AI 中文总结
研究针对背景纹影法中二维与三维方法描述独立及系统误差未统一研究的问题，基于几何光学建立统一偏转估计框架，解构关键假设推导表达式并分类方法，利用多种模拟结合光线追踪定量表征和分析误差，为提高诊断准确性提供理论工具。
AI 中文摘要
背景纹影法（BOS）已成为用于密度变化流的通用定量诊断方法，从测量位移估计光线偏转为将记录图像与折射率场联系起来的关键步骤。二维BOS传统上通过直观偏转角处理，三维断层扫描BOS依赖从光线方程导出的严格偏转矢量。这些描述很大程度上独立发展，连接它们的假设及引入的系统误差未得到统一研究。本研究基于几何光学建立统一偏转估计框架，将主流二维和三维方法统一到单一数学结构，揭示各方法背后近似层次。通过解构四个关键假设，推导二维和三维空间严格统一偏转表达式并对主流方法分类。利用一维啁啾信号构建的相位物体和直接数值模拟的二维湍流场，结合高保真非线性光线追踪作为基准，定量表征并分析解释各方法在均匀和非均匀折射率边界条件下的偏转估计误差。本工作为评估和提高定量BOS诊断准确性提供理论工具包。
英文摘要
Background-Oriented Schlieren (BOS) has become a versatile quantitative diagnostic for density-varying flows, in which estimating the light-ray deflection from the measured displacement is the essential step linking the recorded images to the underlying refractive-index field. Two-dimensional BOS traditionally treats this through the intuitive deflection angle, whereas three-dimensional tomographic BOS relies on the rigorous deflection vector derived from the ray equation. These descriptions have evolved largely independently, and the assumptions bridging them, together with the systematic errors they introduce, have not been examined in a unified manner. Based on geometric optics, this study establishes a unified deflection estimation framework that reconciles the mainstream two- and three-dimensional methods into a single mathematical structure and exposes the hierarchy of approximations underlying each. By deconstructing four key assumptions, namely the thin phase object, the uniform boundary refractive index, the paraxial approximation, and the perpendicularity between the deflection vector and the optical axis, we derive rigorous unified deflection expressions in both two- and three-dimensional space and categorize the mainstream methods accordingly. Using phase objects constructed from one-dimensional chirp signals and two-dimensional turbulent fields from Direct Numerical Simulation, combined with high-fidelity nonlinear ray tracing as the ground truth, we quantitatively characterize and analytically interpret the deflection estimation error of each method under both uniform and non-uniform refractive-index boundary conditions. This work provides a theoretical toolkit for assessing and enhancing the accuracy of quantitative BOS diagnostics.
Comments33 pages, 13 figures
