Wavelet Transform-Based Atomic Force Microscopy: A Computational Paradigm for Dynamic Nanoscale Imaging and Characterisation.

Wavelet transform-based atomic force microscopy (WT-AFM) marks a significant paradigm shift in nanoscale imaging by enabling real-time, simultaneous computational analysis of tip-sample interactions in both the time and frequency domains. Unlike conventional AFM approaches that are limited to steady-state, single-frequency responses-the WT-AFM directly applies wavelet transform techniques to the raw cantilever deflection signal, providing direct access to non-linear, transient and multi-frequency dynamics that remain obscured in traditional modalities. The WT-AFM framework integrates high-speed data acquisition, wavelet decomposition, adaptive noise filtering and a custom unsupervised image fusion algorithm to generate high-contrast, information-rich maps of nanoscale heterogeneity. Coupled with digital twin simulations, this approach bridges experimental measurement with underlying materials physics, offering a powerful interpretative framework for dynamic spectral features. Beyond surpassing the existing multi-frequency AFM techniques in temporal resolution, bandwidth and sensitivity to non-steady-state behaviour, the WT-AFM establishes a dynamic platform for high-speed force mapping, time-resolved Kelvin Probe Force Microscopy and the investigation of complex viscoelastic or multi-layer systems. This perspective highlights how WT-AFM stands to redefine nanoscale characterisation by extending AFM as a computational dynamic platform for probing the temporal evolution of electronic processes, transient interactions and functional heterogeneity at the nanoscale.