数字图像相关反向算法的系统误差和散斑质量优化方法研究

Digital image correlation (DIC) is the most popular and widely used optical metrology in the field of experimental mechanics. One hot area of research is the “optimization of speckle patterns”, which is based on a thorough analysis of measurement errors of DIC. It is believed that the interpolation bias of the high-efficiency inverse strategy approximately equals to that of the traditional forward strategy. However, our numerical experiments have proven this statement incorrect. Based on our previous studies on frequency-domain based model for systematic errors of forward strategy and speckle assessment parameters, within this project, we will build a frequency-domain based model for systematic errors of inverse strategy, clarify the dependence of systematic errors of inverse strategy upon speckle patterns, interpolation algorithms for the deformed image, and gradient operators for the reference image, and uncover the inherent nature of interpolation bias of inverse strategy. Further more, we will study the spectrum of “numerically-designed speckle patterns”, build a theoretical model to characterize the relationship between speckle generation parameters and speckle assessment parameters, propose an algorithm to generate optimized speckle patterns, and develop a software to implement the algorithm. This project will provide more understanding on systematic errors of inverse strategy, and thus have scientific significance; the software developed can generate optimized speckle patterns for engineering practice, which can simplify the application of DIC, and thus have a promising prospect.

数字图像相关是实验力学领域最受关注并被广泛使用的光学测量技术。目前研究热点之一在于“散斑质量优化方法”，而“散斑质量优化方法”的提出基于对“计算误差”的深入分析。现有研究认为高计算效率的反向算法和传统的正向算法的插值偏差相当，故被广泛采用。申请人在先期预研中通过数值模拟实验证明了其不等价性，本项目拟在前期对正向算法插值偏差频域模型和散斑质量评价标准研究的基础之上，开展反向算法系统误差频域模型的研究，阐明散斑图案、变形图插值算法、参考图梯度算子对反向算法插值偏差的作用机制，揭示反向算法插值偏差的物理本质。进一步的，本项目将研究“数字设计散斑”的频谱分布，建立 “数字设计散斑”生成参数与“散斑质量评价参数”关系表征的理论模型，提出最优化散斑的生成算法并开发相应软件。本项目有助于深入理解反向算法的系统误差，具有明确的科学意义；开发的软件可以用于工程实践，减低技术的使用门槛，具有良好的应用前景。

通过优化散斑图案从而提升数字图像相关测量精度在工程上具有重要意义。针对最优化散斑图案设计这一研究目标，本项目建立了反向组合型高斯牛顿法系统误差的理论模型，揭示了正弦形系统误差的本质，阐明了梯度算子对系统误差的重要作用；建立了数字设计散斑唯一性、系统误差、随机误差和空间分辨率的理论模型，提出了最优化散斑的生成策略，可以指导工程实践中散斑图案的生成，提升数字图像相关测量精度；同时，开发了自由开源的散斑图案生成和分析软件：《光绘》，该软件具有散斑图生成、变形图生成、散斑质量评价和散斑图案推荐等功能，可以服务于数字图像相关技术的教学、研究和工程应用，具有广阔的应用前景。