A high-sensitivity frequency counter for free-induction-decay signals

TL;DR

This paper introduces a high-sensitivity, FPGA-based frequency counter for free-induction-decay signals, achieving sub-millihertz sensitivity without prior signal knowledge, suitable for atomic magnetometry applications.

Contribution

The paper presents a novel FPGA implementation of a frequency measurement algorithm based on the Hilbert transform, enhancing sensitivity and real-time capability for FID signals.

Findings

Sensitivity better than 0.1 mHz/Hz^(1/2) at 10 Hz

Output rate of 200 Hz with high sensitivity

Maintains sensitivity better than 0.4 mHz/Hz^(1/2) at 10 Hz at 1000 Hz output rate

Abstract

Real-time frequency readout of time-dependent pulsed signals with a high sensitivity are key elements in many applications using atomic devices, such as FID atomic magnetometers. In this paper, we propose a frequency measurement algorithm based on the Hilbert transform and implement such a scheme in a FPGA-based frequency counter. By testing pulsed exponential-decay oscillation signals in the frequency range of 10 to 500 kHz, this frequency counter shows a frequency sensitivity better than 0.1 mHz/Hz^(1/2) at 10 Hz, with an output rate of 200 Hz. When the output rate is increased to 1000 Hz, the sensitivity remains better than 0.4 mHz/Hz^(1/2) 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 pre-knowledge 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.