发散光束对消光法颗粒粒径测量影响

Influence of Divergent Beam on Particle Size Measurement by Light Extinction Method

采用蒙特卡罗方法模拟光子在散射介质中传输的物理过程,研究发散光束对消光法粒径测量的影响。将平行入射光条件下数值结果与Lambert-Beer模型进行对比验证,分析了入射光发散角变化对消光光谱的影响。搭建基于发散光束的消光实验平台,分别在入射光平行和发散条件下测得三种聚苯乙烯乳胶球标准颗粒消光光谱,其与蒙特卡罗模拟结果变化趋势基本一致。数值和实验消光谱的粒径反演结果表明:随发散角增大,测得粒径与标称值误差越大,发散角为5°时粒径的反演误差均在4.62%以内,但发散角为20°时标称粒径0.2、0.8、2.88μm的颗粒样品测量误差分别为4.25%、12.75%、-9.55%。进行误差修正,通过蒙特卡罗方法建立的发散光束数值模型构造系数矩阵,对粒径0.8μm的颗粒在发散角为5~20°的实验消光谱反演,误差在2.00%以内。

The theoretical basis of extinction method is Lambert-Beer law and Mie scattering theory,the former reflects the transmission and attenuation characteristics of light beam in the medium,while the latter describes the light scattering law of a single homogeneous spherical particle.By measuring the extinction spectrum of the discrete particle system and combining the extinction coefficient matrix constructed by Mie theory,the particle size distribution can be retrieved.This method is usually valid under the parallel incident light conditions,but the incident light is not strictly parallel in some specific application scenarios,such as gaussian beam irradiation or certain LED light source conditions.In addition,when the measurement zone is narrow,optical fiber is often used to transmit and receive signals.Since it has a certain divergence and receiving angle,data processing according to the assumption of parallel incident light can inevitably lead to errors.For this kind of problem,the Monte Carlo modeling method is introduced to manipulate the continuous incident light beam into discrete photons,and the scatterings of light by the suspended particle are regarded as the collision events between photons and particles,in which each scattering is only related to the previous scattering.By tracing a large number of photon trajectories,the entire physical process of light propagating in a scattering medium can be simulated and illustrated clearly.By counting the number of photons received by receivers in different azimuths,together with those escaping from the boundary,experiencing forward transmission,scattering and absorption,the extinction characteristics under different divergence angles can be obtained accordingly,and investigating the influence of divergent beam on particle size measurement by the extinction method.After the comparison and verification of numerical results using the Monte Carlo and Lambert-Beer model under parallel incident light,the effect of the divergence angle of incident light on the extinction spectrum is analyzed numerically.The simulation results show that the influence of divergence angle on the extinction spectrum is different for particles with various sizes,but the extinction spectrum increases gradually with the increase of divergence angle.Furtherly,through a divergent beam-based light extinction experiment device,the extinction spectra for three reference materials of polystyrene latex particles are measured under the conditions of parallel and divergent incident light respectively,which yield a basically accordant tendence with the Monte Carlo simulation results.The inversion results of particle size show that with the increase of divergence angle,the error between particle size measured by extinction method and the nominal value is becoming greater correspondingly.In particular,the error can be kept within 4.62%until the divergence angle is up to 5°,but at the divergence angle of 20°,the errors of the samples with nominal sizes of 0.2,0.8 and 2.88μm are 4.25%,12.75%and-9.55%,respectively.With the established numerical model of divergent beam,the resultant coefficient matrix is modified based on Monte Carlo method,suppressing the inversion error of the experimental spectral inversion within 2.00%for 0.8μm particles at divergence angles from 5°to 20°.Thus,the proposed model can be used to evaluate the particle size measurement for parallel light hypothesis extinction method under divergent beam,and more importantly it can provide a novel idea for the improvement of coefficient matrix and error correction.