A High-Sensitivity Frequency Counter for Free-Induction-Decay Signals

Real-time frequency readout of time-dependent pulsed signals with a high-sensitivity are key elements in many applications using atomic devices, such as free-induction-decay (FID) atomic magnetometers. In this article, we propose a frequency measurement algorithm based on the Hilbert transform and implement such a scheme in a field-programmable gate array (FPGA)-based frequency counter. By testing pulsed exponential-decay oscillation signals in the frequency range of 10–500 kHz, this frequency counter shows a frequency sensitivity better than $100~ \mu \text {Hz}/\sqrt {\text {Hz}} $ at 10 Hz, with an output rate of 200 Hz. When the output rate is increased to 1000 Hz, the sensitivity remains better than $400~ \mu \text {Hz}/\sqrt {\text {Hz}} $ at 10 Hz. The performance on frequency sensitivity is comparable with results obtained by off-line nonlinear fitting processes. In addition, this frequency counter does not require the preknowledge of the analytic expression of the input signals. The realization of such a device paves the way for practical applications of highly sensitive FID atomic magnetometers.