AI 中文总结
本研究设计了偏振与测速联合测量粘弹性应力的方法，通过解析校准和误差传播，证明在Deborah数较高时能有效区分本构模型，并指出分辨能力依赖于Deborah数。
AI 中文摘要
偏振计并不直接报告应力。它报告的是延迟量和方位角，而将这些量转换为应力对，既确定了所需的校准，也确定了后续推断必须承担的协方差。我们针对平面粘弹性流动阐述了这一观测链，并将其与测速技术相结合，进而探究联合测量能够分辨何种信息。校准常数由三个可独立测量的量确定：光程长度、应力-光学系数和波长，而非通过拟合得到。将偏振误差一阶传播，即使输入是独立同方差的，所得的应力协方差也是各向异性且随位置变化的，并且当延迟量趋近于零时，其条件数会恶化，此时线性化本身不再能描述该测量。相位包裹施加了另一个设计约束。在保持总标量数固定并改变测速点与光学点分配比例的情况下，偏向光学点的不均匀分配优于任一纯配置。随后，我们探究在与相同速度数据兼容的本构模型之间，该测量能分辨出何种差异。在有限可扩展非线性弹性Peterlin模型的自洽压力驱动流动中，当可扩展性L^2=50且噪声为3%时，在Deborah数De=2（松弛时间与流动时间尺度之比）下，光学通道在78.1%的实例中拒绝了与速度兼容的Oldroyd-B族，在De=4时拒绝率为100%，而在De低于0.3时拒绝率仅约5%。因此，设计的分辨能力是Deborah数的强函数，必须随其一同给出。两项数值研究均采用理想校准的应力坐标并施加预设协方差；将偏振协方差传播到其中是下一步工作。
英文摘要
A polarimeter does not report stress. It reports a retardance and an azimuth, and converting those to a stress pair fixes both the calibration that is required and the covariance that the subsequent inference must carry. We set out that observation chain for planar viscoelastic flow, combine it with velocimetry, and ask what the combined measurement can resolve. The calibration constant is fixed by three separately measurable quantities (path length, stress-optic coefficient and wavelength) rather than being fitted. Propagating the polarimetric errors to first order gives a stress covariance that is anisotropic and site dependent even for independent homoscedastic inputs, and whose conditioning degrades as the retardance approaches zero, where the linearization itself stops describing the measurement. Wrapping imposes a separate design bound. Two numerical studies follow, both in ideal calibrated stress coordinates under a prescribed covariance rather than the propagated polarimetric one. Holding the total scalar count fixed and varying the split between velocimetric and optical sites, an unequal allocation favoring optical sites outperforms either pure configuration. We then ask what the measurement resolves between constitutive models compatible with the same velocity data. In self-consistent pressure-driven flow of the finitely extensible nonlinear elastic Peterlin model, at extensibility L^2=50 and 3% noise, the optical channel rejects the velocity-compatible Oldroyd-B family in 78.1% of realizations at the Deborah number De=2, the ratio of the relaxation time to the flow timescale, and in 100% at De=4, while rejecting only about 5% below De=0.3. The resolving power of a design is therefore a strong function of Deborah number and must be quoted with it.
Comments16 pages, 4 figures, 1 table. Supplementary material (15 pages) is included as an ancillary file. See also arXiv:2609.25663. v2: reference to arXiv:2609.25663 made resolvable; editorial revisions to the abstract and text; results unchanged
