High-resolution wide-field magnetic imaging with sparse sampling using nitrogen-vacancy centers

Nitrogen-vacancy (NV) centers in diamond enable quantitative magnetic imaging, yet practical implementations must balance spatial resolution against acquisition time (and thus per-pixel sensitivity). Single-NV scanning magnetometry achieves genuine nanoscale resolution, nonetheless requires typically a slow pixel-by-pixel acquisition. Meanwhile, wide-field NV-ensemble microscopy provides parallel readout over a large field of view, however is jointly limited by the optical diffraction limit and the sensor-sample standoff. Here, we present a sparse-sampling strategy for reconstructing high-resolution wide-field images from only a small number of measurements. Using simulated NV-ensemble detection of ac magnetic fields, we show that a mean-adjusted Bayesian estimation (MABE) framework can reconstruct 10000-pixel images from only 25 sampling points, achieving SSIM values exceeding 0.999 for representative smooth field distributions, while optimized dynamical-decoupling pulse sequences yield an approximately twofold improvement in magnetic-field sensitivity. The method further clarifies how sampling patterns and sampling density affect reconstruction accuracy and suggests a route toward faster and more scalable magnetic-imaging architectures that may extend to point-scanning NV sensors and other magnetometry platforms, such as SQUIDs, Hall probes, and magnetic tunnel junctions.

💡 Research Summary

The paper addresses a fundamental trade‑off in nitrogen‑vacancy (NV)‑based magnetic imaging: achieving high spatial resolution typically requires long acquisition times, while wide‑field NV‑ensemble microscopy offers parallel readout but is limited by optical diffraction and sensor‑sample standoff. To overcome these constraints, the authors propose a sparse‑sampling framework combined with a mean‑adjusted Bayesian estimation (MABE) algorithm that can reconstruct a 10 000‑pixel (100 × 100) magnetic field map from only 25 measurement points.

First, the authors model AC magnetic field detection with NV ensembles, incorporating realistic inhomogeneous broadening (Gaussian static detuning) and dynamic noise (Ornstein‑Uhlenbeck process). They demonstrate that conventional XY‑8 sequences with rectangular π‑pulses suffer severe contrast loss (population contrast <0.2) under these noise conditions. By applying a phase‑modulated (PM) pulse optimization to the XY‑8 sequence, they increase gate fidelities from ~0.43 to ~0.68, raising the spin‑population contrast to ~0.6. This improvement translates into a roughly two‑fold increase in the slope ∂P/∂B, yielding magnetic‑field sensitivities of 0.45 nT · Hz⁻¹ᐟ² (for 128 µs evolution) and 0.64 nT · Hz⁻¹ᐟ² (for 256 µs), compared with 0.94 nT · Hz⁻¹ᐟ² and 1.33 nT · Hz⁻¹ᐟ² for the unoptimized case.

The core imaging methodology treats the magnetic field y(x) as a random field with spatially correlated errors ε(x). A covariance function C_orr(ε(x_i), ε(x_j)) is defined via a distance function d(s_i, s_j)=‖s_i−s_j‖^α P, where α≥0 and 1≤P≤2. These hyper‑parameters are optimized by maximizing the likelihood of the sampled data. The MABE predictor is

\hat{y}(x)=\hat{μ}+rᵀ(x) R⁻¹