Advancement in atomic force microscope (AFM) techniques such as bimodal and multifrequency AFM modes provide new ways to discern material property contrast with greater resolution and specificity at the micro- and nano-scales. However, most AFM techniques to date demodulate the cantilever’s deflection signal at each eigenmode’s resonance frequency to infer tip-sample interactions. This approach neglects each mode’s entire contribution, which includes frequency contents away from the modal resonance frequency, and leaves out potentially useful signals. Furthermore, the need to quantify the energy of the individual eigenmode becomes important when there is energy transfer between eigenmodes, as in the case of a soft cantilever in liquid. This thesis uses a receding horizon Kalman filter to decouple the eigenmodes prior to quantifying the average power of the individual mode in the bimodal experiments in air and liquid. It further shows that capturing the average power of the PLMA-PBMA polymer domains from frequencies away from resonance provides a tool to discern the different polymer domains when the input energy level of the two eigenmodes is approximately equal. Finally, a microtubules imaging in buffer protocol that could be used in multifrequency imaging application is presented.