Abstract
High-precision measurements benefit from lock-in detection of small signals. Here we discuss the extension of lock-in detection to many channels, using mutually orthogonal modulation waveforms, and show how the choice of waveforms affects the information content of the signal. We also consider how well the detection scheme rejects noise, both random and correlated. We address the particular difficulty of rejecting a background drift that makes a reproducible offset in the output signal and we show how a systematic error can be avoided by changing the waveforms between runs and averaging over many runs. These advances made possible a recent measurement of the electron's electric dipole moment (Hudson et al 2011 Nature 473 493).
Highlights
Lock-in detection is a well-known method for picking out a small modulated signal of interest in the presence of a large background
After multiplying the signal-plus-background by the modulation waveform, the dc component is proportional to the signal while the background alternates and can be filtered out
Subsequent improvements to the electronics by Michels, Curtis and Redding [3, 4] resulted in a practical, narrow-band detector of high sensitivity, widely known as a lock-in amplifier ‡. This became a ubiquitous laboratory tool after it was commercialised by Robert Dicke and Princeton Applied Research [5]
Summary
Lock-in detection is a well-known method for picking out a small modulated signal of interest in the presence of a large background. Subsequent improvements to the electronics by Michels, Curtis and Redding [3, 4] resulted in a practical, narrow-band detector of high sensitivity, widely known as a lock-in amplifier ‡. This became a ubiquitous laboratory tool after it was commercialised by Robert Dicke and Princeton Applied Research [5]. In the context of high-precision measurement, Harrison, Player, and Sandars (HPS) [6] describe signal modulation with complex, multi-frequency waveforms chosen to be mutually orthogonal.
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