Handheld device for non-contact thermometry via optically detected magnetic resonance of proximate diamond sensors

The general concept of the ODMR-meter and the various components necessary to its implementation are illustrated in Fig. 1a. The readout head is aimed at an object containing ODMR-active material, and comprises the optical and MW components necessary to perform ODMR spectroscopy of the object at some distance, without physical contact. The readout head is connected to a control box containing the necessary electronics and power supplies. The control box is itself connected to a laptop computer operating the device and displaying the ODMR readout, which can be converted to e.g. temperature or magnetic field.

Our design for the readout head is detailed in Fig. 1b. In the present implementation, it is designed to measure the photoluminescence (PL) from NV defects in diamond in an epi-illumination geometry, with a green light-emitting diode (LED) for optical excitation, a photodiode to detect the red PL, and a dichroic beam splitter to separate PL from excitation. A condenser lens on the object side serves both to focus the excitation light onto the object and collect the PL. The MWs are supplied via a loop antenna mounted just under the condenser lens, with the light passing through the loop. A key design parameter is the working distance $h$, i.e. the shortest distance between readout head and object. The various considerations that dictate the choice of $h$ are discussed in Sec. II.2.

As depicted in Fig. 1c, the control box contains a set of MW components (signal generator, switch, amplifier) connected to the MW loop, a data acquisition and control unit (DAQ) which reads the voltage from the photodiode and control the MW signal generator (for MW frequency sweeping) and switch (for amplitude modulation), and power converters to supply power to the LED, photodiode and MW switch. The personal computer (PC) is connected via a universal serial bus (USB) to the DAQ and MW signal generator. A software interface controls the data acquisition and analysis process and displays the outcome.

The purpose of the ODMR-meter is to measure ODMR from an object at a distance, without contact, by simply holding the readout head above the object. Therefore, it is desirable for the working distance $h$ to be as large as possible, at least several millimeters, ideally centimetres. However, this desire competes with the requirement of a short working distance to optimise device performance. Indeed, a long working distance places limits on the efficiency of the MW driving, optical pumping, and PL collection, which in turn affects the measurement sensitivity and speed – defined as the maximum rate at which successive readings (e.g. of temperature) can be made.

We first consider the relationship between working distance and MW driving efficiency. The latter is characterised by the Rabi frequency which is proportional to the strength of the magnetic field associated with the MW, $B_{\rm MW}$. If the object is placed on the symmetry axis of the MW loop, the field it experiences scales with the geometrical parameters as

where $d$ is the diameter of the loop. For a given current in the loop and a given working distance $h$, the field is maximised for a loop diameter $d=2h$ and then scales inversely with $h$, $B_{\rm MW}\propto h^{-1}$. Note that a different antenna geometry, for instance a straight wire, would generally give the same scaling with $h$. The MW power to be supplied to the loop then scales as $P_{\rm MW}\propto B_{\rm MW}^{2}\propto h^{-2}$. Thus, a working distance of $h=1$ cm requires 100 times more MW power to achieve the same driving efficiency as at $h=1$ mm. In our implementation, we will use $h=4$ mm and $d\approx 2h$, which we found (see Sec. III.4) to provide good MW driving (i.e. with a Rabi frequency roughly matching the dephasing rate of the NV spins in our test diamond) at the maximum MW power that can be delivered by the chosen hardware.

Longer working distances can be achieved by scaling the supplied MW power accordingly, however, it also places constraints on the optical design and affects measurement performance. On the one hand, the PL collection efficiency directly affects the measurement sensitivity. Indeed, the sensitivity (to temperature or magnetic field) scales as $\eta\propto I_{\rm PL}^{-1/2}$ where $I_{\rm PL}$ is the collected PL intensity (as detected by the photodiode, assuming shot noise limited measurements) [5]. The PL intensity in turns primarily depends on the numerical aperture (NA) of the collection lens, $I_{\rm PL}\propto{\rm NA}^{2}$, such that $\eta\propto{\rm NA^{-1}}$. For a given NA, the larger the working distance, the larger the diameter of the lens. Aspheric condenser lenses with NA exceeding 0.7 (about $45^{\circ}$ acceptance angle) are available with diameters up to 2” or more. For instance, a working distance of $h=4$ mm can be accommodated using a high-NA 1” lens (e.g. Thorlabs ACL25416U, focal length $f=16$ mm) mounted just above the MW loop (accounting for the finite thickness of the lens and MW loop), while a larger 2” lens (e.g. Thorlabs ACL50832U, $f=32$ mm) allows for $h=12$ mm. In our implementation, we chose the $f=16$ mm 1” lens to keep the readout head relatively compact. Note that ${\rm NA}=0.7$ roughly corresponds to an aperture of $d=2h$ at a distance $h$ from the object, such that the MW loop is not restricting light collection in these conditions. If we restrict ourselves to 1” diameter lenses, longer working distances are possible but at the expense of a reduced NA (larger $f$) and thus degraded sensitivity. For instance, $h=8$ mm can be achieved with a 1” lens for a slightly reduced NA of 0.6 (e.g. Thorlabs ACL2520U, $f=20$ mm), and a working distance exceeding a centimetre can be accommodated with an NA below 0.5 (e.g. Thorlabs LA1252, $f=25$ mm).

On the other hand, the choice of lens also affects the focusing of the LED light onto the object. For given LED characteristics (in particular, emitter size), the minimum size of the illumination spot on the object is proportional to the focal length of the lens, $f$. The power density then scales as $I_{\rm LED}\propto f^{-2}$. Thus, for a given LED power a larger $f$ implies a smaller pumping rate of the NV spins (e.g. by a factor of 2.5 going from $f=16$ mm to $f=25$ mm), which can degrade sensitivity in different ways as well as limit the measurement speed [39, 40, 10, 18], as will be discussed further in Sec. V.1. Moreover, a large illumination spot may reduce the ability to fully collect the PL emission as optical aberrations become more severe. A solution is to use a laser instead of an LED to allow for better control on the focusing, as often employed in realisations of NV magnetometers [18, 20]. Here we opted for an LED as they are widely available and provide higher output power than standard laser-based alternatives. A higher excitation power in turn means a larger total PL intensity from the active material, which is important for a device destined to work in ambient light conditions.

Summarising, increasing the working distance generally degrades the performance of the ODMR-meter (measurement sensitivity and speed), and/or implies more stringent hardware requirements such as higher MW power and optical excitation power. In the next section, we describe a realisation of the ODMR-meter with a working distance of $h=4$ mm, which allows for a simple design with relatively compact hardware. Nevertheless, longer working distances of the order of 1 cm are achievable with standard hardware albeit less compact and portable (e.g. a high-power MW amplifier).

Here we describe the specific details of our prototype. The overall apparatus is photographed in Fig. 2a, with the sub-units shown in Fig. 2b. The readout head is built entirely from Thorlabs components except for the MW loop. A green LED (M530L4) outputs 480 mW power (typical) at the maximum current, centred at 522 nm wavelength (30 nm full width at half maximum intensity). The emitted light is filtered (FESH0600) to remove long wavelengths and collimated by an aspheric condenser lens (ACL2520U-A). The LED-filter-lens assembly (excitation arm) is connected to a cage cube (CM1-DCH) containing a shortpass dichroic beam splitter (DMSP605R). A lens tube (SM1L40) is connected to a port of the cage cube to serve as a handle. The detection arm connected on the output port of the cage cube comprises a longpass filter (FELH0650), an aspheric condenser lens (ACL25416U-B), and an amplified Si photodiode (PDA36A2). On the remaining port of the cage cube, we connect an aspheric condenser lens (ACL25416U-B) and glue a printed circuit board (PCB) directly on the lens-holding tube (SM1L05). Another lens tube (SM1L15) is inserted in between the cage cube and lens to increase physical distance between the handle and the target object. The PCB (shown in Fig. 2c) includes a loop antenna to supply the microwave to the active material, with a hole in the middle to let the light through, and an MMCX connector to connect the MW loop to the control box. The focal point of the lens is located approximately 4 mm below the surface of the PCB, corresponding to the working distance $h$. We tested different loop diameters $d$ and found an optimum at $d\approx 9$ mm, see discussion in Sec. III.4. All the results shown below have been obtained with this optimum.

The readout head is connected to the control box via a bundle of four cables (for LED drive, MW drive, photodiode power supply, photodiode output). The largest and heaviest component in the control box is the DAQ (NI USB-6212 BNC). The enclosure (Spelsberg TK PS Series, RS) is 36 x 25 x 11 cm³ in size. In future, the size and weight of the control box could be significantly reduced by using a compact alternative to the DAQ such as an Arduino microcontroller board, which has been employed in previous NV magnetometry demonstrations [41, 19]. This could also remove the need for a computer, as the Arduino is capable of processing data and outputting the result to a standalone display. The MWs are generated by a USB-powered signal generator (Windfreak SynthNV Pro) and passed through an IQ modulator used as an on/off switch (Texas Instruments TRF37T05EVM) and an amplifier (Mini-Circuits ZRL-3500+). The control box is connected to AC wall power and includes a set of AC/DC converters (15 V, $\pm 12$ V, 3.3 V) to power the LED driver (Thorlabs LEDD1B, housed in the box), photodiode, MW amplifier, and IQ modulator. The total power consumption of the box (including USB inputs) is about 30 W in typical operating conditions.

A standard laptop computer and a LabVIEW interface are used to control the DAQ and MW generator to continuously acquire ODMR spectra, as well as to process the data and display the output in real time. To reduce the impact of low-frequency fluctuations (of LED power, PL intensity, MW driving efficiency), which is especially important for handheld operation, a lock-in detection technique is employed. Here we use amplitude modulation, using the MW switch to turn the MW on and off with the LED kept on at all times. The modulation frequency is limited by the repumping rate of the NV spin, in turn limited by the intensity of the green light [42, 43]. We use a modulation frequency in the range $f_{\rm mod}=100-500$ Hz, e.g. at a typical value of $f_{\rm mod}=167$ Hz the MW is turned on for 3 ms (spin-flip phase) and turned off for 3 ms (repumping phase). To acquire an ODMR spectrum, the MW frequency is then swept across the expected NV electron spin resonances near 2870 MHz, with one modulation cycle per frequency step. To optimize measurement speed and sensitivity, it is possible to use a small set of carefully chosen frequency steps [44, 33, 45]. However, for the tests performed here we will use a linear ramp over a relatively wide range, e.g. from 2860 to 2880 MHz with 41 frequency steps (i.e. 0.5 MHz increments), which gives a full well-resolved ODMR spectrum allowing reliable data fitting. In this case, a single ODMR sweep thus takes about 250 ms.

Meanwhile, the voltage from the photodiode is sampled by the DAQ at the maximum available rate of 400 kHz, which gives 1200 samples per 3 ms period. An example time trace of a single MW on/off cycle (6 ms, $f_{\rm mod}=167$ Hz) is shown in Fig. 3a, with the MW frequency tuned on resonance. For the tests presented in this section and throughout the paper, we used a type-Ib diamond (Element Six, $3\times 3\times 0.3$ mm³ in size) that was electron irradiated and annealed to produce a high density of NV defects [46], and the readout head was held in a fixed position above the diamond using a stand as shown in Fig. 2a. The trace in Fig. 3a illustrates the effect of the MW modulation: when the MW is turned on, the PL intensity decays exponentially with a characteristic decay time of $\approx 1.1$ ms (spin-flip time, dependent on the MW field strength and optical excitation rate); when the MW is turned off, the PL follows an exponential recovery with a characteristic time of $\approx 2.0$ ms (repumping time, dependent on the optical excitation rate). The raw DAQ data is processed by first averaging the samples from the final part of each decay, as indicated by the shaded areas in Fig. 3a. This averaged signal is plotted against MW frequency in Fig. 3b for both the MW-on case (called ‘signal’) and the MW-off case (‘reference’). By dividing the signal by the reference, we obtain the normalised (demodulated) spectrum, shown in Fig. 3c. Note that the reference spectrum still exhibits resonance features, which is due to the modulation being too fast to allow complete spin repumping, causing a reduction in contrast in the normalised ODMR spectrum (nearly 3% here). A slower modulation can increase the contrast up to 6% but at the cost of a reduced measurement speed – it takes longer to complete one sweep. Reducing $f_{\rm mod}$ will also eventually compromise the sensitivity since it reduces the rate of collected PL for a given averaging window (shaded areas in Fig. 3a). Here, $f_{\rm mod}$ was chosen to maximise the signal-to-noise ratio in the normalised ODMR spectrum, while optimising the width of the averaging window for each value of $f_{\rm mod}$. This optimisation resulted in a minimum standard deviation in the resulting temperature trace, discussed below.

In normal operation, ODMR spectra are recorded continuously, i.e. a new spectrum like that in Fig. 3c is produced every 250 ms in our example. In general each spectrum can be fitted by LabVIEW in a time much shorter than this single-sweep time (about 10 ms to fit a full spectrum, which is done in parallel to the acquisition of the next sweep), thus allowing real-time feedback to the user. Here we fit the spectrum with two lines corresponding to the two effective electron spin resonances expected for an ensemble of NV defects in zero magnetic field [47]. These two resonance frequencies can be expressed as $f_{\pm}=D\pm E$ where $D$ and $E$ are the zero-field splitting parameters.

The $D$ parameter depends on temperature, with a linear coefficient of $\frac{{\rm d}D}{{\rm d}T}\approx-75$ kHz/K near room temperature [48]. For better accuracy (see further discussion in Sec. V.3), we use the second-order polynomial

with coefficients $a_{0}=2.875357$ GHz, $a_{1}=4.3998\times 10^{-5}$ GHz/K and $a_{2}=-2.0519\times 10^{-7}$ GHz/K². This polynomial is based on a fit to the third-order polynomial given in Ref. [49] over the range 0-100^∘C relevant to our application. The temperature can thus be estimated by solving for the positive root of $f(T)=D(T)-D_{\rm meas}$ where $D_{\rm meas}$ is the value estimated from the ODMR fit.

To obtain visually good fitting, we use skew normal distributions with skew parameters of identical amplitude but opposite signs for the two resonances, resulting in the green line in Fig. 3c. Symmetric lineshapes fail to capture the narrow central peak, see e.g. the Lorentzian fit in Fig. 3c (orange line). The asymmetric lineshape is understood to be due to the interplay between local random electric fields and magnetic noise [47]. While it is possible to fit the resulting spectrum using a physical model [47], this is a computationally intensive task (the fitting time would exceed the single-sweep time) and therefore we prefer to use a simple skew normal distribution. The implications of this choice on the measurement accuracy will be discussed in Sec. V.3.

By analysing each single-sweep spectrum using a skew normal fit and deducing the temperature via Eq. 2, we obtain a time trace of the temperature sampled every $\approx 250$ ms (the single-sweep time), shown in Fig. 3d. The typical standard deviation calculated from series of 10 samples is 20 mK, which corresponds to a sensitivity of $\eta_{T}\approx 10~{}{\rm mK}/\sqrt{\rm Hz}$. This directly measured value is close to the sensitivity limit set by the noise in the photodiode signal (visible in Fig. 3a) in the case of an optimised single MW frequency measurement (chosen in the steepest part of the ODMR spectrum), of about $\approx 7~{}{\rm mK}/\sqrt{\rm Hz}$. Note, if the noise in the photodiode signal was purely due to photon shot noise, given an estimated detected PL power of about 1.8 mW, the sensitivity would be improved to $\approx 1~{}{\rm mK}/\sqrt{\rm Hz}$. The limits and tradeoffs to sensitivity will be discussed in Sec. V.2.

One important design parameter is the diameter of the MW loop, $d$. For a given working distance $h$, the MW field strength at the object is maximised for a diameter $d=2h$, according to Eq. 1. However, as the loop itself partially blocks light focusing and collection by the lens, it is useful to determine the optimal diameter experimentally. To this end, we compared PCBs with different loop diameters from $d=5.0$ mm to $d=13.4$ mm. The central hole in the PCB is as large as permitted by manufacturing tolerance; for instance a hole diameter of 8 mm corresponds in fact to a mean loop diameter of $d=9.4$ mm (accounting for the finite width of the strip line forming the loop). For each value of $d$, we placed the test diamond at the working distance of $h=4$ mm (set by the lens) and recorded an ODMR spectrum under fixed conditions (in particular, using the maximum LED and MW powers available). We then extract the PL intensity ($I_{\rm PL}$, measured off resonance) and, by fitting the spectrum, the contrast ${\cal C}$ and linewidth $\Delta\omega$ (full width at half maximum) of the resonances.

The three quantities $I_{\rm PL}$, ${\cal C}$, and $\Delta\omega$, are plotted against loop diameter in Fig. 4a-c, respectively. The orange solid lines are the result of simple theoretical considerations. For the PL intensity, we consider clipping by the aperture in the PCB of both the excitation light from the LED and the collected PL (see modelling details in Appendix A). The predicted nearly linear trend agrees well with experiment (Fig. 4a, an arbitrary pre-factor is adjusted to best fit the data). For the contrast (Fig. 4b), the model is based on Eq. 1, with a pre-factor left as a fit parameter, assuming a linear relationship between ${\cal C}$ and $B_{\rm MW}$ approximately valid in this regime of low excitation powers [39]. The data agrees with the expectation of a maximum contrast near the $d=2h$ condition. For the linewidth (Fig. 4c), we expect a negligible variation since here $\Delta\omega$ is close to the limit set by the spin dephasing rate, $1/T_{2}^{*}$ [39]; the data indeed shows a weak dependence with the loop diameter.

In the present case where the noise given by the photodiode is a constant independent of signal amplitude (i.e. $I_{\rm PL}$), the temperature sensitivity scales inversely with the maximum slope in the ODMR spectrum and can thus be expressed as

where the pre-factor $\beta$ characterises the (constant) noise amplitude. The sensitivity thus estimated is plotted against $d$ in Fig. 4d, where the data points are calculated using the values measured in Fig. 4a-c, whereas the solid line uses the models described above for each quantity in Eq. 3. The predicted minimum at $d\approx 10$ mm is in good agreement with the experiment, which finds a best sensitivity for the PCB with a MW loop diameter $d=9.4$ mm and an 8-mm hole.

In summary, the optimal MW loop diameter is found to be close to that given by maximising the MW field strength according to Eq. 1, with a small correction (a larger diameter by about 20%) to allow for more light to go through the hole. This simple design rule can serve to adjust the PCB design for different working distances.

Measurement speed here refers to the maximum rate at which successive temperature readings can be made, and is characterised by the minimum time $t_{\rm read}$ required to get one reading of the temperature. This is an important quantity in the context of a handheld device because $t_{\rm read}$ needs to be short enough to allow one correct reading before moving out of focus. In Sec. IV, we saw that a reading time of $t_{\rm read}=42$ ms was sufficient to get one reading when holding the readout head by hand above a fixed object. However, operation may be facilitated by a shorter measurement time, especially in a less controlled environment (leading to a less steady hand) or if the object itself is moving. While we used 21 frequency points in our demonstration (2 MHz constant spacing between points), it is generally accepted that 4 carefully chosen frequency points are sufficient to enable an accurate estimate of the temperature [44, 33, 45]. Using the same modulation frequency of $f_{\rm mod}=500$ Hz, i.e. 2 ms per frequency step, this 4-point ODMR measurement would correspond to a reading time of $t_{\rm read}=8$ ms.

The modulation period, i.e. the time per frequency step, is limited by the repumping rate, which has a characteristic time of $\approx 2$ ms in our current implementation according to Fig. 3a. This repumping time depends on the optical excitation intensity and the NV absorption cross-section. We measured the excitation power incident on the diamond to be about 160 mW, spread over an area of roughly 3 mm², i.e. a power density of $\sim 5$ W/cm², consistent with the observed repumping time [14]. Increasing the repumping rate requires to increase the optical power, or more feasibly to reduce the excitation area. The latter can be achieved by employing a laser instead of an LED, with characteristic repumping times as short as a few microseconds achievable with tightly focused laser illumination [39]. Consequently, a reading time of $t_{\rm read}\sim 10-100~{}\mu$s is in principle achievable. Note that there may be other hardware limitations, for instance in our case the MW signal generator used has a settling time in frequency sweeping that limits the modulation to $f_{\rm mod}\approx 4$ kHz hence a minimum reading time of $t_{\rm read}\approx 1$ ms. Such a modulation frequency is achievable using laser excitation even in a compact implementation [18].

However, the temperature resolution of a single reading, defined as the minimum detectable temperature change, $\delta T_{\rm min}$, will increase with decreasing reading time according to $\delta T_{\rm min}=\eta_{T}/\sqrt{t_{\rm read}}$ where $\eta_{T}$ is the sensitivity introduced before. Thus, depending on the required resolution for a given application, it may be necessary to use a long reading time or average multiple consecutive readings, such that maintaining mechanical stability over the course of a measurement will still be critical. We will next look at how the sensitivity $\eta_{T}$ itself can be improved.

If the ODMR lineshape remains unchanged apart from the frequency shift induced by a temperature change, then the sensitivity $\eta_{T}$ depends only on the maximum slope in the ODMR spectrum and the noise in that spectrum. An expression for $\eta_{T}$ is given by Eq. 3, where the pre-factor $\beta$ depends on the origin of the noise (for photon shot noise, $\beta\propto\sqrt{I_{\rm PL}}$). We saw in Sec. III.3 that the sensitivity in our case was an order of magnitude above the photon shot noise limit, due to electronic noise from the photodiode. With a faster sampling rate ($\sim 10$ MHz, using a faster DAQ or a proper lock-in amplifier) to render this noise comparatively negligible, it should be possible to obtain a photon shot noise limited sensitivity, which would then scale as [39]

where $\beta^{\prime}$ encapsulates the physical constants.

In our tests, we used a $3\times 3\times 0.3$ mm³ type-Ib single crystal diamond, and estimated a sensitivity of $\eta_{T}\approx 1~{}{\rm mK}/\sqrt{\rm Hz}$ in the photon shot noise limit. For the type of application envisioned for the ODMR-meter (smart dressing for temperature monitoring), rather than a bulk crystal, diamond particles with diameters between $\sim 10$ nm and $\sim 100~{}\mu$m are likely to be employed and embedded in a flexible matrix for ease of application to the target object [31, 34]. Particles made out of type-Ib diamond are commercially available and we can expect to obtain a similar sensitivity to our test bulk diamond if the particles are densely packed within the host matrix.

It is useful to examine Eq. 4 to identify potential pathways to improve the sensitivity below $\sim 1~{}{\rm mK}/\sqrt{\rm Hz}$. The variable quantities in Eq. 4, namely the measured PL intensity $I_{\rm PL}$, the ODMR contrast ${\cal C}$, and the ODMR linewidth $\Delta\omega$, depend on the properties of the diamond material used (e.g. density of NVs, spin dephasing rate $1/T_{2}^{*}$) and the measurement conditions (optical excitation power density, MW driving strength). All of these parameters should be optimised together following the same prescriptions as for NV magnetometry [39, 5, 10], given the constraints set by the application. In particular, for continuous-wave ODMR sensing as performed here, there is an optimal set of optical excitation power density and MW driving strength that minimises the sensitivity for a given dephasing rate [39, 40]. In general, the optimal excitation power density is larger than that employed here ($\sim 5$ W/cm²), which further motivates the switch to laser excitation instead of LED and could provide a several-fold improvement in sensitivity. Moreover, diamond grown by chemical vapor deposition with a precisely tunable density of NVs, rather than type-Ib diamond, should lead to further sensitivity improvements [10], but mass production of optimised diamond particles suitable for incorporation into smart dressings is still an outstanding challenge [50].

The measured PL intensity $I_{\rm PL}$ also depends on the collection efficiency of the system, and on the total excitation power. In our device, we collect the PL via a high-NA condenser lens, and given the non-contact nature of the ODMR-meter design it is unlikely that the collection efficiency can be increased much further. Likewise, the excitation power was about 160 mW supplied by an LED and cannot be easily increased much further. On the contrary, using laser excitation via a laser diode module integrated in the head [20] or via a fiber input [15, 16, 18] may restrict the excitation power to less than that employed here, reducing the benefits of laser excitation over LED.

Finally, for handheld operation, the effect of physical movement of the readout head relative to the object on the measurement sensitivity remains to be characterised. It can be expected that the lock-in detection scheme (with $f_{\rm mod}=500$ Hz as used in Fig. 5) will protect against motion at lower frequencies, but further work is needed to fully characterise the effect of movement or other sources of noise in real-world scenarios.

The accuracy of a temperature reading performed by the ODMR-meter depends mainly on two factors that can be seen in Eq. 2: (i) the a priori knowledge of the $D(T)$ relationship, via e.g. the polynomial coefficients $\{a_{i}\}$; and (ii) the accuracy with which the $D$ parameter is determined experimentally.

The temperature dependence of the NV defect’s zero-field splitting parameter $D$ was initially investigated near room temperature by Acosta et al [48], with a linear coefficient determined to be $\alpha_{T}=\frac{{\rm d}D}{{\rm d}T}=-75.0(6)$ kHz/K, but the four diamond samples employed in their study exhibited different temperature responses from $-71(1)$ kHz/K to $-78(1)$ kHz/K. Subsequent studies performed over wider temperature ranges fitted the $D(T)$ data with a polynomial [51, 49, 52]. According to the polynomials given in these three studies (Refs. [51, 49, 52]), a reading of $D(T)=2870.00$ MHz translates to a temperature of $T=304.6$ K, $T=301.1$ K, and $T=299.3$ K, respectively. That is, the deduced temperature differs by over 5 K depending on which reference is employed for the conversion. This variability may be due to errors in calibrating the temperature or to actually different responses between diamonds, possibly due to different levels of lattice strain. Therefore, it will be critical to carefully calibrate the $D(T)$ dependence on the diamond material used in the final application, for instance type-Ib diamond microparticles embedded in a smart dressing. With proper calibration, an absolute accuracy below 1 K seems feasible. In Sec. III.3, we chose to use the third-order polynomial given in Ref. [49] as it gives the most sensible values near room temperature with our test diamond. For simplicity, we fitted this third-order polynomial with a second-order polynomial over the range 0-100^∘C, with resulting coefficients given in Sec. III.3. With the simplified polynomial, our ODMR-meter reads a minimum temperature of $\approx 22^{\circ}$C under low heating conditions (see next section for details) in agreement with the independently measured room temperature.

On the other hand, the experimental determination of $D$ from the ODMR spectrum is prone to systematic errors mainly due to asymmetries in the overall lineshape, as studied in detail in Ref. [33]. One important source of asymmetry in our implementation is the finite repumping time (set by the modulation frequency $f_{\rm mod}$) which causes a slight slant in the ODMR spectrum due to incomplete spin repumping during the sweep, although the resulting bias can be averaged out by alternating the MW sweep direction. Less trivially, however, any frequency-dependent variation in MW driving efficiency (due to actual change in MW power, or to variations in MW-spin coupling related e.g. to strain-induced spin mixing) can give rise to asymmetries in the ODMR spectrum. Consequently, when fitting the spectrum with two resonances at frequencies $f_{\pm}=D\pm E$, the value of $D$ returned by the fit generally depends on the lineshape assumed for these resonances, unless they are perfectly symmetric with respect to $D$. For instance, the two fitting methods in Fig. 3c give $D$ values that lead to temperatures differing by up to several K in some cases. Importantly, a better visual fit is not a guarantee of accuracy, since the underlying model may be less physically correct. Fitting the data with a complete physical model such as that proposed in Ref. [47] will likely be necessary to obtain good accuracy while being robust against lineshape variations during operation. This will require careful calibration to determine the parameters of this physical model for the diamond material used in the final application. With a properly parametrised fitting method, one can expect an absolute accuracy below 1 K.

A limitation of the ODMR-meter for temperature monitoring applications is that the measurement itself may increase the object’s temperature due to the optical as well as MW excitation being partly absorbed by the object. In our tests, we found that optically-induced heating generally dominates, although MW-induced heating also has a measurable effect. For instance, the trace shown in Fig. 3d indicates a mean diamond temperature in excess of $31^{\circ}$C, obtained with the LED set to its maximum output power (160 mW measured at the object), which decreases to $25^{\circ}$C by reducing the LED power 5 fold while keeping the MW power to its maximum value (200 mW sent to the MW loop). Reducing the MW power by two orders of magnitude further decreases the temperature by less than $1^{\circ}$C.

Obviously, the object’s temperature depends on the heat dissipation pathways available. As an example, by mounting our test diamond more loosely on its support, the diamond temperature reached nearly $70^{\circ}$C under continuous measurement at the maximum LED and MW powers. To reduce the induced heating without reducing the optical power density and MW driving strength during the measurement, we implemented an intermittent reading scheme whereby LED and MW are turned off for some time between consecutive readings. The average power (optical + MW) incident on the object is thus reduced proportionally to the duty cycle $\kappa=t_{\rm read}/t_{\rm repeat}$ where $t_{\rm repeat}$ is the repetition time (see inset in Fig. 6). The temperature traces in Fig. 6 show how reducing the duty cycle dramatically reduces the diamond temperature, from $\approx 70^{\circ}$C at $\kappa=100\%$ to $\approx 27^{\circ}$C at $\kappa=10\%$ with the LED peak power set to its maximum value (160 mW, red trace in Fig. 6). Meanwhile, the sensitivity is degraded by a factor $1/\sqrt{\kappa}\approx 3$ for $\kappa=10\%$, and is about $\eta_{T}\approx 30~{}{\rm mK}/\sqrt{\rm Hz}$ at this duty cycle as estimated from the time trace in Fig. 6. Reducing the LED peak power to 32 mW brings the temperature further down to $\approx 24^{\circ}$C at $\kappa=10\%$. just $\approx 2^{\circ}$C above the room temperature, accompanied by a further reduction in sensitivity.

In practice, the heating induced by the measurement will need to be characterised in the context of the actual use case, for instance a smart dressing applied to skin. The measurement settings will then need to be adjusted to keep the temperature increase below an acceptable value defined by the application’s requirements. Reducing the measurement duty cycle appears to be an efficient way to mitigate heating to the desired level without substantially compromising performance, and can be used in conjunction with reducing the peak LED and MW powers.