In this article, an approach is proposed to achieve simultaneous imaging and broadband nanomechanical mapping of heterogeneous soft materials in air by using atomic force microscope (AFM). Simultaneous imaging and mechanical mapping (SIMM) is developed to, for example, correlate morphological and mechanical evolutions of the sample together. Current methods, however, are limited to nanomechanical mapping at a single frequency one at a time, or at frequencies much higher than those of interests for majority of soft polymers and live biological species. These limitations have been tackled through the recently-developed simultaneous imaging and broadband nanomechanical mapping (SIBNM) technique for materials of relatively small mechanical spatial variations. We propose, in this work, to extend the SIBNM technique to heterogeneous materials by developing a gradient-based adaptive Kalman-filtering technique to account for spatial variations of the sample mechanical properties when decoupling the sample topography tracking and the nanomechanical mapping from each other. A compressed-sensing technique is introduced to adaptively tune the gain of the adaptive Kalman filter. Experimental implementation of the proposed approach shows that both the topography and the broadband mechanical mapping of a heterogeneous soft sample can be reliably quantified.

中文翻译：

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原子力显微镜上异质材料的自适应同步形貌和宽带纳米力学映射

在本文中，提出了一种使用原子力显微镜 (AFM) 实现空气中异质软材料的同步成像和宽带纳米力学映射的方法。例如，同步成像和机械映射 (SIMM) 被开发用于将样品的形态学和机械演变关联在一起。然而，当前的方法仅限于以一次一个频率或比大多数软聚合物和活生物物种感兴趣的频率高得多的频率进行纳米力学映射。这些限制已通过最近开发的同步成像和宽带纳米机械映射 (SIBNM) 技术解决，该技术适用于机械空间变化相对较小的材料。我们建议，在这项工作中，通过开发基于梯度的自适应卡尔曼滤波技术将 SIBNM 技术扩展到异质材料，以在将样品形貌跟踪和纳米机械映射相互解耦时考虑样品机械性能的空间变化。引入了压缩传感技术来自适应地调整自适应卡尔曼滤波器的增益。所提出方法的实验实施表明，异质软样品的地形和宽带机械映射都可以可靠地量化。引入了压缩传感技术来自适应地调整自适应卡尔曼滤波器的增益。所提出方法的实验实施表明，异质软样品的地形和宽带机械映射都可以可靠地量化。引入了压缩传感技术来自适应地调整自适应卡尔曼滤波器的增益。所提出方法的实验实施表明，异质软样品的地形和宽带机械映射都可以可靠地量化。