Lock-in amplifier
Depending on the dynamic reserve of the instrument, signals up to a million times smaller than noise components, potentially fairly close by in frequency, can still be reliably detected.
The device is often used to measure phase shift, even when the signals are large, have a high signal-to-noise ratio and do not need further improvement.
This is not the case in many experiments, so the instrument can recover signals buried in the noise only in a limited set of circumstances.
However, in an interview with Martin Harwit, Dicke claims that even though he is often credited with the invention of the device, he believes that he read about it in a review of scientific equipment written by Walter C. Michels, a professor at Bryn Mawr College.
[4] Whereas traditional lock-in amplifiers use analog frequency mixers and RC filters for the demodulation, state-of-the-art instruments have both steps implemented by fast digital signal processing, for example, on an FPGA.
In essence, a lock-in amplifier takes the input signal, multiplies it by the reference signal (either provided from the internal oscillator or an external source, and can be sinusoidal or square wave[5]), and integrates it over a specified time, usually on the order of milliseconds to a few seconds.
If the averaging time T is large enough (i.e. much larger than the signal period) to suppress all unwanted parts like noise and the variations at twice the reference frequency, the output is where
For a simple so called single-phase lock-in-amplifier the phase difference is adjusted (usually manually) to zero to get the full signal.
More advanced, so called two-phase lock-in-amplifiers have a second detector, doing the same calculation as before, but with an additional 90° phase shift.
Today's digital lock-in amplifiers outperform analog models in all relevant performance parameters, such as frequency range, input noise, stability and dynamic reserve.
In a typical 100 MHz bandwidth (e.g. an oscilloscope), a bandpass filter with width much narrower than 100 Hz would accomplish this.
The averaging time of the lock-in amplifier determines the bandwidth and allows very narrow filters, less than 1 Hz if needed.
In the case of an atomic-force microscope, to achieve nanometer and piconewton resolution, the cantilever position is modulated at a high frequency, to which the lock-in amplifier is again referenced.
between the lock-in amplifier output and the peak amplitude of the signal, and a different factor for non-sinusoidal modulation.
Furthermore, the response width (effective bandwidth) of detected signal depends on the amplitude of the modulation.
Infrared light is band-pass filtered to a region of the frequency spectrum that is predominantly absorbed by some gas of interest.
