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

In this paper, an approach is proposed to achieve simultaneous imaging and broadband nanomechanical mapping of heterogeneous soft materials in air using atomic force microscope (AFM). Simultaneous imaging and mechanical mapping (SIMM) is developed to, for example, correlate morphological and mechanical evolutions of the samples together. Current methods to SIMM, however, are limited to frequency region(s) that is(are) much higher than that of interests for most soft polymers and biological samples. Such a limitation has been addressed in 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. Firstly, a gradient-based adaptive Kalman filter algorithm is proposed to decouple and split the deflection signal into the response to topography variations and the indentation-caused response, respectively. Then, a compressed-sensing-based mechanical property recovery method is introduced to adaptively tune the gain of adaptive Kalman filter. Experiment results show that both topography imaging and qualitative broadband mechanical mapping of heterogeneous soft samples can be reliably quantified by using the proposed technique.