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arXiv:2605.04951

Scalar and Vector Airborne Platform Calibration Using Quantum and Classical Magnetometers and Inertial Sensors

Antonia Hager, Torleiv H. Bryne, Mia Jukić

quant-phphysics.app-phSubmitted May 6, 2026• Announced May 7, 2026
arXivHTMLPDF

Abstract

Airborne magnetometry requires rigorous calibration to isolate geomagnetic signals from sensor errors and platform magnetic fields. This magnetic compensation is needed for applications like geophysical exploration and magnetic anomaly navigation. The standard approach utilizes a quantum scalar Optically Pumped Magnetometer (OPM) and a less sensitive fluxgate vector sensor for attitude information. This configuration typically results in a scalar approximation of the platform field. Advancements in high-sensitivity Diamond Nitrogen-Vacancy (NV) vector magnetometers now enable a re-evaluation of the standard hardware configuration and full vector calibration models. We show through rigorous theoretical analysis that scalar calibration models are robust to misalignment. Vector calibration models, however, are intrinsically first-order sensitive to attitude errors, irrespective of the accuracy of the magnetic field measurements. These errors arise from inaccurate representation of the background field direction in the body frame, and can amplify small orientation errors into noticeable calibration residuals. Using realistic sensor models and flight trajectories, we evaluate different sensor configurations for magnetic calibration and assess the use of onboard Inertial Navigation Systems (INS) as an independent attitude reference to enable stable compensation. Our results suggest that quantum vector magnetometers like NV sensors are not sufficient to solve the attitude bottleneck for airborne vector magnetic calibration. However, as a single sensor capable of providing both absolute field and directional measurements, they may offer benefits regarding sensor placement, synchronization, and scalar calibration accuracy.

Comments
Submitted to IEEE for possible publication

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Airborne magnetometry requires rigorous calibration to isolate geomagnetic signals from sensor errors and platform magnetic fields. This magnetic compensation is needed for applications like geophysical exploration and magnetic anomaly navigation. The standard approach utilizes a quantum scalar Optically Pumped Magnetometer (OPM) and a less sensitive fluxgate vector sensor for attitude information. This configuration typically results in a scalar approximation of the platform field.
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Quantum sensors based on nitrogen vacancy (NV) centers in diamond have been a central topic in the sensing community for more than a decade. The extraordinary properties at room temperature of the spin system in diamond have made it one of the most prominent quantum platforms for the development of commercial quantum sensors. In particular, the sensitivity of the electronic spin in NV centers has made diamond-based magnetic sensors of special interest for their potential application in medical, industrial or navigation solutions. However, the use of these sensors for universal vector magnetometry was constrained by the need for previous knowledge on the field being measured to fully exploit their benefits. In this work, we show a method to perform unconditional vector magnetometry without the need of external information on the magnetic field, based only on the spatial arrangement of the diamond and the microwave antenna combination. While previous NV-based vector magnetometry methods require partial knowledge of the magnetic field (e.g. a calibrated bias field), we exploit the possibilities of selecting particular directions of the spins in the diamond with elliptically polarized microwave fields. We prove that our method allows to estimate both magnitude and direction of external magnetic fields without further assumptions or constraints.
Accurate magnetic field direction sensing in compact platforms is critical in applications spanning magnetic navigation, space science, and biomedical imaging. We demonstrate a single-optical-axis vector optically pumped magnetometer based on Rabi oscillations between Zeeman sublevels driven by a series of resonant radiofrequency (RF) polarization ellipses (PEs). A calibration protocol based on controlled rotations of the DC magnetic field determines the spatial orientation of each PE. We develop a detailed theoretical model describing the angular dependence of the Rabi frequencies, incorporating key systematics including RF Stark shifts and Bloch-Siegert shifts. We also account for an RF-based heading-error systematic affecting Rabi-frequency measurements arising from the nonlinear Zeeman effect. Simultaneous Larmor measurements yield the magnitude of the magnetic field, enabling integrated vector-scalar measurements. The magnetometer achieves deadzone-free vector operation with 80 μμμrad mean angular accuracy and angular noise densities as low as 8 μμμrad/Hz/\sqrt{\mathrm{Hz}}/Hz​, offering a pathway towards miniaturized sensors without requiring 3D optical access or sensor rotations.
Damage in infrastructure is often hidden until it becomes costly or dangerous. Common examples include corrosion under insulation, early fatigue damage in steel, corrosion of embedded reinforcement, and abnormal current flow in batteries and power equipment. Magnetic methods are attractive because they can sense through coatings, insulation, and concrete cover without couplants, but field performance is often limited by lift-off, low-frequency drift, background magnetic noise, and the weak low-frequency response of pickup coils. This review examines two room-temperature quantum receiver platforms: optically pumped atomic magnetometers (OPMs) and nitrogen-vacancy (NV) diamond magnetometers. Rather than treating them as stand-alone sensors, we compare them as parts of a full measurement chain that includes source physics, geometry, readout, calibration, and interpretation. The literature is organized into four magnetic signal classes: driven induction responses, leakage fields in magnetic flux leakage inspection, passive self-fields linked to stress or corrosion, and fields produced by operational currents. OPMs are strongest for low-frequency, phase-referenced induction measurements, while NV sensors are strongest for near-surface field mapping, vector or gradient measurements, and differential current sensing in compact solid-state heads. Across all applications, deployment depends less on best-case sensitivity than on usable bandwidth, dynamic range, background rejection, geometry control, calibration, and validation. The clearest path to field use is therefore robust instrument engineering tied to qualification methods that reflect real inspection conditions.
The nitrogen-vacancy (NV) center in diamond has become a widely used platform for quantum sensing. The four NV axes in monocrystalline diamond specifically allow for vector magnetometry, with magnetic-field sensitivities reaching down to fT / Hz . The current literature primarily focuses on improving the precision of NV-based magnetometers. Here, we study the experimental accuracy of determining the magnetic field from measured spin-resonance frequencies via solving the NV Hamiltonian. We derive exact, analytical, and fast-to-compute formulas for calculating resonance frequencies from a known magnetic-field vector, and vice versa (formulas for calculating the magnetic-field vector from measured resonance frequencies). Additionally, the accuracy of often-used approximations is assessed. Finally, we promote using the Voigt profile as a fit model to determine the linewidth of measured resonances accurately. An open-source Python package accompanies our analysis.
In modern-day quantum metrology, quantum sensors are widely employed to detect weak magnetic fields or nanoscale signals. Quantum devices, exploiting quantum coherence, are inevitably connected to physical constants and can achieve accuracy, repeatability, and precision approaching fundamental limits. As a result, these sensors have shown utility in a wide range of research domains spanning both science and technology. A rapidly emerging quantum sensing platform employs atomic-scale defects in crystals. In particular, magnetometry using nitrogen-vacancy (NV) color centers in diamond has garnered increasing interest. NV systems possess a combination of remarkable properties, optical addressability, long coherence times, and biocompatibility. Sensors based on NV centers excel in spatial resolution and magnetic sensitivity. These diamond-based sensors promise comparable combination of high spatial resolution and magnetic sensitivity without cryogenic operation. The above properties of NV magnetometers promise increasingly integrated quantum measurement technology, as a result, they have been extensively developed with various protocols and find use in numerous applications spanning materials characterization, nuclear magnetic resonance (NMR), condensed matter physics, paleomagnetism, neuroscience and living systems biology, and industrial vector magnetometry. In this chapter, NV centers are explored for magnetic sensing in a number of contexts. In general, we introduce novel regimes for magnetic-field probes with NV ensembles. Specifically, NV centers are developed for sensitive magnetometers for applications where microwaves (MWs) are prohibitively invasive and operations need to be carried out under zero ambient magnetic field. The primary goal of our discussion is to improve the utility of these NV center-based magnetometers.