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Optics Express

Accurate magnetic field estimation in fiber-coupled nanodiamond NV ensembles using model-assisted regression

Jian Gao, Doudou Zheng, chenchen tang, Xiaoqi Gao, jiayuan fu, Yang Li, Chong Li, Mengwei Li, Huan Fei Wen, Xin Li, Hao Guo, Zhonghao Li, Jun Tang, Zongmin Ma, Jun Liu

Published Feb 27, 2026• 12 citations
Publisher

Abstract

Fiber-coupled ensembles of nanodiamonds containing nitrogen-vacancy (NV) centers are widely used for microscopic magnetic field measurements. However, the random distribution of NV crystal axes in nanodiamond ensembles causes resonance frequencies from differently oriented NV centers to overlap in the ODMR spectrum, distorting the spectral line shape and breaking the linear mapping between frequency shift and magnetic field. As a result, conventional magnetic field measurements based on Lorentzian fitting suffer from significant systematic errors. Here, we establish a fiber-nanodiamond ensemble model to analyze the impact of random NV orientations on the ODMR linear response and define an effective ensemble-averaged linear response coefficient K . Fisher information analysis identifies an information-optimal intrinsic magnetic field of approximately 640 µT, at which the ensemble response can be reliably approximated as linear in its vicinity. Building on this condition, we propose a model-assisted regression scheme, in which the physical fiber-nanodiamond ensemble model defines the optimal operating condition and the associated linear frequency-field scaling, while intrinsic-field-guided Gaussian regression (IFGGR) extracts magnetic-field-induced frequency shifts from distorted ensemble ODMR spectra, enabling accurate magnetic field estimation via the response coefficient K . Under identical acquisition conditions, the proposed method reduces the RMSE from 37.21 µT to 8.99 µT and significantly suppresses systematic bias, while achieving an absolute sensitivity approaching the shot-noise limit at optimal averaging time. The relative slope error reduction (≈15.6-fold) further confirms improved local linearity near the optimal operating point.

DOI
10.1364/oe.589141

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Fiber-coupled ensembles of nanodiamonds containing nitrogen-vacancy (NV) centers are widely used for microscopic magnetic field measurements. However, the random distribution of NV crystal axes in nanodiamond ensembles causes resonance frequencies from differently oriented NV centers to overlap in the ODMR spectrum, distorting the spectral line shape and breaking the linear mapping between frequency shift and magnetic field. As a result, conventional magnetic field measurements based on Lorentzian fitting suffer from significant systematic errors. Here, we establish a fiber-nanodiamond ensemble model to analyze the impact of random NV orientations on the ODMR linear response and define an effective ensemble-averaged linear response coefficient K . Fisher information analysis identifies an information-optimal intrinsic magnetic field of approximately 640 µT, at which the ensemble response can be reliably approximated as linear in its vicinity. Building on this condition, we propose a model-assisted regression scheme, in which the physical fiber-nanodiamond ensemble model defines the optimal operating condition and the associated linear frequency-field scaling, while intrinsic-field-guided Gaussian regression (IFGGR) extracts magnetic-field-induced frequency shifts from distorted ensemble ODMR spectra, enabling accurate magnetic field estimation via the response coefficient K . Under identical acquisition conditions, the proposed method reduces the RMSE from 37.21 µT to 8.99 µT and significantly suppresses systematic bias, while achieving an absolute sensitivity approaching the shot-noise limit at optimal averaging time. The relative slope error reduction (≈15.6-fold) further confirms improved local linearity near the optimal operating point.
Nitrogen-vacancy (NV) center ensembles provide a powerful platform for high-precision temperature sensing, with ongoing efforts to further enhance their measurement performance. In ensemble NV optically detected magnetic resonance (ODMR) spectra, commonly used Lorentzian and Voigt fitting models fail to accurately describe the spectral shape near the resonance frequency, leading to degraded precision in resonance-frequency determination and, consequently, temperature estimation. In this work, we analytically establish a new fitting method, termed dip-peak fitting, for extracting the resonance frequency from ensemble cw-ODMR spectra. Starting from a physical model that describes ensemble cw-ODMR spectra as a convolution of single-NV responses with distributed zero-field splitting and strain, we show that the spectral feature near resonance can be accurately approximated by a single Lorentzian function with a background term. The proposed fitting model reproduces the cw-ODMR spectrum around resonance more faithfully than conventional approaches, enabling faster and more accurate resonance-frequency determination under weaker microwave excitation. Experiments using fluorescent nanodiamond ensembles confirm the robustness and applicability of this method for high-precision temperature sensing.
A nanodiamond embedding a single nitrogen-vacancy (NV) center has outstanding optical properties since it is readily manipulated and coupled with nanophotonic devices. Reliable methods to identify the orientation of an NV axis on photonic platforms are important to precisely estimate the coupling efficiency between them. We report on a method to identify the orientation of an NV axis. The proposed method consists of a single dataset of optically detected magnetic resonance (ODMR) measurements taken while rotating the magnetic field in a plane and a single ODMR measurement taken while applying the magnetic field in a single direction. By applying this method to a nanodiamond with a single NV center on a microscope coverslip, the orientation of the NV center is determined to be (θNV, ϕNV)=(144.6°, 52.9°) when the magnetic field is scanned in the xy-plane. When the magnetic field is scanned in the xz-plane, it is determined to be (θNV, ϕNV)=(148.0°, 45.7°) which is consistent within 5.2°. This technique will advance progress toward realizing photon-based quantum networks and quantum communication.
Nitrogen-vacancy (NV) centers in diamond are a leading platform for vector magnetometry, offering intrinsic sensitivity to both the magnitude and direction of magnetic fields. NV magnetometers typically rely on an external bias field to lift the degeneracy of the ground-state spin sublevels, enabling spectral discrimination of different NV orientations and spin transitions. At high accuracy, however, such a bias field systematically introduces errors through thermal, mechanical, and hysteretic drifts, thus hindering the accurate measurement of the magnetic field of interest. Several strategies have been proposed to address this limitation, including optical polarization-based orientation labeling, optical anisotropy, strong coupling to nearby nuclear spins, circular microwave polarization, and tailored pulse sequences. In this work, we introduce an optimization-based pulse-shaping control framework that enables selective and robust manipulation of NV ensembles without relying on a static bias field. Our method achieves both orientation-selective and subspace-selective control through optimal temporal modulation of the driving fields, providing a route to resolving spectral overlaps in degenerate NV systems.
Characterizing nitrogen-vacancy (NV) ensembles requires connecting their collective spectra to individual centers that experience different local environments. We develop a symbolic-regression pipeline that carries single-center spin structure into a calibrated ensemble model by generating individual spectral responses and combining them with explicit weights. A constrained search selects Hermitian operator terms from single-center optically detected magnetic resonance spectra, fits their coefficients, and retains the selected expressions as source models for the ensemble. Ensemble calibration then accounts for resonance shifts, local disorder, orientation, and optical response while keeping the individual spectral contributions accessible. On public single-center and ensemble data, the zero-field ensemble held-frequency root-mean-square error decreases from 0.008835 to 0.003872 in normalized photoluminescence, a 56.2% improvement over matched uncorrected composition. In controlled QuTiP ensembles of 128 sites spanning four NV orientations, models calibrated at 0 and 3 mT predict an independently held-out 5.17 mT spectrum with errors of 0.000207-0.000228 across three random seeds, comparable to the 0.000200 noise standard deviation. Resolving the simulated response into its individual-center contributions shows how local spectral diversity combines into the ensemble line shape. By retaining the source Hamiltonians while calibrating sample-dependent spectral differences, the pipeline connects local spin physics to collective optical readout and makes the contributions to an ensemble line shape available for physical interpretation.
Nitrogen-vacancy (NV) centers in nanodiamonds have emerged as a promising quantum sensing platform for biomedical imaging applications, yet random orientations of individual particles present significant challenges in large-scale sensor calibration. In this study, we demonstrate a novel approach to simultaneously determine each particle's crystallographic axes and the surrounding local vector magnetic field. Specifically, a minimum of four distinct bias fields is required to unambiguously extract both the orientation and the local field. We validate our method experimentally using NV centers in two scenarios: (1) in a bulk diamond with known crystal orientation as a proof of concept, and (2) on various single nanodiamonds to mimic real-world applications. Our work represents a crucial step towards unlocking the full potential of nanodiamonds for advanced applications such as in-situ biomedical imaging and nanoscale sensing in complex environments.
Efficient collection of photoluminescence arising from spin dynamics of nitrogen vacancy (NV) centers in diamond is important for practical applications involving precise magnetic field or temperature mapping. These goals may be realized by the integration of nanodiamond particles with optical fibers and volumetric doping of the particles alongside the fiber core. That approach combines the advantages of robust axial fixation of NV diamonds with a direct spatial overlap of their fluorescence with the guided mode of the fiber. We developed a suspended core silicate glass fiber with 750 nm-diameter nanodiamonds located centrally in the 1.5 µm-core cross-section along its axis. The developed fiber probe was tested for its magnetic sensing performance in optically detected magnetic resonance measurements using a 24 cm-long fiber sample, with the NV excitation and fluorescence collection from the far ends of the sample and yielding optical readout contrast of 7% resulting in 0.5 µT·Hz-1/2 magnetic field sensitivity, two orders of magnitude better than in earlier designs. Thanks to its improved fluorescence confinement, the developed probe could find application in magnetic sensing over extended fiber length, magnetic field mapping or gradiometry.