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

Abstract

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.

Figures (7)

• Figure 1: (a) Schematic illustration of an NV center in the diamond lattice. (b) Schematic representation of the temporal correspondence among the target AC magnetic field, the control pulses, and the filter function. From top to bottom: amplitude of the target AC magnetic field; ideal infinite-duration pulse sequence applied at the zero crossings; the corresponding filter function for the ideal pulse sequence; XY-8 rectangular-pulse sequence with finite pulse width; and XY-8-PM sequence with finite pulse width. In our simulation, we set the pulse duration $T_{\mathrm{pulse}}=50$ ns, the pulse interval $\tau_{p}=950$ ns, and the total evolution time $t = 8N\left(T_{\mathrm{pulse}}+\tau_{p}\right)=400~\mu$s, with the sequence number $N = 50$. (c) Time evolution of the NV spin population. The gray line with square markers corresponds to the noiseless case using ideal infinite pulses, whereas the blue line with dot markers and the red line with triangular markers correspond to rectangular pulses and PM pulses, respectively, in the presence of inhomogeneous broadening noise and the dynamical noise (see the main text). (d) Comparison of the Pauli-$X$ and Pauli-$Y$ gate fidelities for rectangular pulses and PM pulses, with fidelity defined in Eq. (7) and PM pulse forms given in Eqs. (8)--(9). (e) Dependence of the normalized spin population for $N=16$ ($t=128~\mu$s). The starred markers denote the points of maximum slope: $k=0.00012$ for rectangular pulses and $k=0.00025$ for PM pulses. (d) Dependence of the normalized spin population for $N=32$ ($t=256~\mu$s). The starred markers denote the points of maximum slope: $k=0.00018$ for rectangular pulses and $k=0.00039$ for PM pulses.
• Figure 2: Imaging performance for magnetic-field distributions with different numbers of extrema. (a),(e),(i) Simulated ground-truth magnetic-field maps containing single, two, and three extrema. (b),(f),(j) Measurement results at $25$ randomly distributed sampling points (marker size enlarged for clarity). (c),(g),(k) Magnetic-field maps reconstructed directly from the sampled data using Bayesian estimation method, yielding $10^{4}$-pixel images. (d),(h),(l) Magnetic-field maps reconstructed from the same sampled data using the MABE method, also producing $10^{4}$-pixel images.
• Figure 3: Illustration of the reference-based mean-adjustment procedure. (a) Values at the reference points, shown as nominal values, measured values, bias-calibrated values, and proportionally calibrated values. The reference values are uniformly chosen so as to span the range covered by the 25 sampling-point measurements. (b) Ground-truth values, unadjusted measurements, bias-calibrated values, and proportionally calibrated values for the 25 sampling points, where the calibration coefficients are obtained from the reference points. (c) Error comparison for the reference points before calibration, after bias calibration, and after proportional calibration. (d) Error comparison for the sampling points before calibration, after bias calibration, and after proportional calibration. For both the reference and sampling points, proportional calibration produces error distributions that are more tightly centered around zero than bias calibration.
• Figure 4: Quantitative image-quality metrics for the MABE reconstruction under irregular magnetic-field distributions containing single, two, and three extrema, as the sampling number $n$ varies: (a) mean absolute error (MAE); (b) root mean square error (RMSE); (c) peak signal-to-noise ratio (PSNR); (d) coefficient of determination ($R^2$); (e) structural similarity index (SSIM). In the figure captions, the arrows shown after each metric indicate whether smaller values ($\downarrow$), larger values ($\uparrow$), or values closer to unity ($\rightarrow 1$) correspond to better reconstruction performance.
• Figure 5: (a) Mean absolute error (MAE) over all $10^{4}$ pixels of the reconstructed image as a function of the number of sampling points used in the MABE method. Each data point represents the average over 20 independent reconstructions. (b) MAE of reconstructed images obtained using MABE under five sampling strategies (see the main text). (c) Sampling-point locations for the five strategies and the corresponding reconstructed $10^{4}$-pixel images obtained using MABE.