Adaptive Simultaneous Topography and Broadband Nanomechanical Mapping of Heterogeneous Materials on Atomic Force Microscope

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.