In contact resonance force microscopy and related dynamic atomic force microscopy methods, an accurate description of the real-time cantilever dynamics is essential to the mapping of local material properties, such as viscoelasticity, piezo response, and chemical composition. Stiffness and damping variations of the tip-sample contact result in variations in the cantilever's resonance frequency and quality factor as it scans a sample of interest. When measuring characteristics of the resonance, generally, there is a tradeoff between full spectral coverage, best obtained by sweeping the amplitude versus frequency response in the time or frequency domain, and high-speed information, obtained by observing the cantilever response at one or two discrete frequencies, that may be required to track a resonance frequency that changes spatially. Here, we introduce a new option for performing contact resonance force microscopy with a low-cost multifrequency lock-in amplifier system with up to eight simultaneous independent excitation and detection frequencies. We demonstrate how the multifrequency approach can measure contact resonance frequency, quality factor, amplitude, and phase during imaging, with high precision and error estimation, without the need for frequency-tracking feedback. We show, using a wood composite sample, that this multifrequency approach can determine resonance frequency and quality factor, and associated uncertainty. This ability to estimate uncertainty of resonance parameters is not possible with 1 and 2 frequency methods. We further utilize the multifrequency lock-in to develop a novel means of increasing the stiffness range for highly sensitive nanomechanical sensing by dividing the eight lock-in frequencies to monitor two or four simultaneous eigenmodes, each of which is optimized for sensitivity in a particular stiffness regime. Overall, we show how multifrequency lock-in amplifiers with observation frequency chosen to coincide with an expected eigenmode's contact resonance can benefit the characterization of strongly heterogeneous samples, while maintaining fast measurement speed.

中文翻译：

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带有多个任意频率锁定放大器 (MAFLIA) 的接触共振力显微镜中的误差估计和增强的刚度灵敏度

在接触共振力显微镜和相关的动态原子力显微镜方法中，实时悬臂动力学的准确描述对于局部材料特性的映射至关重要，例如粘弹性、压电响应和化学成分。当悬臂扫描感兴趣的样品时，尖端-样品接触的刚度和阻尼变化会导致悬臂的共振频率和品质因数发生变化。在测量谐振特性时，通常需要在全光谱覆盖范围（最好通过在时域或频域中扫描幅度与频率响应来获得）和高速信息（通过观察一或两个处的悬臂响应获得）之间进行权衡离散频率，可能需要跟踪空间变化的共振频率。这里，我们引入了一种新选项，用于使用低成本多频锁定放大器系统执行接触共振力显微镜，该系统具有多达八个同时独立的激发和检测频率。我们展示了多频方法如何在成像过程中测量接触共振频率、品质因数、幅度和相位，具有高精度和误差估计，而无需频率跟踪反馈。我们使用木质复合材料样品表明，这种多频方法可以确定共振频率和品质因数，以及相关的不确定性。使用 1 和 2 频率方法无法估计共振参数的不确定性。我们进一步利用多频锁定开发了一种增加高灵敏度纳米机械传感刚度范围的新方法，方法是将八个锁定频率分开来监测两个或四个同时发生的本征模式，每个本征模式都针对特定刚度的灵敏度进行了优化政权。总体而言，我们展示了选择观察频率与预期本征模式的接触共振重合的多频锁定放大器如何有利于强异质样品的表征，同时保持快速的测量速度。