Diamond-Based Magnetic Imaging with Fourier Optical Processing

Mikael P. Backlund, Pauli Kehayias, and Ronald L. Walsworth

Phys. Rev. Applied 8, 054003 – Published 3 November 2017

Abstract

Diamond-based magnetic field sensors have attracted great interest in recent years. In particular, wide-field magnetic imaging using nitrogen-vacancy (NV) centers in diamond has been previously demonstrated in condensed matter, biological, and paleomagnetic applications. Vector magnetic imaging with NV ensembles typically requires a significant applied field ( $> 10 G$ ) to resolve the contributions from four crystallographic orientations, hindering studies of magnetic samples that require measurement in low or independently specified bias fields. Here we model and measure the complex amplitude distribution of NV emission at the microscope’s Fourier plane and show that by modulating this collected light at the Fourier plane, one can decompose the NV ensemble magnetic resonance spectrum into its constituent orientations by purely optical means. This decomposition effectively extends the dynamic range at a given bias field and enables wide-field vector magnetic imaging at arbitrarily low bias fields, thus broadening potential applications of NV imaging and sensing. Our results demonstrate that NV-based microscopy stands to benefit greatly from Fourier optical approaches, which have already found widespread utility in other branches of microscopy.

Received 22 June 2017

DOI:https://doi.org/10.1103/PhysRevApplied.8.054003

Physics Subject Headings (PhySH)

Imaging & optical processing Micromagnetism Quantum sensing

Nitrogen vacancy centers in diamond

Optical microscopy Optically detected magnetic resonance

Atomic, Molecular & Optical

Authors & Affiliations

Mikael P. Backlund, Pauli Kehayias, and Ronald L. Walsworth^*

Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

^*rwalsworth@cfa.harvard.edu

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Vol. 8, Iss. 5 — November 2017

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Images

Figure 1
Setup and Fourier-plane patterns of NV ensemble photoluminescence. (a) Sketch of NV center pointing along ${\hat{u}}_{1}$ , including three carbon atoms (black spheres), nitrogen atom (red), and vacancy (gray). Lines parallel to each NV orientation class ${\hat{u}}_{j}$ are labeled. Facets of the illustrated rectangular prism coincide with those of the diamond samples used in our experiments and are perpendicular to the [110], $[1 \bar{1} 0]$ , and [001] crystal axes. (b) $x y$ perspective of lattice shown in (a). (c) View of NV along its axis, with transition electric dipole moments (orange). (d) Simplified NV energy-level diagram (level spacings not to scale). The electronic ${{}^{3}A}_{2}$ ground state consists of $m_{s} = 0$ and $m_{s} = \pm 1$ magnetic sublevels split by $D = 2.87 GHz$ . The Zeeman effect further splits $m_{s} = \pm 1$ in response to a magnetic field. Applied microwaves (magenta) facilitate transitions from $m_{s} = 0$ to $m_{s} = \pm 1$ . A 532-nm laser is applied to drive optical transitions to the ${}^{3}E$ manifold. Red PL is collected upon radiative relaxation to the ground state. Nonradiative relaxation through the singlet-state channel is responsible for the spin-state-dependent PL contrast and initialization into $m_{s} = 0$ . (e) Schematic of optical setup, tracing collected PL from the diamond chip to the camera: microscope objective (MO), intermediate Fourier-plane (IFP), tube lens (TL), intermediate image plane (IIP), $4 f$ lens ( $L 1$ ), Fourier plane (FP), linear polarizer (LP), and either $4 f$ lens ( $L 2$ ) or Bertrand lens (BL) depending on whether the measurement calls for imaging real or Fourier space. (f) Simulation of PL contrast distribution in the Fourier plane for a NV oriented along ${\hat{u}}_{1}$ with a $NA = 1.49$ oil objective. (g) Experimentally measured NV ensemble PL contrast distributions in the Fourier plane due to each NV orientation.
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Figure 2
Fourier decomposition of optically detected magnetic resonance spectrum. (a) Schematic depicting the passed polarization as well as the integrated or discarded portions of the pupil for measurement of each spectrum ${\tilde{c}}_{i} (f)$ . (b) Conventional NV ensemble ODMR spectrum realized by computing the average of four measurements $⟨ {\tilde{c}}_{i} (f) ⟩$ at high $Δ_{B} (= 19.52 G)$ such that eight resonances are clearly resolved. Each resonance appears as a triplet due to approximately 2.16-MHz splitting from the ${}^{14}N$ hyperfine interaction. (c) Same as (b) but at low $Δ_{B} (= 0.42 G)$ such that resonances from different NV orientations are not resolved. (d) ODMR measured under each of the four conditions sketched in (a) at $Δ_{B} = 19.52 G$ . (e) Same as (d) but instead at $Δ_{B} = 0.42 G$ . (f) Resulting ODMR spectra after Fourier decomposition at $Δ_{B} = 19.52 G$ . (g) Same as (f) but instead at $Δ_{B} = 0.42 G$ . The highly overlapping ODMR peaks obscure the hyperfine splittings in (c) and (e), whereas (g) shows that they are clearly revealed by the transformation. Different spectra within the same panel in (d)–(g) are offset for clarity.
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Figure 3
Magnetic bead imaging with Fourier optical decomposition. (a) Spatially averaged NV ensemble ODMR spectrum at $Δ_{B} = 22.16 G$ such that resonances are well resolved. Inset: illustration of magnetic bead on diamond surface with magnetic field lines (red). (b)–(d) images of $x$ , $y$ , and $z$ components of magnetic field due to a magnetic bead determined at $Δ_{B} = 22.16 G$ without optical decomposition. Insets show calculated field components from least-squares fit to magnetic dipole source. Scale bar: $10 μ m$ . (e) Spatially averaged NV ensemble ODMR spectrum from measurement at $Δ_{B} = 1.99 G$ such that resonances are not resolved. (f)–(h) Images of $x$ , $y$ , and $z$ components of stray magnetic field due to the same magnetic bead as in (b)–(d) but determined at $Δ_{B} = 1.99 G$ with Fourier optical decomposition. Insets show calculated field components from least-squares fit to magnetic dipole source. (i) Decomposed ODMR spectra of an arbitrary pixel of the low- $Δ_{B}$ measurement showing estimated $c_{1} (f)$ (blue), $c_{2} (f)$ (orange), $c_{3} (f)$ (yellow), and $c_{4} (f)$ (purple), offset for clarity.
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Figure 4
Meteorite magnetic imaging with Fourier optical decomposition. (a)–(c) Images of $x$ , $y$ , and $z$ components of the magnetic field due to a subregion of the Allende meteorite sample, as determined using Fourier optical decomposition to resolve ambiguities from overlapping ODMR peaks. $Δ_{B} = 8.42 G$ . Scale bar: $25 μ m$ . (d) Reflection bright-field image of same region of the meteorite as in (a)–(c). Scale bar: $25 μ m$ . (e) Reflection bright-field image showing larger field of view around the region imaged in (a)–(d) indicated by the magenta square. Scale bar: $500 μ m$ . In each of (a)–(d), the fit $x y$ positions of two magnetic dipole sources are marked with magenta circles (see Fig. S6 in Ref. [24]). (f) Example ODMR spectra without Fourier decomposition in the pixels marked with “x” in (a)–(c). The eight resonances collapse into two or four features in some pixels, resulting in ambiguity. (g) Fourier optical decomposition applied to the same ODMR spectra as in (f) showing individual contributions due to only $c_{1} (f)$ (blue), $c_{2} (f)$ (orange), $c_{3} (f)$ (yellow), and $c_{4} (f)$ (purple). Hyperfine features in (f) and (g) are blurred due to a combination of strong spatial gradients of the sample and a boxcar filter applied to improve the SNR (see Appendix pp3). Spectra within the same panel in (f) and (g) are offset for clarity.
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