Optimization of Frequency Measurements for Quantum Magnetometers

Most known quantum magnetometers have a periodic signal at the output. By measuring its frequency, it is possible to estimate the value of the magnetic field induction. In many applications, such as aeromagnetic measurements, one needs to increase the sampling rate, but this also increases the measurement error. The article describes two algorithms for obtaining frequency measurements depending on the characteristics of the equipment. One averages the periods over one sample, the other averages the frequency over the same time gate. It is shown that the frequency estimate can perform better than the period estimate. As an example, a 133Cs optically pumped sensor and a reference frequency of 1 GHz at a sampling rate of 1 kHz were considered. In the case of an ideal input signal, the frequency estimation error corresponds to ±0.074 nT around some regular values every 9 nT, and the period estimation error corresponds to ±0.049 nT every 0.05 nT. In the case of signal noise of 0.5 pT/
$\sqrt {\text {Hz}}$
, the frequency estimation error corresponds to ±0.058 nT, and for the period estimation error, it is ±0.278 nT under the same conditions. The article also describes how to use a satellite navigation system as a time reference to ensure frequency estimation accuracy. In this case, the uncertainty can be as low as
$2\cdot 10^{-{8}}$
or about 1 pT in terms of magnetic field induction. All the ideas are illustrated by experiments. It is shown that, for this frequency counter, a sampling rate of up to 1 kHz can be used with the considered sensors.