summary
The singular value decomposition method was used to analyze the characteristics of the light energy coefficient matrix of the laser particle size analyzer. Sensitivity parameters that can reflect the variation of particle size distribution with light energy distribution were defined, and the measurement upper limit under specific parameter conditions was given The analytical expression between the measurement upper limit of the instrument and the physical parameters was derived, and it was found that the instrument's measurement upper limit is determined by the small reception angle of scattered light when the incident light wavelength remains unchanged The experimental results verified the correctness of the expression

Keyword scattering; Measurement upper limit; Laser particle size analyzer; Singular Value Decomposition

Introduction
Laser particle size analyzer is an instrument that analyzes particle size and distribution by measuring the spatial (angular) distribution of particle scattered light, and has been widely used in particle size measurement of various powders, liquid spray, slurry, lotion, etc. [1] The basic theory and application technology of laser particle size analyzer are still constantly developing, among which there are many studies on application technologies such as inversion algorithm [2G3] and expansion of measurement range [4G5] Wang Tianen et al. [2] proposed an iterative algorithm based on vector similarity to solve the inversion problem of multimodal distributions In order to extend the measurement lower limit, laser particle size analyzer manufacturers have successively adopted inverse Fourier transform optical system [6] dual lens technology, dual excitation light source technology [5], polarized light scattering intensity difference technology [7], and multi angle technology Among them, Pan Linchao et al. [4] proposed a structurally simple annular sample cell method, which has the characteristics of low measurement limit, high measurement accuracy and reliability for submicron particles; They also studied the anomalous movement of particle scattering light distribution, the anomalous movement of Airy spot size, and their impact on particle size analysis [8G10], which improved the theoretical basis of laser particle size analyzer The particle size of large particles that can be measured by an instrument is called the upper limit of measurement, which is one of the important technical indicators of a particle size analyzer The dimensionless criterion proposed by Swithenbank et al. [11] provides the correspondence between the angular position of the photoelectric detection unit and the optimal representative particle size value, while implying the value of the measurement upper limit (i.e. the representative particle size corresponding to the small angle detector), but it does not match the current measurement upper limit of various commercial instruments There are few reports on the measurement upper limit and calculation method of a laser particle size analyzer with a determined physical structure This article conducts theoretical analysis and experimental verification, and finally provides an analytical expression for the measurement upper limit