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# Diamond-on-chip infrared absorption magnetic field camera

Julian M. Bopp  Humboldt-Universität zu Berlin, Department of Physics, 12489
Berlin, Germany  Ferdinand-Braun-Institut gGmbH, Leibniz-Institut für
Höchstfrequenztechnik, 12489 Berlin, Germany  Hauke Conradi  Fraunhofer-
Institut für Nachrichtentechnik, Heinrich-Hertz-Institut, 10587 Berlin,
Germany  Felipe Perona  Ferdinand-Braun-Institut gGmbH, Leibniz-Institut für
Höchstfrequenztechnik, 12489 Berlin, Germany  Anil Palaci  Humboldt-
Universität zu Berlin, Department of Physics, 12489 Berlin, Germany  Jonas
Wollenberg  Humboldt-Universität zu Berlin, Department of Physics, 12489
Berlin, Germany  Thomas Flisgen  Ferdinand-Braun-Institut gGmbH, Leibniz-
Institut für Höchstfrequenztechnik, 12489 Berlin, Germany  Armin Liero
Ferdinand-Braun-Institut gGmbH, Leibniz-Institut für Höchstfrequenztechnik,
12489 Berlin, Germany  Heike Christopher  Ferdinand-Braun-Institut gGmbH,
Leibniz-Institut für Höchstfrequenztechnik, 12489 Berlin, Germany  Norbert
Keil  Fraunhofer-Institut für Nachrichtentechnik, Heinrich-Hertz-Institut,
10587 Berlin, Germany  Wolfgang Knolle  Leibniz-Institut für
Oberflächenmodifizierung e.V., 04318 Leipzig, Germany  Andrea Knigge
Ferdinand-Braun-Institut gGmbH, Leibniz-Institut für Höchstfrequenztechnik,
12489 Berlin, Germany  Wolfgang Heinrich  Ferdinand-Braun-Institut gGmbH,
Leibniz-Institut für Höchstfrequenztechnik, 12489 Berlin, Germany  Moritz
Kleinert  Fraunhofer-Institut für Nachrichtentechnik, Heinrich-Hertz-Institut,
10587 Berlin, Germany  Tim Schröder  Humboldt-Universität zu Berlin,
Department of Physics, 12489 Berlin, Germany  Ferdinand-Braun-Institut gGmbH,
Leibniz-Institut für Höchstfrequenztechnik, 12489 Berlin, Germany
Corresponding author: Tim Schröder<EMAIL_ADDRESS>
###### Abstract

Integrated and fiber-packaged magnetic field sensors with a sensitivity
sufficient to sense electric pulses propagating along nerves in life science
applications and with a spatial resolution fine enough to resolve their
propagation directions will trigger a tremendous step ahead not only in
medical diagnostics, but in understanding neural processes. Nitrogen-vacancy
centers in diamond represent the leading platform for such sensing tasks under
ambient conditions. Current research on uniting a good sensitivity and a high
spatial resolution is facilitated by scanning or imaging techniques. However,
these techniques employ moving parts or bulky microscope setups. Despite being
far developed, both approaches cannot be integrated and fiber-packaged to
build a robust, adjustment-free hand-held device. In this work, we introduce
novel concepts for spatially resolved magnetic field sensing and 2-D
gradiometry with an integrated magnetic field camera. The camera is based on
infrared absorption optically detected magnetic resonance (IRA-ODMR) mediated
by perpendicularly intersecting infrared and pump laser beams forming a pixel
matrix. We demonstrate our 3-by-3 pixel sensor’s capability to reconstruct the
position of an electromagnet in space. Furthermore, we identify routes to
enhance the magnetic field camera’s sensitivity and spatial resolution as
required for complex sensing applications.

Solid-state magnetic field sensors offer outstanding sensitivities at room
temperature. Particularly, sensing with negatively-charged nitrogen-vacancy
(NV) centers in diamond has evolved into a well-established technique not only
limited to material sciences [1, 2, 3, 4] and biological applications [5, 6,
7, 8, 9, 10, 11]. This is the case since operating NV centers under bias
magnetic fields up to several Tesla is feasible and since the involved
measurement sensitivities are approaching fundamental quantum limits [12, 13].

Nowadays, there are three different NV-based sensor types. Each type is
suitable for certain applications, but none of them combines the advantages of
fully integrated photonic devices and multi-pixel imaging sensors. Firstly,
there are miniaturized single-pixel hand-held devices [14, 15, 16, 17, 18,
19]. Secondly, scanning magnetometers provide highest spatial resolutions by
scanning a diamond tip across a sample [20, 3, 21, 22]. However, their moving,
and thus sensitive parts prevent scanning magnetometers from becoming mobile
devices by on-chip integration. Thirdly, approaches utilizing lock-in
amplifier cameras are capable of recording entire magnetic field images with
sub-millisecond temporal resolution without the need for any moving
components. Though, lock-in camera approaches suffer from limited per-pixel
sensitivity [23, 24]. Photonic integration of lock-in camera magnetometers is
hardly possible due to the involved bulky optical components like a microscope
objective. Consequently, full photonic integration remains an obstacle for
next-generation NV magnetic field imagers suitable for neuroscience
applications [6].

In our work, we bridge the gap between single-pixel hand-held sensors and
complex imaging magnetometers involving either sensitive moving parts or bulky
optics. We propose and demonstrate an integrated magnetic field camera capable
of measuring magnetic fields with pixels aligned as a two-dimensional matrix
in a diamond substrate. Being fiber-packaged, the camera does neither require
any free-space optical components nor a strong pump laser beam illuminating a
sample from the top, which might damage biological samples. In contrast to the
vast majority of NV-based magnetic field sensors, we exploit the NV-
${}^{1}\\!A_{1}\leftrightarrow{}^{1}\\!E$ singlet transition, which emits and
absorbs $1042\text{\,}\mathrm{nm}\text{/}$ infrared light upon
$532\text{\,}\mathrm{nm}\text{/}$ pumping if the NV-’s electron spin is
flipped to the $m_{\mathrm{s}}=\pm 1$ state [25, 26]. This infrared absorption
optically detected magnetic resonance (IRA-ODMR) technique opens up entirely
new routes to NV magnetometry despite its to date inferior measurement
sensitivity compared to red fluorescence ODMR [27, 28, 29]. In this way, IRA-
ODMR merged with our novel sensor design allows for spatially defining
magnetic field sensitive pixels: an array of collimated green pump laser beams
intersects perpendicularly with an array of collimated infrared laser beams
(Figure 1a). Turning on the respective pump beam in row $i\in\left[1,N\right]$
and the infrared beam in column $j\in\left[1,N\right]$ enables selective
addressing and readout of the pixel $\left(i,j\right)$ within the sensor
matrix. To reconstruct an image of the magnetic field across the sensor, the
pixels are subsequently selected and read out using an IRA-ODMR measurement.
Such images intrinsically contain information on a two-dimensional magnetic
field gradient applied to the sensor.

## A multi-pixel magnetic field camera

To enable IRA-ODMR by driving the NV-’s electron spin, we place microwave
inductor lines RFi on top of the diamond substrate (Figure 1a). We modulate
the time $t$-dependent spin-driving microwave electromagnetic field’s
frequency according to

$f_{\mathrm{RF}}\\!\left(t\right)=f_{\mathrm{c}}+f_{\mathrm{dev}}\cos\\!\left(2\mathrm{\pi}f_{\mathrm{mod}}t\right)$
(1)

around a center frequency $f_{\mathrm{c}}$ with a modulation frequency
$f_{\mathrm{mod}}$ and a modulation depth $f_{\mathrm{dev}}$. The center
frequency-dependent difference signal of a balanced photodetector proportional
to the infrared absorption is demodulated with a lock-in amplifier and
recorded as the ODMR signal $U\\!\left(f_{\mathrm{c}}\right)$ (refer to
methods section). By sweeping $f_{\mathrm{c}}$, we first perform IRA-ODMR
measurements on each pixel to verify their integrity. Without any offset
magnetic field applied, each pixel reveals a clear ODMR signature in
$U\\!\left(f_{\mathrm{c}}\right)$ around $2.87\text{\,}\mathrm{GHz}\text{/}$.
For pixel $\left($1$,$1$\right)$, the ODMR signature is very weak due to a
reduced local overlap between intersecting pump and infrared beams. All ODMR
signatures vanish turning either the pump or the infrared beams off (refer to
supplementary information B.1). This unambiguously proves that the recorded
ODMR signatures originate from infrared absorption.

To render our sensor magnetic field sensitive, we split the four possible NV
orientations into two ensembles by applying an offset magnetic field aligned
along the $\left[0\bar{1}1\right]$-direction: The $\left[111\right]$\- and
$\left[1\bar{1}\bar{1}\right]$-oriented subensembles constitute ensemble $1$.
They do not respond to the offset magnetic field in first approximation.
Whereas, the $\left[\bar{1}1\bar{1}\right]$\- and
$\left[\bar{1}\bar{1}1\right]$-oriented subensembles (ensemble $2$) are split
by the same frequency of about $133\text{\,}\mathrm{GHz}\text{/}$. Figure 1b
shows a resonance-split ODMR signature exemplarily for the center pixel
$\left($2$,$2$\right)$. Data for the other pixels is displayed in
supplementary information B.2. The pixel $\left($1$,$1$\right)$ is excluded
from the following analysis for an insufficient signal-to-noise ratio. For
each of the two ensembles, there are two resonances caused by the two
$m_{\mathrm{s}}=0\rightarrow\pm 1$ transitions. We attribute the different
magnitudes of the four visible resonances to the microwave polarization: the
microwave magnetic field produced by a ring-shaped inductor stacked on top of
the diamond substrate’s $\left(111\right)$-oriented top surface is parallel to
the $\left[111\right]$-oriented NV centers (and perpendicular to the offset
magnetic field), thus reducing the magnitude of the first ensemble’s
resonances [30]. To determine the lower $f_{-}$ and higher $f_{+}$ resonance
frequencies of the NV ensemble $2$ used for sensing as well as the
corresponding slopes $a_{\pm}$, we perform linear fits
$U\\!\left(f_{\mathrm{c}}\right)=a_{\pm}\left(f_{\mathrm{c}}-f_{\pm}\right)$
around the $m_{\mathrm{s}}=0\rightarrow\pm 1$ resonances. An additional fit of
the $f_{+}$ resonance by the derivative of a Gaussian function yields the
pixel-averaged inhomogeneously broadened linewidth as
$6.4(3)\text{\,}\mathrm{MHz}\text{/}$ standard deviation. Inhomogeneous
broadening occurs due to the high NV density and $f_{\mathrm{dev}}$ spanning
all hyperfine transitions [31]. Despite causing line broadening, such a high
modulation depth $f_{\mathrm{dev}}$ is necessary to achieve reasonable signal-
to-noise ratios in the ODMR measurements. Integrating the Gaussian-type fit
leads to the ODMR contrast $C$ [32] after normalization with the detected
infrared power (refer to supplementary information D.2). For pixel
$\left($3$,$3$\right)$, we obtain the highest contrast
$C_{$3$,$3$}=$5.1\text{\times}{10}^{-6}$$, for pixel $\left($3$,$2$\right)$
the lowest contrast $C_{$3$,$2$}=$0.5\text{\times}{10}^{-6}$$, and for the
pixel-average $\bar{C}=$23(16)\text{\times}{10}^{-7}$$. The observed values
agree with the contrast of $2.3\text{\times}{10}^{-06}$ obtained by modeling
the NV including its neutral charge state [33] (refer to supplementary
information D.1). Non-optimal pump and infrared beam overlaps may reduce the
measured contrast compared to the simulated value. Increased values might
originate from uncertainties in measuring the infrared power impinging on the
balanced photodetector and from uncertainties in the transition rates and
absorption cross sections employed to model the contrast.

The frequency-dependent magnetic field sensitivity of each pixel is best
characterized by the amplitude spectral densities (ASD) of different noise
contributions as depicted in Figure 1c. Magnetic sensitive (insensitive) noise
ASDs $S^{\mathrm{on}}$ $\left(S^{\mathrm{off}}\right)$ are derived using a
Fourier transform of a $100\text{\,}\mathrm{s}\text{/}$-long time series of
the demodulated ODMR signal $U$ recorded at $f_{\mathrm{c}}=f_{+}$
$\left(f_{\mathrm{c}}=$2.98\text{\,}\mathrm{GHz}\text{/}$\right)$ as detailed
in supplementary information C.1. Up to the lock-in cutoff frequency, both
$S^{\mathrm{on}}$ and $S^{\mathrm{off}}$ show a coinciding flat plateau which
closely matches the ASD of optical shot noise $S^{\mathrm{SN}}$ caused by
infrared photons impinging on the balanced photodetector (refer to
supplementary information C.2). Contrarily, the electronic noise floor
$S^{\mathrm{el}}$ recorded at $f_{\mathrm{c}}=f_{+}$ with the infrared beam
turned off remains at lower values compared to $S^{\mathrm{SN}}$ emphasizing
that our sensor is currently limited by the low intensity of the detected
infrared signal. In accordance with the contrast estimation, pixel
$\left($3$,$3$\right)$ reveals the best sensitivity of
$$10.6\text{\,}\mathrm{\SIUnitSymbolMicro T}\text{/}$_{\mathrm{rms}}$ and
pixel $\left($3$,$2$\right)$ the worst sensitivity of
$$44.0\text{\,}\mathrm{\SIUnitSymbolMicro T}\text{/}$_{\mathrm{rms}}$ by
integrating the respective $S^{\mathrm{on}}_{i,j}$ up to the lock-in cutoff
frequency. Thus, the pixel-averaged sensitivity becomes
$$25(10)\text{\,}\mathrm{\SIUnitSymbolMicro T}\text{/}$_{\mathrm{rms}}$ (refer
to supplementary information B.2).

Figure 1: Working principle of the chip-integrated NV-based multi-pixel
magnetic field camera. a A diamond substrate and single-mode fibers (SMF)
terminated by beam-collimating graded-index fibers (GF) are glued into
trenches etched into a polymer substrate. The polymer covers a silicon
submount (Si) for stability. Intersecting $532\text{\,}\mathrm{nm}\text{/}$
pump and $1042\text{\,}\mathrm{nm}\text{/}$ infrared laser beams define the
magnetic sensitive pixel $\left(i,j\right)$ inside the diamond substrate.
$$10$\,\%$ of the injected infrared light is split off by a fiber coupler (FC)
and directed to the reference input of a balanced photodetector (BPD) after
passing an adjustable fiber attenuator (A). The infrared light transmitted
through the diamond substrate passes a $1000\text{\,}\mathrm{nm}\text{/}$
longpass filter (LP) located in a fiber U-bench before it reaches the BPD’s
signal input. The BPD’s difference signal is amplified by a lock-in amplifier
(LIA) and processed with a computer. A signal generator (SG) provides a
reference for the LIA-demodulation and generates a frequency-modulated
microwave signal which is amplified (AMP) and fed into the respective
microwave inductor line (RFi) located above the row of active (pumped) pixels.
The full mechanical setup is detailed in supplementary information A.1. b
Exemplary IRA-ODMR signature (red curve) of pixel $\left($2$,$2$\right)$ with
an offset magnetic field. The light blue curves represent linear fits around
the two resonances used for sensing. One resonance is fitted by a derivative
of a Gaussian function (dark blue curve). c Noise amplitude spectral densities
$S$ related to the $2.939\text{\,}\mathrm{GHz}\text{/}$ resonance displayed in
b recorded on-resonance (magnetic sensitive), off-resonance (magnetic
insensitive), and with the infrared beam turned off (electronic noise). The
cyan line visualizes the infrared optical shot noise imposed on the signal
detected by the BPD. The gray dashed line indicates the lock-in cutoff
frequency.

### Magnetic field imaging

After confirming the pixels’ integrity, we now apply the magnetic field camera
to capture an image of the magnetic field generated by a current-driven
solenoid coil with $N_{\mathrm{s}}=$15$$ windings, a radius of
$R_{\mathrm{s}}=$450\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$$, and a
length of $L_{\mathrm{s}}=$6.1\text{\,}\mathrm{mm}\text{/}$$. The solenoid is
located above pixel $\left($3$,$3$\right)$ on top of the diamond substrate.
The magnetic field to be probed points along the $\left[111\right]$-direction.
Hence, it affects both the $\left[\bar{1}1\bar{1}\right]$\- and
$\left[\bar{1}\bar{1}1\right]$-oriented NV subensembles (ensemble $2$) in the
same way.

Figure 2a depicts the magnetic field measured for each pixel for two different
solenoid currents $I_{\mathrm{s}}$ (refer to methods section). The measured
magnetic field increases for each pixel at the higher current. Furthermore,
for both currents, the magnetic field is strongest underneath the solenoid
coil’s center around pixel $\left($3$,$3$\right)$. Moving away from pixel
$\left($3$,$3$\right)$, the magnetic field decreases, which complies within
sensitivity and uncertainty bounds (refer to supplementary information B.2)
with a simulation of the solenoid’s magnetic field as shown color-coded in
Figure 2b.

We use the higher current
$\left(I_{\mathrm{s}}=$963\text{\,}\mathrm{mA}\text{/}$\right)$ magnetic field
image and the solenoid’s simulated magnetic field to reconstruct the position
of the camera relative to the solenoid. Minimizing the position-dependent
difference in the absolute values of the measured $B_{i,j}$ and simulated
$B_{\mathrm{s}}\\!\left(x,y,z\right)$ magnetic fields summed over all pixels
(refer to supplementary information B.3) yields the position of the magnetic
field camera. Blue crosses in Figure 2b indicate the retrieved camera pixel
positions. The retrieved camera position matches the experimental conditions
since the solenoid coil was indeed positioned above pixel
$\left($3$,$3$\right)$. We determine the camera’s position uncertainty
$(\delta x,\allowbreak\delta y,\allowbreak\delta
z)\allowbreak=\allowbreak($30$,\allowbreak$20$,\allowbreak$10$)\,$\mathrm{\SIUnitSymbolMicro
m}\text{/}$$ by Monte Carlo sampling of each pixel’s magnetic field normal
distribution spanned by the measured mean values $B_{i,j}$ and their
uncertainties $\tilde{B}_{i,j}$.

Figure 2: Magnetic field imaging for magnetic object detection. a A solenoid
coil driven by a current $I_{\mathrm{s}}$ is placed above pixel
$\left($3$,$3$\right)$. For two different currents, the coil produces a
magnetic field, which is spatially resolved by the magnetic field camera for
the pixels $\left(i,j\right)$. The measured magnetic field $B_{i,j}$ is shown
color-coded. Readout from pixel $\left($1$,$1$\right)$ is not possible due to
insufficient local pump and infrared beam overlap. Supplementary information
B.2 presents the magnetic field uncertainty extracted for each pixel and each
solenoid current as well as each pixels’ sensitivity. Blue crosses denote
pixel values employed for retrieving the camera position relative to the
solenoid coil as depicted in b. b Schematic drawing of the solenoid coil (gray
spiral) with radius $R_{\mathrm{s}}$, length $L_{\mathrm{s}}$ and the absolute
value of the magnetic field $B_{\mathrm{s}}$ it produces for
$I_{\mathrm{s}}=$0.96\text{\,}\mathrm{A}\text{/}$$ at a vertical position of
$z=$-4.53\text{\,}\mathrm{mm}\text{/}$$, where the magnetic field camera was
localized by a minimization procedure applied to the data visualized in a.
Blue crosses indicate the retrieved locations of the camera pixels
$\left(i,j\right)$.

### Single-pixel benchmarking

We successfully captured an image of a solenoid coil’s spatial magnetic field
distribution despite the sensitivity limitations of our multi-pixel magnetic
field camera. These limitations originate from (i) the non-optimal pump and
infrared beam overlap within the pixel volumes, (ii) restricted laser powers
due to the adhesive’s damage threshold, and (iii) the weak interaction cross
section between infrared photons and the NV- singlet transition without
cavity-enhancement [33]. Whereas overcoming constraint (iii) is not
straightforward without employing an optical cavity for infrared photons, we
now examine a single-pixel sensor which relieves constraints (i) and (ii). In
a setup utilizing free-space optics, the pump and infrared beams are adjusted
to intersect perfectly within a second diamond substrate (Figure 3a). A
similar infrared power but an at least $64$ times higher pump power compared
to the multi-pixel sensor is applied (refer to methods section). Figure 3b
depicts the corresponding IRA-ODMR signature. Besides the expected increase in
the signal-to-noise ratio under optimized measurement conditions, the ODMR
signature resembles the multi-pixel sensor’s ODMR signatures closely (compare
with Figure 1c). The upper resonance at
$f_{+}=$2.936\text{\,}\mathrm{GHz}\text{/}$$ features a
$4.8\text{\,}\mathrm{MHz}\text{/}$ inhomogeneously broadened linewidth
(standard deviation) as well as an ODMR contrast of
$C=$6.6\text{\times}{10}^{-5}$$. The difference between the contrast of
$1.7\text{\times}{10}^{-5}$ as modeled for the single-pixel sensor
configuration according to [33] (refer to supplementary information D.1) and
the measured contrast hints at the need to determine the NV transition rates
and absorption cross sections more precisely.

Last, we find significantly better sensitivities as shown in Figure 3c. Within
the $10$ times larger measurement bandwidth compared to the multi-pixel
sensor, the sensitivity improves to
$$390\text{\,}\mathrm{nT}\text{/}$_{\mathrm{rms}}$ in the magnetic sensitive
case. While the magnetic insensitive amplitude spectral density is completely
flat up to the lock-in cutoff frequency, there is some excess noise below
about $0.8\text{\,}\mathrm{Hz}\text{/}$ in the magnetic sensitive case raising
the magnetic sensitive amplitude spectral noise density above the magnetic
insensitive one. We attribute this excess noise to low-frequency technical
noise in our system. Particularly, we do not compensate for intensity
fluctuations in the pump light. An infrared power $P_{\mathrm{IR}}$-dependent
measurement of the magnetic sensitive rms noise $\delta
B^{\mathrm{on}}_{\mathrm{rms}}$ reveals a dependency $\delta
B^{\mathrm{on}}_{\mathrm{rms}}\sim 1/\sqrt{P_{\mathrm{IR}}}$, which allows to
derive the spin dephasing time
$T_{2}^{*}=$520(110)\text{\,}\mathrm{ns}\text{/}$$ (refer to supplementary
information D.3). Hence, the single-pixel sensor still operates in a nearly
shot noise-limited regime.

The measured single-pixel sensor’s sensitivity indicates the multi-pixel
sensor’s potential when addressing solely the above-mentioned issues (i) and
(ii). The single-pixel sensor avoids optical losses which exist in the multi-
pixel case where infrared light is coupled from a fiber into the diamond
substrate and collected at the opposite side facet. These losses reduce the
amount of detected infrared photons, and thus raise the relative shot noise
contribution emphasizing the relevance of reducing optical losses in the
infrared path through the diamond substrate. For the multi-pixel sensor, the
increased relative infrared shot noise as well as further frequency-
independent electronic noise contributions obscure the technical excess noise
at lower frequencies causing the magnetic sensitive and insensitive amplitude
spectral densities to coincide (Figure 1c).

Figure 3: Single-pixel reference measurements. a A free-space green pump beam
intersects with a free-space infrared beam within a bulk diamond substrate
with $\left(111\right)$-oriented top surface. A copper wire coil is located
directly above the intersection to drive the NV-’s spin transitions for IRA-
ODMR measurements. The RF input as well as the laser inputs and outputs are
connected to the measurement system as depicted in Figure 1a replacing the
integrated sensor but maintaining the same pixel volume as defined by the beam
waists (refer to methods section). b Corresponding IRA-ODMR signature (red
curve) with an offset magnetic field in $\left[0\bar{1}1\right]$-direction. c
Noise amplitude spectral densities $S$ related to the
$2.936\text{\,}\mathrm{GHz}\text{/}$ resonance displayed in b. In the magnetic
sensitive case, the sensitivity is
$$390\text{\,}\mathrm{nT}\text{/}$_{\mathrm{rms}}$. The curves shown in b and
c match the description in the caption of Figure 1b and Figure 1c,
respectively.

### Time-varying magnetic fields

After proving the multi-pixel sensor’s imaging capabilities as well as
determining the single-pixel sensor’s sensitivity for IRA-ODMR, we now
investigate how the multi-pixel sensor responds to time-varying magnetic
fields produced by current-driven solenoid coils (Figure 4a). The solenoid
coil already employed for magnetic field imaging (Figure 2b) is moved directly
above the multi-pixel sensor’s center pixel $\left($2$,$2$\right)$. Acquiring
one ODMR signature and fixing the microwave center frequency to the upper
resonance frequency enables time-dependent magnetic field measurements (refer
to methods section). When the solenoid current $I_{\mathrm{s}}$ is ramped up
and down with a frequency $f_{\mathrm{s}}=$10\text{\,}\mathrm{mHz}\text{/}$$,
the measured magnetic field follows the current directly. Before the
modulation starts ($t<$0\text{\,}\mathrm{s}\text{/}$$), the field fluctuates
around $0\text{\,}\mathrm{T}\text{/}$ with a standard deviation of
$$12.9\text{\,}\mathrm{\SIUnitSymbolMicro T}\text{/}$_{\mathrm{rms}}$.
Corresponding to the magnetic sensitive rms noise, this value agrees well with
the one extracted from data displayed in Figure 1c. In comparison to the
magnetic field modulation amplitude of about
$80\text{\,}\mathrm{\SIUnitSymbolMicro T}\text{/}$, it suggests that a higher
time resolution is achievable to the disadvantage of reducing the signal-to-
noise ratio.

The multi-pixel sensor’s bandwidth is currently limited by its moderate
sensitivity and the associated need for long averaging times. For
benchmarking, we repeat the same measurement to demonstrate that already the
single-pixel reference setup’s sensitivity suffices to temporally resolve a
ramp signal with a frequency $f_{\mathrm{s}}=$1\text{\,}\mathrm{kHz}\text{/}$$
(Figure 4b). The measured magnetic field preserves the triangular shape of the
solenoid current illustrating that the single-pixel sensor’s bandwidth exceeds
the ramp signal’s higher frequency components. However, the measured field is
slightly delayed with respect to the applied current by the lock-in
amplifier’s filtering step. For $t<$0\text{\,}\mathrm{s}\text{/}$$, we extract
a magnetic sensitive noise floor of $$2.2\text{\,}\mathrm{\SIUnitSymbolMicro
T}\text{/}$_{\mathrm{rms}}$. Due to the increased bandwidth, this noise floor
is slightly worse compared to the aforementioned optimized single-pixel
sensor’s sensitivity.

Figure 4: Time-dependent magnetic field measurements a for the central
$\left($2$,$2$\right)$ pixel of the magnetic field camera and for b the
single-pixel reference setup. The measurements in a (b) are performed at
resonance $f_{\mathrm{c}}=$2.939\text{\,}\mathrm{GHz}\text{/}$$
$\left(f_{\mathrm{c}}=$2.936\text{\,}\mathrm{GHz}\text{/}$\right)$ and belong
to the ODMR signatures displayed in Figure 1b (Figure 3b). Red plots show the
measured magnetic fields for currents $I_{\mathrm{s}}$ applied to a solenoid
coil put on top of the respective sensor in close proximity to the active
pixel. The periodic triangular current modulations (blue curves) start at
$t=$0\text{\,}\mathrm{s}\text{/}$$ as indicated by the dashed lines and
possess frequencies of $f_{\mathrm{s}}=$10\text{\,}\mathrm{mHz}\text{/}$$ and
$f_{\mathrm{s}}=$1\text{\,}\mathrm{kHz}\text{/}$$ in a and b, respectively.

## Towards real-time imaging of neural signals

We have demonstrated an integrated, fiber-packaged magnetic field camera. Our
single-pixel measurements show the possibility to achieve measurement
bandwidths required to sense neural signals with a duration around the
millisecond regime [6]. Multiple technical improvements will lead to
sensitivity enhancements and finally to a magnetic field camera for recording
neural signals in real-time: (i) Higher laser powers facilitated by non-
absorbing adhesives and polymer-integrated components enhance the pixels’
sensitivity as reinforced with the single-pixel sensor benchmarks. (ii) The
overlap between the pump and the infrared beams within the pixel volumes has
to be optimal. Our magnetic field camera suffers from a reduced overlap due to
suboptimal polishing of the diamond side facets, which are not entirely
parallel. (iii) Local electron irradiation only within the pixel volumes
allows for way higher NV densities compared to a homogeneously irradiated
diamond substrate. In this case, the pump light absorption occurs solely at
the pixels. (iv) Incorporating cavities with finesse $F$ into the infrared
path enhances the contrast by a factor $2F/\mathrm{\pi}$ [28]. Such cavities
might be fabricated by coating the diamond substrate’s facets. (v) Magnetic
flux concentrators amplify external magnetic fields by at least two orders of
magnitude [34]. Altogether, the integrated magnetic field camera’s fundamental
spin-projection noise limit [35] of about
$200\text{\,}\mathrm{f}\mathrm{T}\,\mathrm{Hz}^{-1/2}$ certainly becomes
approachable, whereas already sensitivities of about
$100\text{\,}\mathrm{p}\mathrm{T}\,\mathrm{Hz}^{-1/2}$ enable the detection of
biological signals [8, 1].

The camera’s spatial resolution depends on the pixel density, which is limited
by the diameter of the fibers attached to the diamond side facets. In this
proof of principle, the pixel spacing is
$500\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$. Ultimately, the Rayleigh
length restricts the beam diameters inside the diamond substrate to an order
of magnitude of about $10\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$.
However, reducing the beam diameters to obtain smaller pixels also reduces the
volume where the pump and the infrared beams interact with the NV centers.
Likewise, the ODMR contrast is reduced. To quantify the effect of the camera
pixels’ diameter on the ODMR contrast $C$ and on the magnetic sensitive noise,
we exemplarily consider camera pixel $\left($3$,$3$\right)$. We model its ODMR
contrast for different pixel diameters to firstly rescale its ODMR signature
slope $a_{+}$ and secondly its magnetic sensitive rms noise $\delta
B_{\mathrm{rms}}^{\mathrm{on}}$ (refer to supplementary information D.2, D.3,
and C.1). While the ODMR contrast linearly rises with increasing pixel
diameter, the noise rapidly drops following its $\delta B_{\mathrm{rms}}\sim
1/a_{+}$ dependency (Figure 5). In this work, the pump and infrared beam
waists set the camera pixels’ diameter to
$D_{\mathrm{px}}=$80\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$$. Reducing
the diameter to its half doubles the noise. Increasing the diameter instead
does not significantly improve the pixel sensitivity. The contrast related to
$D_{\mathrm{px}}$ deviates slightly from the measured $C_{$3$,$3$}$ due to
uncertainties in the transition rates and absorption cross sections employed
for contrast modeling.

Constraints on the spatial resolution as well as on the laser powers imposed
by the adhesive to attach the components to the polymer can be relieved by
further integrating laser diodes and photodetectors on-chip, directly next to
the diamond facets. For larger $N\times N$ pixel matrices and with prospective
CMOS integration [36], more sophisticated readout schemes enable faster
magnetic field image acquisition. The lock-in demodulation technique renders
simultaneous readout of multiple pixels with a single photodetector but
multiple lock-in amplifier channels possible if the pixels’ ODMR signals are
modulated at distinct frequencies $f_{\mathrm{mod}}$. We emphasize that the
multi-pixel magnetic field camera can also act as a multi-pixel temperature
sensor by slightly adapting the measurement procedure [37]. Moreover, we
suggest to fabricate the microwave inductors on top of the polymer platform,
i.e., directly underneath the diamond substrate in a future design iteration
of the magnetic field camera. Doing so exposes the diamond surface to samples,
which can be put directly on top of the diamond substrate. Besides the desired
close proximity between sensor and sample, the chemically inert and non-toxic
diamond surface is compatible with biological samples as well as with the
investigation of chemically aggressive substances. Consequently, we envision
our integrated and fiber-packaged magnetic field camera to be applied in a
broad range of fields: regarding the lifetime and quality assessment of
lithium-ion batteries required for the present energy revolution [38], our
sensor is already able to spatially resolve magnetic field changes of several
$\mathrm{\SIUnitSymbolMicro T}\text{/}$. Furthermore, we foresee applications
in microfluidic lab-on-a-chip devices for drug discovery [39] and in
spaceborne quantum magnetometry [40].

Figure 5: Contrast (red) and sensitivity (blue) dependence on camera pixel
diameter. The depicted data assumes the $\left($3$,$3$\right)$ camera pixel’s
properties and that they, except the ODMR contrast $C$ and the magnetic
sensitive rms noise $\delta B_{\mathrm{rms}}^{\mathrm{on}}$, remain constant
for changing pixel diameters. The dashed line indicates the magnetic field
camera’s pixel size from this work.

## Methods

### Multi-pixel sensor

To realize our magnetic field camera with $$3$\times$3$$ pixels, we firstly
irradiate a $$1.4$\times$1.4$\times$0.2\text{\,}\mathrm{m}\mathrm{m}^{3}$$
large, $\left(111\right)$-oriented CD1411 HPHT diamond substrate A from
Sumitomo Electric Industries with an electron beam and anneal it to increase
the NV density to
$n_{\mathrm{A}}=$3.0\text{\times}{10}^{23}\text{\,}\mathrm{m}^{-3}$$ (refer to
supplementary information A.2). Secondly, the substrate’s four side facets are
polished by Delaware Diamond Knives. Last, the diamond substrate as well as
three single-mode fibers at either of the four side facets are integrated into
trenches etched into a polymer board (Figure 1a) and fixed with an UV-curing
adhesive (refer to supplementary information A.3). A graded-index (GRIN) fiber
terminates each single-mode fiber to collimate the pump and infrared beams
injected into the diamond and to couple the infrared beams back into the
fibers attached to the opposite facet. Inside the diamond substrate, both the
pump and infrared beams possess beam waists of approx.
$40\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$. Collimating the beams
allows for infrared transmission measurements across the diamond substrate and
defines the pixels as the intersections of pump and infrared beams.

Due to the NV- (NV0) pump light absorption cross section of
$\sigma_{\mathrm{g}}=$3.1\text{\times}{10}^{-21}\text{\,}\mathrm{m}^{2}$$ [41]
($\sigma_{\mathrm{g0}}=$1.8$\sigma_{\mathrm{g}}$ [42]), only about $$19$\,\%$
of the pump light injected into the fiber at the first pixel of a row reaches
the last pixel of the same row (with $$70$\,\%$ of the NV centers being
ionized in the steady state, refer to supplementary information D.1). To
equalize the pump intensity at every pixel within a row, we inject approx.
$18\text{\,}\mathrm{mW}\text{/}$ pump light into either of the two fibers
defining a row.

The infrared transmission measurement is based on a balanced detection scheme
for common mode rejection (CMR) of laser intensity fluctuations superimposing
the detected signal [14]: a 90:10 fiber coupler splits $$10$\,\%$ of the
infrared light off and directs this small fraction to the positive input
(BPD+) of a balanced photodetector (PDB450C from Thorlabs with $\times 10^{5}$
difference output gain). The large infrared light fraction passes through the
diamond and through a $1000\text{\,}\mathrm{nm}\text{/}$ longpass filter to
remove remaining red fluorescence light before it arrives at the negative
input (BPD–) of the balanced photodetector. An adjustable fiber attenuator in
the infrared path bypassing the diamond substrate balances the detected
intensities. Hence, the balanced photodetector’s difference signal vanishes
without any ODMR-related infrared absorption. After the $$90$\,\%$ output port
of the fiber coupler and before the fiber interfacing the diamond substrate,
we measure an infrared power of about
$P_{\mathrm{IR}}=$15\text{\,}\mathrm{mW}\text{/}$$.

Driving spin transitions to perform ODMR requires microwave magnetic fields.
For compatibility with full photonic integration, we use three impedance-
matched inductor lines RFi consisting of three connected rings each fabricated
onto an AlN printed circuit board (refer to supplementary information A.4).
The AlN board is aligned in close proximity to the diamond substrate’s surface
such that the three inductor lines lie parallel to the pump laser paths and
that the pixels are centered with respect to the corresponding inductor ring.
A Rohde & Schwarz SMB100B signal generator connected to a Mini-Circuits
ZHL-16W-43-S+ amplifier and eventually to the inductor line belonging to the
active pump row produces the driving microwave electromagnetic field with a
time $t$-dependent frequency $f_{\mathrm{RF}}\\!\left(t\right)$ and a power of
$16\text{\,}\mathrm{W}\text{/}$. A JCC2300T3600S2R1 circulator from JQL
Electronic in between the amplifier and the inductor protects the signal
generator and the amplifier from reflected microwaves. Employing the frequency
modulation ODMR measurement scheme described well in [28], we modulate the
microwave signal according to Equation 1 around a center frequency
$f_{\mathrm{c}}$ with a modulation frequency
$f_{\mathrm{mod}}=$20\text{\,}\mathrm{kHz}\text{/}$$ and a modulation depth
$f_{\mathrm{dev}}=$10\text{\,}\mathrm{MHz}\text{/}$$. $f_{\mathrm{c}}$ is
swept from $2.72\text{\,}\mathrm{GHz}\text{/}$ to
$3.02\text{\,}\mathrm{GHz}\text{/}$ with a scan speed of
$1\text{\,}\mathrm{s}\text{/}\mathrm{MHz}$ and a step width of
$1\text{\,}\mathrm{MHz}\text{/}$. $f_{\mathrm{mod}}$ and $f_{\mathrm{dev}}$
are chosen to optimize the measurement sensitivity by discarding low-frequency
technical noise and by involving all NV- hyperfine transitions split by
$2.16\text{\,}\mathrm{MHz}\text{/}$ [43] in the frame of lock-in detection: a
Zurich Instruments MFLI lock-in amplifier demodulates the balanced
photodetector’s difference signal using a time constant
$\tau_{\mathrm{c}}=$100\text{\,}\mathrm{ms}\text{/}$$ with a
$$24$\,\mathrm{dB}/\mathrm{oct}$ filter roll-off. Yielding the ODMR signal
$U$, this enables the measurement of the infrared transmission’s derivative.
The diamond substrate temperature is stabilized to
$21\text{\,}\mathrm{\SIUnitSymbolCelsius}\text{/}$ to counteract heating by
pump light and microwave absorption.

For magnetic field imaging as in Figure 2a, we record full ODMR signatures for
three solenoid currents
$I_{\mathrm{s}}=\left\\{0,482,963\right\\}\,$\mathrm{mA}\text{/}$$ for each
pixel (refer to supplementary information B.2). We then calculate the
frequency spacing $\Delta
f_{i,j}\\!\left(I_{\mathrm{s}}\right)=f_{i,j,+}\\!\left(I_{\mathrm{s}}\right)-f_{i,j,-}\\!\left(I_{\mathrm{s}}\right)$
between the lower and upper resonances. Subtracting the zero-current spacing
yields the pixels’ magnetic fields according to

$\displaystyle B_{i,j}\\!\left(I_{\mathrm{s}}\right)=\frac{\Delta
f_{i,j}\\!\left(I_{\mathrm{s}}\right)-\Delta
f_{i,j}\\!\left($0$\right)}{2\gamma}$ (2)

with the NV’s gyromagnetic ratio
$\gamma=$28\text{\,}\mathrm{GHz}\text{/}\mathrm{T}$$ [44].

### Single-pixel reference

The single-pixel sensor’s diamond substrate preparation (substrate B) equals
the preparation of substrate A. Though, the NV density of substrate B is
slightly lower
$\left(n_{\mathrm{B}}=$1.1\text{\times}{10}^{23}\text{\,}\mathrm{m}^{-3}$\right)$.
For IRA-ODMR measurements, the pump and infrared beams are collimated with
free-space optics to maintain beam waists of
$40\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$. Subsequently, the beams
are adjusted with mirrors such that they perfectly intersect within diamond
substrate B, close to its top surface and close to the side facet acting as
the pump input port. Instead of microwave inductors integrated into an AlN
board, an enameled copper wire coil with a radius of
$500\text{\,}\mathrm{\SIUnitSymbolMicro m}\text{/}$, a length of
$4\text{\,}\mathrm{mm}\text{/}$, and $10$ windings located directly above the
beam intersection drives spin transitions with a microwave power of
$16\text{\,}\mathrm{W}\text{/}$ (refer to Figure 3a). Besides the sensor and
the microwave inductor, measurements are performed with the setup introduced
in Figure 1a. Using free-space optics instead of fibers to interface the
diamond substrate, the pump laser power is risen to
$1.16\text{\,}\mathrm{W}\text{/}$ (measured directly in front of the diamond’s
pump entrance facet). The infrared power directly in front of the diamond’s
respective entrance port is $9.8\text{\,}\mathrm{mW}\text{/}$, which
corresponds to $1.4\text{\,}\mathrm{mW}\text{/}$ at either photodiode of the
balanced photodetector. Sweeping $f_{\mathrm{c}}$ is now performed across the
same frequency interval and with the same scan speed but with a step width of
$0.1\text{\,}\mathrm{MHz}\text{/}$. A microwave modulation frequency
$f_{\mathrm{mod}}=$87.7\text{\,}\mathrm{kHz}\text{/}$$, a modulation depth
$f_{\mathrm{dev}}=$5\text{\,}\mathrm{MHz}\text{/}$$, and a lock-in amplifier
time constant $\tau_{\mathrm{c}}=$10\text{\,}\mathrm{ms}\text{/}$$ optimize
the ODMR sensitivity for the single-pixel measurement. All other parameters
remain unchanged compared to the multi-pixel sensor measurements.

### Time-dependent measurements

A solenoid coil stacked on top of the multi- or the single-pixel sensor
generates a time-varying magnetic field being driven with a current
$I_{\mathrm{s}}$ delivered by a Thorlabs LDC210C laser diode current
controller. For the single-pixel sensor, a Mini-Circuits VLFG-1400+ lowpass
filter protects the LDC210C from microwaves coupled into the solenoid coil.
The measurements in Figure 4 involve a current modulation according to a
periodic triangular function with a minimal current of
$0\text{\,}\mathrm{A}\text{/}$, a maximal current $I_{\mathrm{s,max}}$, and a
frequency $f_{\mathrm{s}}$. In case of the multi-pixel sensor,
$I_{\mathrm{s,max}}$ is set to $958\text{\,}\mathrm{mA}\text{/}$, while for
the single-pixel sensor, it is
$I_{\mathrm{s,max}}=$512\text{\,}\mathrm{mA}\text{/}$$. Recording the ODMR
signal $U\\!\left(t\right)$ over time $t$ at a microwave center frequency
$f_{\mathrm{c}}=f_{+}\\!\left(0\right)$ fixed to the upper resonance frequency
for zero solenoid current and converting it with
$B\\!\left(t\right)=U\\!\left(t\right)/\left(a_{+}\gamma\right)$ to a magnetic
field allows for the comparison between the applied solenoid current and the
measured field strength.

For the single-pixel sensor, a solenoid coil with a radius of
$1.5\text{\,}\mathrm{mm}\text{/}$, a length of
$2\text{\,}\mathrm{mm}\text{/}$, and $2.5$ windings produces the time-varying
magnetic field to be gauged. Possessing a larger diameter than the microwave
coil, it is located above the intersecting pump and infrared beams surrounding
the microwave coil. Here, the lock-in amplifier’s time constant is decreased
to $\tau_{\mathrm{c}}=$20\text{\,}\mathrm{\SIUnitSymbolMicro s}\text{/}$$ to
prevent averaging over the current ramps. Thus, the lock-in cutoff frequency
becomes $3.9\text{\,}\mathrm{kHz}\text{/}$ and the ODMR scan speed
$20\text{\,}\mathrm{ms}\text{/}\mathrm{MHz}$.

#### Acknowledgements

This project is funded by the German Federal Ministry of Education and
Research (BMBF) within the ‘DiNOQuant’ project (No. 13N14921) as well as by
the European Research Council within the ERC Starting Grant ‘QUREP’ (No.
851810). We acknowledge further funding from the Einstein Research Unit
‘Perspectives of a quantum digital transformation: Near-term quantum
computational devices and quantum processors’. The authors thank Laura Orphal-
Kobin and Masazumi Fujiwara for fruitful discussions on applications of the
magnetic field camera as well as Viviana Villafane for annealing the diamond
substrates.

#### Author contributions

J.M.B., H.Co., F.P., M.K., and T.S. invented the magnetic field camera
concept. J.M.B. designed and performed the multi-pixel sensor experiments and
analyzed the data. F.P. designed the multi-pixel sensor’s electronic and
mechanical parts. H.Co. and M.K. designed the multi-pixel sensor’s optical
parts, H.Co. assembled them. N.K. supervised the multi-pixel sensor polymer
design and manufacturing process. A.P. performed the single-pixel experiments.
J.W. measured the diamond substrates’ NV density and Rabi frequency. H.Ch.
developed the infrared laser diode, supervised by A.K. W.K. was responsible
for the diamond substrate electron irradiation. T.F., A.L., and W.H. developed
and fabricated the microwave inductors. T.S. supervised the project. J.M.B.,
F.P., T.F., M.K., and T.S. wrote the manuscript. All authors reviewed it.

#### Additional information

Supplementary information is available in the online version of the paper.
Correspondence and requests for materials should be addressed to T.S.

#### Competing interests

J.M.B., H.Co., F.P., M.K., and T.S. filed the patents US11719765B2 (active)
and EP4099041A1.

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