# Noninvasive Magnetic-Marking-Based Flow Metering with Optically Pumped Magnetometers
## 1 Introduction  
Flow is one of the most important variables in industrial environments, and its precise measurement is the foundation of process automation. It is an established method in the production, infrastructure and process industry [1]. Electromagnetic flow metering (EMFM) is widely used for flow monitoring in research and industry [1]. However, it requires a minimum conductivity of 5 \(\upmu\)S/cm of the fluid of interest. For nonconductive and multiphase media, which include non-ionized gases, ceramics, fuels or oils, there is no equivalent volumetric flow-metering technique [2].  
NMR-based flow metering has proven to be a viable tool for multiphase flow detection in clinical applications and does not require a minimum conductivity [3, 4]. Conventional high-field NMR measuring devices established on the market are rarely used in industry [5]. The difficult system integration and the associated costs limit its applicability [6]. In the high field NMR regime, strong alternating magnetic fields are a compromise between signal strength and field generation effort. For noninvasive flow metering through metal pipes, the reduced penetration depth of the radiofrequency (RF) signals is an additional obstacle [7].  
For field strengths similar to the Earth's magnetic field or lower (<50 \(\upmu\)T), these disadvantages are significantly attenuated. Low magnetic fields are easy to generate, can be varied rapidly, and the low frequency RF-signals penetrate deeper through metallicenclosures such as pipes [7]. Initial research on low-field NMR techniques applied to flow metering is available [8; 9]. This research has already demonstrated the feasibility of NMR-based flow measurement in the Earth's magnetic field using induction coils [10; 11]. However, for a precise flow-metering method at field strengths below 50 uT, magnetometers are the better choice. In this field regime, signal frequencies are expected to be in the lower kHz to Hz range. For these frequencies, magnetometers show a higher signal-to-noise ratio compared to induction coils [7; 12].  
While the most sensitive magnetometers were cryogenically cooled SQUID detectors for a long time, the first optically pumped magnetometers (OPM) are now commercially available. They allow measurements with comparable sensitivity at room temperature [13]. The working principle of an OPM is based on alkali atoms in a vapor cell, which are spin-polarized by a laser. The spin polarization of the atoms couples to the magnetic field to be measured and generates a measurable frequency [14].  
Utilizing the high magnetic sensitivity of OPM also renders magnetic tracer particles obsolete. Magnetic tracer particles are ferromagnetic clusters of atoms or molecules. When mixed in a liquid, these particles differ from the solution in their magnetic properties. Thus, the determination of the fluid movement is facilitated by monitoring the positions of the magnetic particles [15].  
The present research demonstrates a noninvasive tracer-free flow metering procedure, which uses an OPM operating in the zero-to-ultra-low-field (ZULF) regime as the signal detector. In a first step, the medium to be analyzed (here: water) is pre-polarized. Then, a resonant RF-pulse applies a magnetic time stamp to the medium by changing the water polarization locally. This time stamp can be detected with magnetometers such as OPM downstream. The time difference between pulsing and detecting indicates the flow velocity of the medium. In essence, the apparatus performs a time-of-flight measurement, which also makes the procedure calibration-free.