Phase-Based Approaches for Rapid Construction of Magnetic Fields in NV Magnetometry

TL;DR

The paper tackles rapid construction of magnetic-field maps from wide-field NV ODMR signals by converting frequency-domain shifts into a phase signal. It derives $f_{SP}(t) = f_{SA}(t) e^{j 2π t Δf_i}$ and $f_{B_{src}}(t)= e^{j 2π t Δf_i}$ with $Δf_i = γ_{NV} B_{src_i}$, then applies a time-domain filter before estimating $Δf_i$ via (i) linear curve fitting on the unwrapped phase or (ii) ESPRIT frequency estimation. Compared to conventional Lorentzian fitting, the proposed phase-based methods use FFT-based preprocessing and simple univariate fitting, achieving substantial speedups while maintaining accuracy. Experimental results on real ODMR data show about a 70× reduction in processing time with similar magnetic-field maps, and robustness against noise is demonstrated via SSIM analysis. This work suggests that integrating signal-processing techniques into NV magnetometry pipelines can enable real-time, portable quantum sensing and motivates broader adoption of phase-based and subspace methods in quantum sensing.

Abstract

With the second quantum revolution underway, quantum-enhanced sensors are moving from laboratory demonstrations to field deployments, providing enhanced and even new capabilities. Signal processing and operational software is becoming integral parts of these emerging sensing systems to reap the benefits of this progress. This paper looks into widefield Nitrogen Vacancy Center-based magnetometry and focuses on estimating the magnetic field from the Optically Detected Magnetic Resonances (ODMR) signal, a crucial output for various applications. Mapping the shifts of ODMR signals to phase estimation, a computationally efficient approaches are proposed. Involving Fourier Transform and Filtering as pre-processing steps, the suggested approaches involve linear curve fit or complex frequency estimation based on well-known super-resolution technique Estimation of Signal Parameters via Rotational Invariant Techniques (ESPRIT). The existing methods in the quantum sensing literature take different routes based on Lorentzian fitting for determining magnetic field maps. To showcase the functionality and effectiveness of the suggested techniques, relevant results, based on experimental data are provided, which shows a significant reduction in computational time with the proposed method over existing methods

Figures (5)

• Figure 1: A typical ODMR has PL recorded over a band of MW frequencies. Here, two ODMRs for a single $i^{th}$ NV axis are shown in the presence and absence of a magnetic source demonstrating magnetic field-dependent shifts in resonant frequencies; elaborated in (\ref{['bias']}). However, since a diamond crystal allows four different orientations of NV centers, eight dips are expected in the ODMR of NV ensemble system, enabling the construction of a 3D vectorial magnetic field through wide-field microscopy using full ODMR.
• Figure 2: Existing Non-linear Curve fitting
• Figure 3: Proposed Linear Curve fitting approach
• Figure 4: Proposed ESPRIT approach
• Figure 6: Robustness against the addition of noise: Zero-mean Gaussian noise was added in the ODMR with varying Signal-to-Noise ratio (SNR) and a magnetic field map was produced. This map was compared to the magnetic field map obtained using the original ODMR signal using the respective method.