Lock-in Amplification and Signal Averaging

If a signal is modulated at a specific frequency, one can observe only at that frequency, selecting against noise and interference at other frequencies. The narrower the range of frequencies contributing to a signal, in general the higher the signal to noise ratio, since noise at all but the chosen frequency is eliminated. For this strategy to work, one must be able to generate the desired signal at a well-defined frequency and to select that frequency away from common interferences such as the power grid frequency, radio stations, and so on. In atomic emission, one might modulate the rate at which sample is introduced. A peristaltic pump provides sample in a periodic, time-varying manner, so one might lock onto the modulation so introduced. Interestingly, this won't eliminate background, since the background will be modulated by the introduction of sample. It will, however, remove many other noise sources. Had atomic fluorescence ever become a commercially-viable technology, modulating excitation would have been simple. Alas, at least to date, atomic fluorescence lives in the world of "might have been."

In a sense, a lock-in amplifer is a low frequency version of an interferometer. If the signal being sought is in phase with the reference frequency, there is constructive interference between the two waves and the in-phase signal can be averaged or accumulated. Any other frequency that is other than an odd harmonic of the lock-in's selected frequency, will average to zero since the non-selected frequency will have positive and negative contributions at random phases with respect to the reference waveform. Odd harmonics will give non-zero, in-phase averaging, but one can use broad-band electronic filtering to block those distant frequencies before the signal gets to the lock-in. The bandwidth of the lockin is (approximately) the reciprocal of the averaging time. Average a signal for 1 s, and the bandwidth is 1 Hz. One has nearly limitless tradeoffs between bandwidth and frequency selectivity.

An on-line simulation allowing you to play with how lock-ins work is also an available module.