带激励扫描探针显微术中用于成像中最佳动态模型选择的贝叶斯推断
Bayesian inference in band excitation Scanning Probe Microscopy for optimal dynamic model selection in imaging
摘要：
在过去的二十年里，扫描探针显微镜（SPM）的普遍趋势是从简单的二维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的数据解释的挑战，即从检测到的信号转换到特定于尖端-表面相互作用的描述符，随后转换到材料特性。在这里，我们实现了一个贝叶斯推断的带激发（BE）SPM的成像机制的分析方法。与经典函数拟合方法中的点估计相比，贝叶斯推断允许以相应的先验分布的形式并入材料和探针行为的现有知识，并以易于解释的后验分布的形式返回关于材料功能的信息。我们注意到，在贝叶斯方法的应用中，应特别注意在模型选择与建立实际参数等效的问题上的适当设置。我们进一步探讨了经典铁电材料PbTiO 3中拓扑缺陷处的非线性力学行为。我们观察到的非平凡的Duffing共振频率和样品表面的非线性演化，这表明域结构的隐藏元素的存在。这些观察结果表明，在铁电畴壁的异常行为的频谱可以显着比以前认为的更广泛，可以扩展到非常规的机械性能，除了静态和微波电导。
英文摘要：
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.
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