基于多采样时间的光子相关测量法研究

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摘要

随着纳米技术的快速发展，迫切需要对纳米颗粒粒径测量方法进行深入研究，

以满足对纳米材料尺寸质检的需要。传统线性自相关测量法数据点计算量大,动态

范围难以提高，功率谱估计法需要对数据加窗，造成频谱泄露，分辨率下降。因

此，需要研究一种通道资源有限的情况下，动态范围较大，分辨率较高，自相关

函数曲线较均滑的光子相关测量法。针对这一问题，本文提出了基于多采样时间

的光子相关测量法。

本文所述的多采样时间光子相关法的测量原理是对散射光信号做处理，计算

光强自相关函数，然后经过反演求取颗粒粒径。散射光信号的产生是基于被光束

照射颗粒所做的布朗运动，由于布朗运动是带稳定增量的非平稳随机过程，相关

函数是无法定义的，本文提出了结构函数的概念，并建立了其与自相关函数的关

系，论述了光子噪声和信号噪声对自相关函数的影响及死区时间误差。

本文通过对采样间隔采集到的光子和激光谐振产生的基模辐射场横截面上的

振幅的分析，分别提出了泊松模型和伽马（Gamma）模型，用以生成自相关函数。

重点研究了多采样时间自相关函数原理，设计了多采样时间自相关算法程序，分

析了多采样时间自相关算法动态范围有限时的通道开销。从自相关函数数据点运

算耗时的角度分析了多采样时间捆绑率

的取值及系统误差与



（





）取值

的关系，通过 matlab 编程进行了量化分析。

此外，本文搭建了动态光散射实验系统，设计了动态光散射信号模拟器，增

强了实验的完备性。通过对标准聚苯乙烯颗粒的测量实验，本文比较了多采样时

间光子相关法、线性自相关法、功率谱估计法绘制的相关函数曲线形状及优劣，

并绘出相应延迟时刻的残差图。得到自相关函数曲线后通过反演算法，测得样品

颗粒粒径，并比较测量结果和运算耗时。

关键词：颗粒测量多采样时间光子相关法自相关函数功率谱估计

ABSTRACT

With the development of nanotechnology, in order to supervise the quality of

nano-material dimension, there is an urgent need to conduct the research work of

nanoparticle size measurement. Traditional linear autocorrelation is difficult to improve

dynamic range, power spectrum estimation need to windowing original date, resulting

in spectrum leakage. With limited channel resources , we hope to find a photon

correlation spectroscopy methodology, which have larger dynamic range, higher

resolution and smoother curves of autocorrelation function. To solve this problem, this

paper presents multiple tau scheme which are used in photon correlation spectroscopy.

The multiple tau scheme photon correlation spectroscopy are based on the

computation of dynamic light signal, first we calculate its autocorrelation function , then

by inversion algorithm , we can get the particle size. The appearance of scattered light is

due to the Brown motion of the nanoparticles, which are irradiated by the laser. As the

Brown motion is a non-stationary process with stationary increments, the

autocorrelation function cannot be defined, this paper presents the concept of structure

function, and build up the relationship with autocorrelation function, meanwhile, make

a noise performance analysis for both functions.

Through the analysis of photons detected within a sampling interval of a constant

light intensity and the amplitude of cross section characterized by the laser resonant,

this paper presents Poisson Process and Gamma Process to evolve into autocorrelation

function. Focused on the multiple tau scheme, developed software program, analyzed

the consumption of channels with limited dynamic range. Considering the

computational time per point and system absolute error, we analyze the binning ratio m

and



(





) in quantity by matlab.

In addition, this paper build a dynamic light scatting system, develop a dynamic

light scattering signal simulator to enhance the completeness of the experiment. By the

measurement of standard polystyrene, this paper make a comparison among the curves

of autocorrelation function calculated by multiple tau scheme, liner autocorrelation and

power spectrum estimation, draw the residual figure. Then, by inversion algorithm,

figure out the particle size as well as the computational time.

Key Words: Measurement of Particle Size, The Multiple Tau Scheme

Photon Correlation Spectroscopy, Autocorrelation Function, Power

Spectrum Estimation

中文摘要

ABSTRACT

第一章绪论 .......................................................................................................................... 1

§1.1 概述 ......................................................................................................................... 1

§1.2 纳米颗粒及其粒径测量的意义 ............................................................................. 1

§1.3 颗粒粒径测量方法 ................................................................................................. 2

§1.4 光子相关测量法的发展概况 ................................................................................. 4

§1.5 本课题的研究内容 ................................................................................................. 6

第二章光子相关测量法的数学原理 .................................................................................. 8

§2.1 概述 .......................................................................................................................... 8

§2.2 双随机过程的相关性 ............................................................................................. 8

§2.3 结构函数 ................................................................................................................. 9

§2.4 随机模型 ............................................................................................................... 11

§2.5 噪声对相关函数和结构函数的影响 ................................................................... 13

§2.6 死区时间误差 ....................................................................................................... 14

§2.7 光子相关 ............................................................................................................... 17

§2.7.1 光子相关的两种类型 .................................................................................. 17

§2.7.2 反演算法 ...................................................................................................... 19

第三章多采样时间光子相关测量法 ................................................................................ 21

§3.1 概述 ........................................................................................................................ 21

§3.2 线性结构及指数结构自相关函数算法 ............................................................... 21

§3.3 多采样时间自相关函数 ....................................................................................... 22

§3.3.1 采样时间造成的系统误差 .......................................................................... 22

§3.3.2 多采样时间自相关函数的结构及算法 ...................................................... 26

§3.3.3 对相邻相关器采样时间捆绑率取值的讨论 .............................................. 29

§3.4 多采样时间光子相关法硬件实现的初探 ........................................................... 31

第四章光子相关测量法实验系统 .................................................................................... 34

§4.1 概述 ........................................................................................................................ 34

§4.2 光子相关测量法实验原理 ................................................................................... 34

§4.3 光路系统 ............................................................................................................... 35

§4.3.1 激光器 .......................................................................................................... 35

§4.3.2 入射光路 ...................................................................................................... 35

§4.3.3 散射光路 ...................................................................................................... 36

§4.4 光子计数系统 ....................................................................................................... 37

§4.4.1 光电倍增管及外围电路设计 ...................................................................... 38

§4.4.2 光子计数卡 .................................................................................................. 42

§4.5 动态光散射信号模拟系统 ................................................................................... 43

§4.6 数据处理系统 ....................................................................................................... 46

第五章实验和讨论 ............................................................................................................ 48

§5.1 概述 ........................................................................................................................ 48

§5.2 实验过程 ............................................................................................................... 48

§5.3 自相关函数曲线的绘制 ....................................................................................... 48

§5.4 自相关函数曲线残差分析 ................................................................................... 52

§5.5 粒径测量结果 ....................................................................................................... 55

§5.6 误差分析 ............................................................................................................... 56

§5.6.1 实验硬件的非理想性 .................................................................................. 56

§5.6.2 实验环境的非理想性 .................................................................................. 58

第六章总结和展望 ............................................................................................................ 59

§6.1 本文的主要工作及成果 ....................................................................................... 59

§6.2 存在的问题及改进设想 ....................................................................................... 60

参考文献 .............................................................................................................................. 61

在读期间公开发表的论文和承担科研项目及取得成果 .................................................. 64

致谢 ...................................................................................................................................... 65

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摘要：

摘要随着纳米技术的快速发展，迫切需要对纳米颗粒粒径测量方法进行深入研究，以满足对纳米材料尺寸质检的需要。传统线性自相关测量法数据点计算量大,动态范围难以提高，功率谱估计法需要对数据加窗，造成频谱泄露，分辨率下降。因此，需要研究一种通道资源有限的情况下，动态范围较大，分辨率较高，自相关函数曲线较均滑的光子相关测量法。针对这一问题，本文提出了基于多采样时间的光子相关测量法。本文所述的多采样时间光子相关法的测量原理是对散射光信号做处理，计算光强自相关函数，然后经过反演求取颗粒粒径。散射光信号的产生是基于被光束照射颗粒所做的布朗运动，由于布朗运动是带稳定增量的非平稳随机过程，相关函数是无法定义的，本文...

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