The universal tendency in scanning probe microscopy (SPM) over the last two decades is to transition from simple 2D imaging to complex detection and spectroscopic imaging modes. The emergence of complex SPM engines brings forth the challenge of reliable data interpretation, i.e. conversion from detected signal to descriptors specific to tip-surface interactions and subsequently to materials properties. Here, we implemented a Bayesian inference approach for the analysis of the image formation mechanisms in band excitation (BE) SPM. Compared to the point estimates in classical functional fit approaches, Bayesian inference allows for the incorporation of extant knowledge of materials and probe behavior in the form of corresponding prior distribution and return the information on the material functionality in the form of readily interpretable posterior distributions. We note that in application of Bayesian methods, special care should be made for proper setting on the problem as model selection vs. establishing practical parameter equivalence. We further explore the non-linear mechanical behaviors at topological defects in a classical ferroelectric material, PbTiO3. We observe the non-trivial evolution of Duffing resonance frequency and the nonlinearity of the sample surface, suggesting the presence of the hidden elements of domain structure. These observations suggest that the spectrum of anomalous behaviors at the ferroelectric domain walls can be significantly broader than previously believed and can extend to non-conventional mechanical properties in addition to static and microwave conductance.

中文翻译：

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带激发扫描探针显微镜中的贝叶斯推理用于成像中的最佳动态模型选择

在过去的二十年中，扫描探针显微镜 (SPM) 的普遍趋势是从简单的 2D 成像过渡到复杂的检测和光谱成像模式。复杂 SPM 引擎的出现带来了可靠数据解释的挑战，即将检测到的信号转换为特定于尖端-表面相互作用的描述符，然后是材料特性。在这里，我们实施了贝叶斯推理方法来分析带激励 (BE) SPM 中的图像形成机制。与经典函数拟合方法中的点估计相比，贝叶斯推理允许以相应先验分布的形式结合现有的材料知识和探测行为，并以易于解释的后验分布的形式返回有关材料功能的信息。我们注意到，在应用贝叶斯方法时，应特别注意正确设置模型选择与建立实际参数等价的问题。我们进一步探索了经典铁电材料 PbTiO3 拓扑缺陷处的非线性机械行为。我们观察到 Duffing 共振频率的非平凡演变和样品表面的非线性，表明存在域结构的隐藏元素。