# Nitric Oxide Isotopic Analyzer Based on a Compact Dual-Modulation Faraday Rotation Spectrometer

^{1}

^{2}

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## Abstract

**:**

^{15}NO) detection sensitivity of 0.36 ppbv·Hz

^{−1/2}, corresponding to noise-equivalent Faraday rotation angle (NEA) of 1.31 × 10

^{−8}rad·Hz

^{−1/2}and noise-equivalent absorbance (αL)

_{min}of 6.27 × 10

^{−8}Hz

^{−1/2}. White-noise limited performance at 2.8× the shot-noise limit is observed up to ~1000 s, allowing reliable calibration and sample measurement within the drift-free interval of the spectrometer. Integration with wet-chemistry based on acidic vanadium(III) enables conversion of aqueous nitrate/nitrite samples to gaseous NO for total nitrogen isotope analysis. Isotopic ratiometry is accomplished via time-multiplexed measurements of two NO isotope transitions. For 5 μmol potassium nitrate samples, the instrument consistently yields ratiometric precision below 0.3‰, thus demonstrating potential as an in situ diagnostic tool for environmental nitrogen cycle studies.

## 1. Introduction

^{14}N,

^{15}N) provides unique insight into nitrogen cycling dynamics [1,2,3,4,5] and enables environmental diagnostics by differentiating various natural and anthropogenic chemical processes [6,7]. This bears particular significance in light of recent studies [8,9] indicating comparable rates of anthropogenic and natural nitrogen fixation due to combustion of fossil fuels and fertilizer production via the Haber-Bosch process. Additionally, nitric oxide (NO) is known to play a key physiological role as a signal molecule in the human body [10], and isotopic analysis of nitrogen isotopes (in the form of nitrates/nitrites in blood and urine as well as NO in breath) are utilized in medical diagnostics of physiopathological processes [11,12]. In the case of environmental studies, sub-per mille precision is frequently required [1,4,5] as deviations from natural abundance remain small; in the case of medical analysis, isotopically labeled precursors may be introduced into the patient’s body for metabolic studies and the requirements for isotopic sensitivity can be relaxed [11,13]. Presently, stable-isotope mass-spectrometry is the state-of-art technique for precision isotopic ratiometry [5,6,7,11,12], but the substantial capital investment and maintenance requirements involved prevent nitrogen isotope analysis from being used as a mainstream diagnostic tool. Furthermore, the lack of instrument transportability has eliminated the possibility of in situ measurements, thus requiring environmental samples to be shipped to the laboratory, which presents practical limits on sample sizes.

## 2. Signal and Noise in DM-FRS: Theoretical Analysis and Practical Limitations

_{2}O, CO

_{2}), as well as the noise-suppression capabilities that allow near shot-noise detection [13]. In its most general form, FRS exploits the magnetic field induced circular birefringence observed for Zeeman-split transitions of paramagnetic molecules (e.g., NO, O

_{2}, OH, etc.). This results in the rotation of polarization of light as it passes through the sample. The rotation is converted to intensity change by projection onto a polarizer (nominally called the analyzer), and the resulting intensity is measured by the photodetector. Conventional techniques generally utilize either: (i) magnetic field modulation (AC-FRS) [18,19] or (ii) laser wavelength modulation (DC-FRS) [17,18,20], where the former eliminates optical etalon effects through sample modulation (enabling baseline-free performance) and the latter provides effective reduction of 1/f noise. Both techniques have been extensively studied, though the individual use of either AC-FRS or DC-FRS allows for only mutually exclusive noise reduction techniques. Recent work on hybrid-FRS [20] combined DC-FRS with balanced-detection for etalon cancellation and intensity-noise reduction, enabling measurements near (1.4×) the shot-noise limit. However, the lack of low-noise, high common-mode suppression balanced detectors in the mid-infrared limited the implementation of these techniques in this highly desirable molecular fingerprint spectral region.

_{L}) and magnetic field (f

_{M}) modulation, thus combining the laser intensity-noise reduction with etalon-free measurements, enabling near shot-noise and baseline free detection. This dual-modulation method encodes the FRS signal into high-frequency sidebands (N·f

_{L}± f

_{M}) where the appropriate harmonic (N) may be chosen for signal demodulation (Figure 1). This DM-FRS approach has consistently yielded detection sensitivities beyond what is experimentally realizable using conventional FRS techniques, achieving record noise-equivalent angles (Θ

_{NEA}) below 10

^{−8}rad·Hz

^{−1/2}[13,14]. In the following sections, we rigorously consider the effect of dual-sideband signals and harmonic detection on the fundamental limits of measurement, and analytically compare DM-FRS with the conventional FRS techniques.

**Figure 1.**Spectral schematic of DM-FRS signal frequencies. Modulation of the laser occurs at f

_{L}= 50 kHz, resulting in wavelength modulated carrier frequencies at N·f

_{L}and a corresponding decrease in 1/f noise. Further modulation of the magnetic field (f

_{M}= 100 Hz) results in generation of sum and difference frequency sidebands N·f

_{L}± f

_{M}(scales in schematic are exaggerated for clarity). In DM-FRS, the demodulation bandwidth Δf must be considered around each sideband, resulting in 2·Δf total noise bandwidth.

#### Comparison of DM-FRS to Conventional FRS Methods

_{90°}) and noise (σ

_{90°}) is given by [17]:

_{0}is the power incident upon the analyzer, with α and Θ

_{FRS}denoting the analyzer uncrossing angle and Faraday rotation angle respectively. The signal power incident on the photodetector is given by P

_{sig}= P

_{0}·sin

^{2}(α). Δf is defined as the equivalent noise bandwidth (ENBW), related inversely to the minimum time between adjacent data samples ensuring independent (uncorrelated) measurements. Both AC-FRS and DC-FRS can be implemented using the 90°-method, and the above nomenclature can be used for signal and noise analysis (with a distinction of the RIN measured at frequencies that correspond to harmonics of field modulation or laser wavelength modulation in AC-FRS and DC-FRS respectively).

_{L}), and dual-sideband demodulation doubles the bandwidth required for signal retrieval (i.e., for ENBW of Δf = 1 Hz, dual sideband detection introduces noise from actual bandwidth of 2·Δf = 2 Hz), these effects are taken into account in signal and noise modeling. We thus have:

_{L}) of 0.55 is achieved yielding α = 0.39, hence, fundamentally, DM-FRS can achieve ~40% of the detection limit of shot-noise limited AC-FRS techniques. However, the ultimate shot-noise limit is difficult to attain in conventional FRS methods, whereas even though the fundamental limit in Equation (8) is inferior to Equation (7) by the factor α, DM-FRS is able to reach this limit far more easily in practical systems.

^{−1/2}to represent the signal demodulation bandwidth about each DM-FRS sideband (Figure 1), which is understood to be the fastest rate at which we are able to resolve signal changes. Although this notation symbolizes only half the noise bandwidth under consideration, figures of merit quoted in Hz

^{−1/2}(implying values normalized to 1 Hz ENBW) represent single-sideband ENBW (consistent with AC-FRS notation), and should be understood as having already accounted for the √2× noise increase from the dual-sidebands.

## 3. Spectrometer Design

^{15}N

^{16}O Q(3/2) transition at 1842.763 cm

^{−1}(minor isotope) and

^{14}N

^{16}O P(19/2)e doublet transition at 1842.946 cm

^{−1}(major isotope) using a distributed-feedback quantum cascade laser (Alpes Lasers). A Mercury-Cadmium-Telluride photodetector (Vigo Systems, PVI-3TE-6, current responsivity R

_{i}= 3.8 A/W and voltage transimpedance R

_{v}= 4.5 × 10

^{4}V/A) was used. Substantial spectrometer size/weight reduction was accomplished by replacement of the water chiller with a fan and coolant-based heat-sink (Corsair H100i), and use of a miniaturized class-D audio amplifier (Sure Electronics TK2050), data acquisition card (NI USB-6001) and vacuum pump (KNF UN84.3 ANDC). Sample measurement is accomplished through the triple pass gas cell (L

_{cell}= 15 cm) operating in continuous flow configuration at 80 Torr and magnetic field B = 150 Gauss. The DM-FRS spectrometer (Figure 2) utilizes simultaneous modulation of laser wavelength (f

_{L}= 50 kHz) and magnetic field (f

_{M}= 100 Hz) [15], where the former reduces 1/f noise and the latter eliminates optical etalon effects as described in the previous section. The magnetic field modulation frequency was reduced from [15] to lower electromagnetic interference effects, eliminating the need for high-permeability shielding. Retrieval of DM-FRS spectra is performed via demodulation at signal sideband harmonics (2f

_{L}± f

_{M}), enabling low laser-technical noise, near baseline-free measurement capability, along with intrinsic immunity to interferences from water and other diamagnetic absorbers in the mid-infrared region. A reference branch with a gas cell containing both NO isotopes (~1%

^{15}NO, and ~1%

^{14}NO in N

_{2}) is used to perform spectral line-locking of the laser wavelength to the major or minor NO isotope transitions for continuous measurements.

**Figure 2.**Integrated sensor schematic. (

**a**) Dual-modulation Faraday rotation spectrometer for NO isotopic analysis. The system is optimized for minor isotope sensitivity (

^{15}NO Q(3/2) transition, 1842.763 cm

^{−1}) with a detection limit of 0.36 ppbv·Hz

^{−1/2}using a triple-pass gas cell (45 cm optical pathlength). A reference gas cell (~1%

^{15}NO, and ~1%

^{14}NO in N

_{2}) is utilized as wavelength reference for line-locking; (

**b**) Photograph of spectrometer housed in 12U 19” rack, integrated with breath sampler; (

**c**) Chemical system for nitrate/nitrite conversion to NO via heated acidic vanadium(III).

## 4. DM-FRS System Performance

^{15}NO. In Section 4.2 the mechanism newly developed in this system to provide time-multiplexed isotopic analysis via line-switching between the major and minor isotopic transitions is also described.

#### 4.1. Signal-to-Noise Ratio Optimization

_{det}), laser intensity-noise (σ

_{int}), and shot-noise (σ

_{shot}). These noise contributions are characterized by controlled variation of the analyzer uncrossing angle (α), thereby altering the signal power as P

_{sig}= P

_{0}·sin

^{2}(α), where P

_{0}= 6.4 mW is the power incident upon the analyzer. Analysis of the noise yields a laser relative intensity-noise (RIN) of 2.19 × 10

^{−7}Hz

^{−1/2}, and a photodetector noise equivalent power (NEP) of 1.25 × 10

^{−12}W·Hz

^{−1/2}. The optimum uncrossing is well approximated (for small α) by the point where σ

_{int}= σ

_{det}and the effective extinction ratio of the optical system of ε = 1.86 × 10

^{−4}[15] (polarizers and optical gas cell) is assumed to have negligible noise contribution, yielding a calculated optimum angle consistent with the measured α

_{opt}= 1.71° at P

_{sig}= 5.7 μW.

#### 4.2. DM-FRS Spectrum Acquisition and Time-Multiplexed Isotopic Analysis

^{14}NO and

^{15}NO are obtained by current-tuning of the laser across both transitions (Figure 3). A G-Cal permeation device (Vici Metronics) was used to generate NO in N

_{2}gas sample. The acquired spectrum (Figure 3a) includes both

^{14}NO P(19/2)e at 1842.946 cm

^{−1}and

^{15}NO Q(3/2) at 1842.763cm

^{−1}lines (blue and red respectively) in the fundamental v

_{2}ro-vibrational band of NO. The spectrum was acquired using 1500 points at Δf = 1 Hz ENBW per point, resulting in a total acquisition time of ~1500 s. The inset of Figure 3a shows a corresponding typical 3f

_{L}wavelength modulated absorption spectrum for

^{14}NO measured in the reference channel, which was used to line-lock to the maxima of the DM-FRS spectra of the major isotope. Qualitative analysis of line-lock stability yielded a lock-speed of ~2.5 s, whereupon the oscillations of the PID (proportional-integral-derivative) controlled feedback loop resulted in signal oscillations below the detection limit of the system. Within the lock-speed limitations, line-switching (isotopic multiplexing) was performed by hopping the laser current set-point between the

^{15}NO and

^{14}NO transitions at predefined time intervals for quasi-simultaneous measurements of isotopic variations. It is important to note that the ratio of the raw FRS signals is not directly indicative of the isotopic abundance as system parameters were optimized for maximum

^{15}NO sensitivity by targeting the Q(3/2) transition with the highest effective magnetic moment, which despite lower line intensity produces the highest FRS signals at low magnetic fields. Therefore, an appropriate signal calibration must be utilized to measure relative isotopic abundances (see Section 5 for details).

^{15}NO spectra acquired with pure nitrogen as sample gas, indicating zero-baseline performance near the fundamental shot-noise limit. This demonstrates the benefit of lower magnetic field modulation frequency causing the reduction of EMI without the need for any extraneous shielding material for our laser or detector systems. Figure 3c is the

^{15}NO Q(3/2) transition measured for uncalibrated cylinder gas containing ~1–2 ppmv of NO in N

_{2}mixture. Along with the measurement is a spectra simulated for the same transition using the model from [23]:

^{−1}) and Δῦ as the modulation depth, which for 2nd harmonic DM-FRS corresponds to 1.2× the full-width half maximum of the AC-FRS spectrum [13]. G is the lock-in amplifier input transimpedance, and the signal reduction factor D accounts for the root-mean square measurement (D = √2) performed by the lock-in during the demodulation process. The spectral fit yields a

^{15}NO concentration of 4.56 ppbv. With an assumption of the natural abundance (0.368%) one can calculate the concentration of the

^{14}NO to be at a level of 1.24 ppmv, which is consistent with the expected concentration levels in this non-certified gas mixture.

**Figure 3.**(

**a**) Spectra of

^{14}NO P(19/2)e (blue) and

^{15}NO Q(3/2) (red) transitions from a G-Cal permeation device. Quasi-simultaneous isotopic analysis via line switching can be performed by alternately locking to the 3f

_{L}WMS zero-crossing each isotope; (

**b**) Zero-gas spectrum using cylinder nitrogen demonstrating near-zero baseline spectra; (

**c**) Measurement of

^{15}NO spectra using non-certified NO in N

_{2}mixture. Spectral modeling gives

^{15}NO concentration of 4.56 ppbv, corresponding to 1.24 ppmv

^{14}NO at natural abundance.

#### 4.3. Minimum Detection Limits and Long-Term Stability

^{15}NO transition (Figure 4c, inset shows WMS spectrum used for line-locking). Pure nitrogen is utilized for the test, and all drifts are therefore attributable to instrumental instabilities. The raw measurement data over a span of ~1 h is shown in Figure 4a. A slow positive signal drift is noticeable over this long measurement period, which indicates possible electronic interferences that indirectly modulate optical etalons into FRS signal sidebands. In the case of a practical implementation of the system for measurements of small liquid samples, residual NO produced in the chemical conversion unit must be nulled for each measurement, which requires baseline correction based on the data acquired before and after the sample peak. Typically, sample measurements follow known reference injections, each lasting approximately 500 s at a typical system flow-rate of ~100 sccm. A linear correction for each 500 s measurement interval utilizing the first 50 s and last 100 s is used for baseline correction anyway; therefore to understand instrumental stability in a practical measurement scenario such sample-peak baseline correction technique was applied to data in Figure 4a followed by Allan deviation analysis shown in Figure 4c (corrected data is shown in Figure 4b). As shown in Figure 4c, system precision is set by a noise level of 234 nV·Hz

^{−1/2}, which is 2.8× the shot-noise limit (σ

_{shot}= 84 nV·Hz

^{−1/2}). The system is white-noise limited up to 1000 s, which indicates that sequential reference and sample measurements (500 s each) may be performed with linear baseline correction without introducing any substantial drifts in measurement accuracy. Furthermore, the detection limit for

^{15}NO is derived using the ratio of

^{15}NO signal (Figure 3c) and system noise (Figure 4c): SNR = 3 μV/(234 nV·Hz

^{−1/2}) = 12.8 Hz

^{1/2}, resulting in a bandwidth normalized minimum

^{15}NO detection limit of 4.56 ppbv/(12.8 Hz

^{1/2}) = 0.36 ppbv·Hz

^{−1/2}. This corresponds to a noise-equivalent Faraday rotation angle Θ

_{NEA}of [13]:

_{SNEA}is the shot-noise equivalent Faraday rotation angle (i.e., the rotation angle corresponding to shot-noise fluctuations), and a modification factor 1/α = √2/ξ(2f

_{L}) from Equations (7) and (8) is used to account for harmonic signal detection and dual-sideband noise. For comparison to absorption-based spectrometers, we calculate a minimum fractional absorption of ΔP/P

_{0}≈ (αL)

_{min}= 6.27 × 10

^{−8}Hz

^{−1/2}, which compares favorably to typical spectroscopic systems which provide ΔP/P

_{0}in the ~10

^{−4}Hz

^{−1/2}range [24].

**Figure 4.**(

**a**) Measurement of pure nitrogen by line-locking to the zero-crossing of the

^{15}NO 3f

_{L}wavelength modulated spectrum. Slight baseline deviation is visible over the ~1 h of measurement, indicating EMI influence; (

**b**) Linear baseline correction every ~500 s is necessary for liquid samples analysis and similar correction is applied here to demonstrate the Allan deviation in a practical measurement scenario; (

**c**) Allan deviation of the baseline-corrected measurement, demonstrating white-noise performance up to ~1000 s at 2.8× the shot-noise limit. The inset is a typical 3f

_{L}WMS spectra used for line-locking.

## 5. Isotopic Ratiometry and Real-Time Fractionation Studies

#### 5.1. Real-Time Analysis of Gas Samples

^{15}N) are typically presented as permil (‰) values, defined according to [25]:

_{S}and [N]

_{R}represent the true sample and reference volume concentrations of NO. In the case of experimentally determined concentrations, we define an analogous ratiometric quantity:

^{15}Ñ] = [

^{15}N]·γ

_{15}and [

^{14}Ñ] = [

^{14}N]·γ

_{14}where γ is the ppmv to μV instrumental conversion factor for each isotope. Assuming sequential reference and sample measurements are made within the drift-free time-frame of the instrument (see Section 4.3), we expect γ to remain the same (i.e., γ

_{S14}= γ

_{R14}and γ

_{S15}= γ

_{R15}), and therefore we expect δ

^{15}N = δ

^{15}Ñ (i.e., the reference ratio to remain unchanged) within the stability time of the spectrometer. Within the preceding stability constraints and also for notational clarity, we use δ

^{15}N to denote our measured isotopic ratio in the following discussion.

^{15}N)(t):

^{15}Ñ]

_{s}(t) and [

^{14}Ñ]

_{s}(t) to be time dependent and our uncertainties Δ[

^{15}Ñ]

_{s}and Δ[

^{14}Ñ]

_{s}represent errors for data reported every 1 s (1 Hz measurements). The reference measurement error is assumed to be negligible, which can be assured through application of high concentration reference gases/liquid samples. By applying isotopic line switching with 50% measurement duty cycle between major and minor isotopes, it is appropriate to assume Δ[

^{15}Ñ]

_{s}/[

^{15}Ñ]

_{s}> Δ[

^{14}Ñ]

_{s}/[

^{14}Ñ]

_{s}. Propagation of the uncertainties in Equation (13) then gives:

^{15}Ñ]

_{s}(t). Thus, any noise and drifts in the system can be compensated by increasing the sample size for isotopic ratiometry measurements. As a rough approximation, with Δ[

^{15}Ñ]

_{s}= 234 nV·Hz

^{−1/2}indicated in Figure 4c, a sub-permil precision can be achieved for 1 Hz measurements if ~100 ppmv NO samples are used, which would result in [

^{15}Ñ]

_{s}> 234 μV. With this relationship, one can predict minimum sample size required to achieve desirable instantaneous ratiometric precision.

_{2}mixture from the cylinder (with 1.24 ppmv

^{14}NO concentration as calculated in Section 4.2), which was manually diluted over a time span of 1200 s via mixing with dry nitrogen to produce a gradual concentration variation in the sample gas concentration with no modification to the relative isotopic composition of NO. For this test, only relative excursion from the mean isotopic composition is of importance, and the sample was assumed to have natural abundance of NO isotopes with nominal δ

^{15}N = 0. The line-switch interval was set to 50 s (Figure 5), with the gray shaded regions denoting

^{14}NO measurement periods and the non-shaded regions denoting

^{15}NO. Inherent to the line-switch process is the presence of gaps in the measurement of each isotope. To enable direct ratiometric calculation in the measurement regions of

^{15}NO, we perform a polynomial interpolation of the

^{14}NO signal (which has significantly higher SNR and negligible effect on the ratiometric error as shown in Equation (14)).

^{−1/2}. This confirms the previous estimate predicting that a sub-permil precision for a 1 Hz measurement near natural abundance requires NO concentrations of >100 ppmv.

**Figure 5.**Quasi-simultaneous isotope measurement of 1.24 ppmv

^{14}NO in N

_{2}mixture diluted using pure nitrogen. Line-switching occurs every 50 s, and polynomial interpolation of

^{14}NO is used to calculate the isotopic ratio (top graph). Gray regions denote

^{14}NO measurements and white regions denote

^{15}NO. Permil ratiometric values are calculated according to Equation (12), demonstrating fractionation-free system performance. A concentration-normalized precision of Δ(δ

^{15}N) = 120‰·ppmv·Hz

^{−1/2}was determined from a typical measurement segment.

#### 5.2. Fluid Sample Analysis

_{3}(potassium nitrate) into the acidic vanadium(III) for measurement of NO isotopes as shown in Figure 6. Broad peaks of ~100 s full-width half-maximum (FWHM) were obtained at a flow rate of 64 sccm, and line-switching at 15 s intervals was selected to ensure sufficient time resolution during the sample peak. In principle, the measurement duty cycle for each isotope (

^{14}NO and

^{15}NO) should be optimized such that the majority of time is spent on

^{15}NO measurement (which has a lower SNR); however, this results in sparse and short

^{14}NO segments, which in turn yields lower peak interpolation accuracy. From these experimental considerations we have chosen a simple 50% duty cycle between major/minor isotope switching. As mentioned in Section 4.2, the PID line-lock requires 2.5 s settling time, and such an interval of data at the beginning of each measurement segment has been discarded prior to analyses. The final isotopic ratio (δ

^{15}N

_{T}) is referenced to a NO permeation device (G-Cal, Vici Metronics), whose isotopic ratio (B

_{R}) has been characterized to remain independent of flow rate (tested from 10 sccm to 140 sccm) and concentration, and is therefore suitable as a stable reference for our measurements.

**Figure 6.**(

**a**) Real-time measurement of 5 μmol injection of KNO

_{3}(500 μL of 10 mM solution) via line-switching every 15 s at 50% duty cycle for each isotope. The blue, red and black segments correspond to [

^{14}Ñ]

_{S}, [

^{15}Ñ]

_{S}and interpolated [

^{14}Ñ]

_{S}respectively. The resulting peak has FWHM of ~100 s, obtained in a flow rate of 64 sccm, and the inset shows three more repeat injections (only [

^{15}Ñ]

_{S}is shown for clarity); (

**b**) Ratiometric curves derived from the quotient of [

^{15}Ñ]

_{S}(t) and interpolated [

^{14}Ñ]

_{S}. A clear time dependent curvature is apparent, with a maxima occurring at the measurement peak; (

**c**) Calculation of ratiometric precision vs. sample size, using data obtained from (

**a**). Generally, samples >1 μmol NO

_{3}

^{−}are required to ensure sub-permil precisions over the span of the peak.

^{15}NO and

^{14}NO peaks, and the δ

^{15}N(t) at any given point in time may not be an accurate representation of the sample composition. Therefore to reduce the effects of time-dependent fractionation it is critical to measure the entire peak (i.e., integrating the entire peak ensures we have taken all chemically produced NO molecules into account). To calculate the total permil value δ

^{15}N

_{T}the ratio of the integrated peaks is used according to:

_{R}as the reference ratio (G-Cal permeation device), and T as the time-span used for

^{15}NO measurement (peak integration time is ~50% total peak time due to isotope switching). Using [

^{15}Ñ]

_{s}(t) = B

_{R}·[δ

^{15}N(t)/10

^{3}+ 1]·[

^{14}Ñ]

_{s}(t) from Equation (12), we obtain

^{14}Ñ]

_{s}(t) degrades near the wings of the peak, the relative contribution of δ

^{15}N(t) to δ

^{15}N

_{T}becomes proportionally smaller. Qualitatively, the accuracy of the final ratiometric calculation is hardly affected by the integration of the wings, and any residual accuracy deviation is corrected via calibration with known references.

^{15}Ñ]

_{s}are uncorrelated and sum in quadrature, will result in a simple extension of Equation (14) of the following form:

^{3}for samples near B

_{R}abundance) to convert to ratiometric (‰) units. Since in case of the liquid samples the entire sample peak is used for measurement, the time-averaging further improves ratiometric precision, which is also sample size dependent. The effect of sample size variation on ratiometric precision is plotted in Figure 6c, which indicates sub-‰ precision for sample sizes >1 μmol. For the peak shown in Figure 6a derived from a 5 μmol KNO

_{3}sample, we calculate δ

^{15}N

_{T}= 200.1‰ and Δ(δ

^{15}N

_{T}) = 0.25‰, demonstrating ratiometric precision well within sub-permil range. Multiple repeat injections yielded very similar ratiometric values (three [

^{15}Ñ]

_{S}(t) measurements are shown in the inset, and [

^{14}Ñ]

_{S}(t) is excluded for clarity) with the average isotopic ratio of (δ

^{15}N

_{T})

_{avg}= 199.0‰. The standard deviation of (δ

^{15}N

_{T})

_{stdev}= 5.08‰ was calculated for the best four out of five injections, which is significantly higher than: (i) instrument precision of 0.25‰ (calculated for 5 μmol KNO

_{3}) and (ii) instrument drift (sub-‰ for ~10

^{3}s as calculated from Figure 4c); therefore, we conclude the principal contribution to the measurement error originates from uncertainty introduced by the chemical reduction of nitrates within the sampling front-end.

#### 5.3. Ratiometric Linearity

^{15}N enriched potassium nitrate (Cambridge Isotopes) with natural abundance nitrate (Fisher Scientific). The samples injected were substantially smaller (by roughly 12.5×) than prior injections demonstrated in Section 5.2, thus yielding lower ratiometric precision of Δ(δ

^{15}N) = 2‰ (consistent with Equation (18) and Figure 6b). Four repeat injections were conducted for each ratiometric sample, and the results are plotted in Figure 7b. The ratiometric analyses demonstrate excellent linearity (R

^{2}= 0.999), with a ratiometric offset of 177.9‰ that is consistent with those observed with near-natural abundance samples shown in Figure 6a. Additionally, it is interesting to note that the ratio of measured to calculated isotopic ratio is not unity (dδ

^{15}N

_{meas}/dδ

^{15}N

_{calc}= 0.782), indicating possible preference of

^{14}NO in the vanadium(III) conversion process. Different temperature dependence of the transition linestrength between

^{14}NO and

^{15}NO have been considered as a source of this effect, but calculations yield slope modification factors far below the observed deviation for temperature differences up to hundreds of Kelvin. Nevertheless, the excellent linearity demonstrates consistency in the sample conversion and measurement process, thus allowing any sample to be calibrated via known references.

**Figure 7.**(

**a**) Multiple injections of known isotopically labeled references spanning from 5‰ to 5536‰, where the

^{15}NO signal is clearly enhanced for enriched samples. The smaller 400 nmol injection size reduces ratiometric precision (Δ(δ

^{15}N) ≈ 2‰), consistent with Figure 6c and Equation (18); Plotted in (

**b**) are multiple labeled reference injections (4 points per calculated δ

^{15}N value, and the plot demonstrates excellent linearity (R

^{2}= 0.999) with measured δ

^{15}N offset consistent with fractionation observed in Figure 6a. The inset shows the shape of real-time fractionation curve of the most enriched reference injection (δ

^{15}N

_{calc}= 5536‰), demonstrating results similar to those in Section 5.2.

## 6. Conclusions

^{−1/2 15}NO sensitivity, at 2.8× the shot-noise limit and 1.31 × 10

^{−9}rad·Hz

^{−1/2}noise-equivalent angle. Ratiometric analysis indicates sub-permil precision for micro-mole level nitrate samples, allowing real-time ratiometric diagnostics with excellent linearity (R

^{2}= 0.999) up to 10

^{3}‰ levels. The combination of sensitivity and transportability demonstrates promise for in situ environmental and medical diagnostics. Development of a next-generation portable prototype is underway, with goals of further miniaturization of the signal processing electronics, and integration with a total nitrogen combustion-based conversion unit for measurement of organic nitrogen samples, which is expected to eliminate isotopic uncertainty introduced by the current chemical conversion unit.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Zhang, E.; Huang, S.; Ji, Q.; Silvernagel, M.; Wang, Y.; Ward, B.; Sigman, D.; Wysocki, G.
Nitric Oxide Isotopic Analyzer Based on a Compact Dual-Modulation Faraday Rotation Spectrometer. *Sensors* **2015**, *15*, 25992-26008.
https://doi.org/10.3390/s151025992

**AMA Style**

Zhang E, Huang S, Ji Q, Silvernagel M, Wang Y, Ward B, Sigman D, Wysocki G.
Nitric Oxide Isotopic Analyzer Based on a Compact Dual-Modulation Faraday Rotation Spectrometer. *Sensors*. 2015; 15(10):25992-26008.
https://doi.org/10.3390/s151025992

**Chicago/Turabian Style**

Zhang, Eric, Stacey Huang, Qixing Ji, Michael Silvernagel, Yin Wang, Bess Ward, Daniel Sigman, and Gerard Wysocki.
2015. "Nitric Oxide Isotopic Analyzer Based on a Compact Dual-Modulation Faraday Rotation Spectrometer" *Sensors* 15, no. 10: 25992-26008.
https://doi.org/10.3390/s151025992