Single shot linear response functions

The MLA synthesizes a multifrequency signal consisting of a carefully tuned linear superposition of many tones. A comb of closely-spaced tones gives a sinc pulse in the time domain. When this signal drives a linear system-under-test, it responds to the each tone independent of all other tones. The MLA measures the response at each tone with zero leakage between tones. The Linear response function of the system-under-test is found by dividing complex numbers at each tone - drive divided by response. This simple division does not work for a nonlinear system because the tones intermodulate.

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A schematic showing experimental data on an AFM cantilever. The resonance curve, both amplitude and phase, is extracted by simple division of response comb with the excitation comb. No frequency sweep is needed. All frequencies are measured at the 'same time', or in the same measurement time window.

Multifrequency sweeping

Single shot can be combined with frequency sweeping to speed up acquisition of broad frequency sweeps with high resolution. See the video for a comparison between first a regular, single frequency sweep taking 30 s, followed by the same sweep with the multifrequency option taking just a few seconds.

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Probing liquid Helium with Quartz Tuning Forks

Quartz crystal tuning forks oscillating in superfluid helium at ultra-low temperatures have extremely high Q mechanical resonance. A group at the University of Lancaster uses the MLA to simultaneously and rapidly measure resonance curves of many tuning forks. Intermodulation measurements reveal subtle nonlinear damping damping effects when the velocity of the tines reaches the Landau critical velocity.

Link to publication