Thermal tune method for AFM oscillatory resonant imaging in air and liquid

Continuous development of atomic force microscopy and its applications is not always supported by a rigorous theoretical treatment of the related phenomena. A proper understanding of the behavior of microscopic probes and their response to tip-sample force interactions are crucial for a microscope control, optimization of experimental procedures and rational data analysis in the frameworks of quantitative models. Several issues of the probe dynamics and instrument functionality are addressed with a rigorous theoretical analysis of the thermal tune method, which is presented in this paper. It covers theoretical derivation of the method, development of stable convergent algorithms, different averaging techniques, and implementation with high-speed acquisition or a heterodyne technique for low speed acquisition. The developed thermal tune procedure allows for precise determination of the probe resonant frequency, quality factor and spring constant. It was verified practically with AFM probes operating in different environments. It is also shown that this method is applicable for measurements of the microscope functional parameters such as optical deflection noise and inverse optical sensitivity.