Amplitude noise spectrum of a lock-in amplifier: application to microcantilever noise measurements

The lock-in amplifier is a crucial component in many applications requiring high-resolution displacement sensing; it's purpose is to estimate the amplitude and phase of a periodic signal, potentially corrupted by noise, at a frequency determined by a reference signal. Where the noise can be approximated by a stationary Gaussian process, such as thermal force noise and electronic sensor noise, this article derives the amplitude noise spectral density of the lock-in-amplifier output. The proposed method is demonstrated by predicting the demodulated noise spectrum of a microcantilever for dynamic-mode atomic force microscopy to determine the cantilever on-resonance thermal noise, the cantilever tracking bandwidth and the electronic noise floor. The estimates are shown to closely match experimental results over a wide range of operating conditions.