Standardizing Force Reconstruction in Dynamic Atomic Force Microscopy

Atomic force microscopy (AFM) enables high-resolution
imaging and
quantitative force measurement, which are critical for understanding
nanoscale mechanical, chemical, and biological interactions. In dynamic
AFM modes, however, interaction forces are not directly measured;
they must be mathematically reconstructed from observables such as
the amplitude, phase, or frequency shift. Many reconstruction techniques
have been proposed over the last two decades, but they rely on different
assumptions and have been applied inconsistently, limiting reproducibility
and cross-study comparison. Here, we systematically evaluate major
force reconstruction methods in both frequency- and amplitude-modulation
AFM, detailing their theoretical foundations, performance regimes,
and sources of error. To support benchmarking and reproducibility,
we introduce an open-source software package that unifies all widely
used methods, enabling side-by-side comparisons across different formulations.
This work represents a critical step toward achieving consistent and
interpretable AFM force spectroscopy, thereby supporting the more
reliable application of AFM in fields ranging from materials science
to biophysics.

原子力显微镜（Atomic Force Microscopy, AFM）可实现高分辨率成像与定量力测量，这对于理解纳米尺度的力学、化学及生物相互作用至关重要。然而在动态原子力显微镜模式下，相互作用力无法直接测得，需通过振幅、相位或频率偏移等可观测量进行数学重构。近二十年来，学界已提出多种力重构技术，但这些技术基于各异的假设，且应用标准不统一，极大限制了研究的可重复性与跨研究对比性。本研究系统评估了频率调制与振幅调制原子力显微镜中的主流力重构方法，详细阐明了其理论基础、性能适用区间与误差来源。为支撑基准测试与研究可重复性，我们推出了一款统一整合所有主流力重构方法的开源软件包，可实现不同方法表述间的并行对比。本研究为实现统一且可解释的原子力显微镜力谱术迈出了关键一步，从而助力原子力显微镜在从材料科学到生物物理学等多个领域的更可靠应用。