution curve is obtained from a set of original particle size test data, and then the R-R distribution curve is obtained by setting the initial values of α （D50）and β（D84）

The solution of the optimization equation is to minimize the error between the R-R distribution curve and the free distribution curve.

The optimization objective is Fmin = SRR-Sfree

Remarks:

1, α , β are real numbers

2, Fmin: Function Minimum

3. SRR:  Area of RR Distribution Curve

4, Sfree: Area of Free Distribution Curve

After iterative operation, the optimal solutions of α and β are obtained, alpha and beta need not to be input.