A mid-infrared continuous-wave distributed-feedback laser (cw-DFB laser, Nanoplus GmbH) emitting at 2.8 µm is used as the probe laser. The current and temperature of the laser chip are controlled by a laser controller (LDC501, Stanford Research Systems). By changing the injection current from 90 to 130 mA at an operating temperature of 33 °C, the wavelength of the DFB laser can be tuned from 3568.939 to 3568.362 cm-1. The current tuning coefficient is about 0.0024 cm-1mA-1 near the target Q(1.5e) line of the 2Π3/2 state of OH at 3568.523 cm-1. The selected line has the strongest line strength of S = 9.032 × 10⁻²⁰ cm-1(molec.cm-2) at 296 K (Gordon, et al., 2022) with the largest effective g_J value of 0.936 in the infrared region, which make it preferable for the FRS detection (Zhao et al., 2011, 2012). The collimated beam output from the laser head passes through a Rochon prism (Foctek Photonics), with an extinction ratio of ξ < 5 × 10⁻⁶, to establish a linearly polarized state, and then is incident into a Herriott-type pump–probe MPC. A He-Ne laser serves as an indicator. The beam waists of both lasers are aligned at the centre of the MPC to minimize beam divergence after each reflection (Pilgrim et al., 1997). A flipper optical mount facilitates switching between the two lasers. A second Rochon prism is placed at the output path to analyse the polarization state. The exit beam from the MPC is focused on a thermoelectrically cooled mercury cadmium telluride (MCT) photodetector (PVI-4TE-3.4, VIGO system). To effectively modulate the magnetic circular birefringence in a static magnetic field (Zhao et al., 2018; Fang et al., 2020; Wei et al., 2020), a 33 kHz sinusoidal wave from a lock-in amplifier (SR830, Stanford Research Systems) is added to the laser injection current. The detector signal is processed by the lock-in amplifier to demodulate the second harmonic (2f) of the FRS signal. As the laser current is fixed at the absorption peak of the OH radical, a time-resolved Faraday rotation spectrum that directly reflects the concentration variation in OH radicals can be measured (Wei et al., 2020; Cheng et al., 2023).

The pump–probe MPC, as shown in Fig. b, consists of a cylindrical stainless steel tube with an inner diameter of 5 cm, a total length of approximately 89 cm, and a sample volume of 1.5 L. At both ends, a pair of 6.8 cm diameter calcium fluoride (CaF2) windows are used for sealing and light transmission. Two gold-coated concave spherical mirrors, each 5 cm in diameter, are spaced 77.2 cm apart within the cell. Each mirror features a 5 mm diameter hole for probe light incidence and exit and a central 32 mm diameter hole (i.e. the maximum diameter permissible for the UV beam passage) for the expanded photolysis beam. Mirror tilt and spacing are adjustable via three screws distributed circularly on the mirror mount. At each end of the MPC, there are eight circular quartz observation windows near the mirrors to facilitate multi-pass light adjustments. A total of 25 reflection spots are arranged on the mirror surfaces in a circular pattern with 2 cm radius. The total path length of the MPC is 37.8 m.

A solenoid coil, wrapped with 1 mm diameter red-copper enamelled wires, is wound around the stainless steel tube and operates in DC mode to offer a static magnetic field for FRS. The length and the outer diameter of the coil are 59 cm and 10 cm, respectively. The magnetic intensity tuning coefficient at the centre of the coil is 73 G/A. A water-cooling interlayer is designed for temperature control of both the solenoid coil and the cell.

A flashlamp pumped Nd:YAG laser (Big Sky Laser Ultra 100, Quantel) is employed as the photolysis laser. The laser wavelength is frequency doubled to generate the fourth harmonic radiation at 266 nm with a pulse energy of 25 mJ, energy stability of ∼ 2 %, pulse length of ∼ 6 ns, and beam diameter of ∼ 4 mm. The water-cooled laser head has a size of ∼ 30.6 cm × 7.6 cm × 5.6 cm and is controlled by an integrated cooling and electronics unit. The 266 nm pulse emitted from the laser head is directed coaxially into the MPC using two dielectrically coated 1 in. diameter mirrors. Prior to entering the cell, the diameter of the 266 nm beam is expanded to 32 mm using a beam expander consisting of a quartz concave lens with a focal length of 12.5 mm and a quartz convex lens with a focal length of 100 mm.

A digital delay generator (DG645, Stanford Research Systems) was used to control the time sequence of laser-flash photolysis to record the time-resolved OH decay curve. The pump and Q switch of the Nd:YAG laser are synchronized with two 4 Hz transistor–transistor logic (TTL) pulses delayed by 30 ms relative to the data acquisition to achieve the baseline of the OH decay curve. The rising edges of the pulses are used for triggering. The spectrum is sampled with 1000 data points, each separated by a time interval of 0.2 ms.

The MPC in the instrument determines the effective absorption path length of the FRS system for OH measurement (Wei et al., 2020; Yan et al., 2020). As shown in Fig. a, the mid-infrared light undergoing multiple passes between two mirrors within the MPC is used for OH detection; the expanded 266 nm UV pulse is employed for producing OH. The overlapping factor (η=l/d) can be defined as the ratio of the overlapping length (l) to the base length (d) of the MPC. To develop portable instruments, increasing the overlapping factor is crucial for achieving a long effective path length while reducing the MPC base length. The Herriott MPC in the developed LP-FRS instrument is specially designed with a small multi-pass light distribution circle radius at the centre to achieve a high overlapping factor. The radius of the multi-pass light distribution circle at the centre of the Herriott MPC can be calculated with (Trutna and Byer, 1980) 2rc=rg1+2g1g2+g24g21/2, where g (g=g1=g2=cos⁡θ=1-d/R) is the parameter that describes the optical resonance stability of the optical cavity or MPC. When the g value is less than zero, the base length of the multi-pass cell exceeds the curvature radius of the mirror, causing the resonance to become unstable. An incident parallel beam or a beam whose waist is not properly aligned with the cell's centre will quickly diverge and cannot be collected. However, a beam with its waist well matched to the centre can effectively prevent divergence. θ is half of the angle between two adjacent reflection light points on the mirror surface. d is the base length, and R1=R2=R is the curvature radii of the mirrors. r is the radius of the spot distribution circle.

Figure b illustrates the variations in rc, g, and η as functions of θ. When the θ value is below 79.2, rc exceeds the 16 mm radius of the photolysis beam, resulting in no overlapping path. As θ approaches -1, the value of rc decreases, and the η value increases. Considering the difficulties in processing and testing mirror curvature, θ was set to 158.4°, yielding an rc value of 3.7 mm. The achieved η was up to ∼ 75.4 %, corresponding to an overlapping path length of ∼ 28.5 m.

In fact, from an optical structure perspective, the overlap factor characterizes both the utilization efficiency of the optical path length and the compactness of the pump–probe MPC, making it an ideal parameter for performance characterization. To demonstrate the efforts in reducing instrument size, a comparison of effective overlapping path lengths and overlapping factors with the literature-reported pump–probe MPCs is shown in Table . The effective overlapping path length of these MPCs ranged from several metres to tens of metres with base lengths around 100 cm (Pilgrim et al., 1997; Luo et al., 2019; Qian et al., 2000; Lewis et al., 2018; Luo and Horng, 2020; Luo, 2020; Wei et al., 2020; Yan et al., 2020; Teng et al., 2021; Cheng et al., 2023). The overlapping factor of our MPC was comparable to that developed by Luo et al. (2019) for a similar base length, while our effective overlapping path length was twice as long.

For weak absorption, the FRS signal (SFRS) and total noise (Ntot) of the system can be expressed as functions of the analyser offset angle (ϕ) from the crossed polarization of the light (Zhao et al., 2011; Wei et al., 2020): 3SFRS(ν)=γNSLP0sin⁡(2ϕ)χ(ν),4Ntot(ϕ)=N02+N1(sin⁡2(ϕ)+ξ)2+N2(sin⁡2(ϕ)+ξ)2, where ν is the laser frequency, γ is the instrumentation factor, N is the OH concentration, S is the absorption line strength of OH, and χ is the Faraday rotation line shape (Westberg and Axner, 2014). N0, N1(sin⁡2(ϕ)+ξ), and N2(sin⁡2(ϕ)+ξ) are the detector noise, shot noise, and laser noise of the system, respectively. It is noted that the FRS signal reaches its maximum value when ϕ = ± 45°, while the total noise is more sensitive to sin⁡2(ϕ). The maximum signal-to-noise ratio (SNR) usually occurs at a small offset angle, which depends on system noise (Lewicki et al., 2009).

The total noises at various offset angles and the detector noise were measured with the lock-in amplifier to determine the noise sources and the optimum angle (ϕopt) for maximizing the SNR of the FRS system (Zhao et al., 2011). Figure a shows a fit analysis of the data using Eq. (). For offset angles below 5.5°, detector noise is the main noise of the system. The measured detector noise was 300 nVHz-1/2, which closely agreed with the manufacturer's specified value of 290 nVHz-1/2. Laser noise dominates and rapidly increases beyond an offset angle greater than 11.5°. Since the FRS signal is proportional to sin⁡(2ϕ), the relative SNR for a given absorption at a fixed laser frequency can be evaluated from SNR∝sin⁡(2ϕ)/Ntot. As shown in Fig. b, the SNR of our system peaks at the ϕopt of ∼ 8°. At this angle, the laser noise was suppressed to 310 nVHz-1/2, equivalent to the detector noise level. The total system noise was 610 nVHz-1/2, which was 1.4 times higher than the measured shot noise of 440 nVHz-1/2.

In this work, the magnetic circular birefringence of OH was effectively modulated with wavelength modulation in a static magnetic field generated by the DC coil. The modulation amplitude and magnetic field strength are critical parameters that affect the intensity of the demodulated FRS signal (Zhao et al., 2018; Fang et al., 2020). The theoretical optimum modulation amplitude is 2.2 times the half-width at half-maximum (HWHM) of the absorption line shape (Schilt et al., 2003). The optimum magnetic field strength (Bopt) is the value that can make the Zeeman splitting comparable with the HWHM (Brecha et al., 1997). A direct and effective approach for determining the two optimum parameters is recording the signal intensity values under series amplitudes of the sinusoidal wave output from the lock-in amplifier and different coil currents. As shown in Fig. , the FRS signal intensity value is calculated from the difference before and after the laser flash. The maximum intensity occurred at an amplitude of 360 mV and a coil current of 4.2 A, which corresponds to a wavelength modulation amplitude of ∼ 0.048 cm-1 (∼ 2.45 times the calculated OH absorption linewidth of ∼ 0.020 cm-1 in air) and a Bopt of 307 G, respectively.

To produce sufficient OH in the MPC, a small flow rate (∼ 0.25 Lmin-1) of zero air, which passed through a UV lamp (UVP Pen-Ray, Analytik Jena) and a bubbling bottle to generate O3 and water vapour, is added to the main sampling flow (∼ 6.0 Lmin-1), resulting in a total flow rate of 6.25 Lmin-1. The operation pressure in the MPC is set to 200 mbar and maintained by a butterfly valve (DN40, VAT). The flow velocity in the cell is 27 cms-1, corresponding to a Reynolds number of ∼ 170, which met the laminar flow condition. OH is produced by the 266 nm laser photolysis of O3 and then followed by reaction of O(1D) with water vapour (Sadanaga et al., 2004): R1O3+hv(λ=266nm)→O2+O(1D),R2O(1D)+H2O→2OH.

The concentrations of O3 and the water vapour directly influence the OH produced. A dew point sensor was used to measure the water vapour mixing ratio of the total flow. Based on the Magnus–Tetens formula (Lawrence, 2005), the absolute water vapour mass concentration can be evaluated from ρ(H2O)=e/(Rw⋅T), where Rw = 461.52 J(kgK)-1, T is the sample temperature, e=C×10(A⋅Td/(B+Td))⋅(P/P0) is the actual water vapour pressure at a current pressure of P, A = 17.625, B = 243.04 °C, C = 610.94 Pa, P0 is the standard atmospheric pressure, and Td is the measured dew point temperature. The calculated water vapour volume concentration was ∼ 0.13 % when using zero air for the system test, while it increased to ∼ 1.5 % when measuring the real atmosphere. The O3 concentration is estimated by measuring the energy of the photolysis laser pulse with the UV lamp on and off. Only about 0.3 % of the pulse energy was absorbed by O3. Based on the Beer–Lambert law and the O3 absorption cross section of σ = 9.65 × 10⁻¹⁸ cm2 at 266 nm (Sadanaga et al., 2004), the O3 concentration is determined to be ∼ 800 ppbv. The recommended quantum yield of the O(1D) produced by laser-flash photolysis is ∼ 0.9 (Atkinson et al., 2004), resulting in ∼ 2.2 × 10¹¹ molec.cm-3 of O(1D). The number density of OH produced by each O(1D) can be estimated by (Wei et al., 2020) 5[OH]=2k6[O(1D)][H2O](k5[M]+k6[H2O])[O(1D)]≅2k6k5χH2O, where [OH], [O(1D)], [H2O], and [M] represent the number densities of the corresponding molecule. M is the “bath” gas during the chemical reaction of OH formation. χH2O is the volume concentration of water vapour. k5 and k6 are 2.9 × 10⁻¹¹ and 2.2 × 10⁻¹⁰ cm3molec.-1s-1 at 298 K, respectively. The concentration of OH produced in the cell was ∼ 4.3 × 10⁹ molec.cm-3 during the system test and ∼ 5 × 10¹⁰ molec.cm-3 during the field application due to different χH2O in the sample.

The performance of the LP-FRS instrument in measuring different reaction rates was verified with three well-known reactions (Wei et al., 2020; Yan et al., 2020). Reactants from the cylinders (i.e. CH4 (99.999 %, Nanjingteqi), CO (2.01 %, Nanjingteqi), and NO (100 ppmv, Linde)) were added to the main flow at different flow rates. When the concentrations of reactants are much higher than those of OH, the OH decay rate (kdecay) follows pseudo-first-order kinetics and can be determined by fitting the measured decay spectra to the following exponential equation: 6St=Sbackground+S0exp⁡(-kdecayt), where S0 and St are the FRS signal intensities proportional to the OH concentration at the time when the fitting started and at the time t, respectively. Sbackground is the background signal intensity. Since the fitted values for y and kdecay do not depend on the selected time period of the decay curve (Stone et al., 2016), the fit is started at the time of 36 ms rather than the peak to avoid any fluctuations affecting the fitting result. Figure  shows two typical decays with loss rates of kdecay = 8.4 s-1 and kdecay = 50.2 s-1, which are given with a 60 s averaging time during the measurements. The recorded time-resolved decay spectra clearly depict the entire event, including the baseline, the instant generation of OH by laser photolysis, and the decay process.

The OH decay rates in the reactions with three different species were measured and can be expressed as kdecay=kOH+X[X]+k0, where kOH+X is the measured rate constant for the reaction of OH with X, [X] is the concentration of reactant X, and k0 is a background value. As shown in Fig. , the obtained reaction rate constants for OH + CH4, OH + CO, and OH + NO at 298 K were found to be kOH+CH4=6.4+0.1-0.1× 10⁻¹⁵, kOH+CO=1.6+0.1-0.1× 10⁻¹³, and kOH+NO=3.0+0.1-0.1× 10⁻¹² cm3molec.-1s-1, respectively. The measured values are in agreement with the International Union of Pure and Applied Chemistry (IUPAC) recommended values of 6.4+1.3-1.1× 10⁻¹⁵, 1.6+0.2-0.2× 10⁻¹³, and 3.0+0.8-0.6× 10⁻¹² cm3molec.-1s-1, respectively (Atkinson et al., 2004, 2006).

When the LP-FRS instrument is used for measuring atmospheric kOH′, the fitted kdecay value requires corrections for dilution and instrument zero (kzero). Incorporating these corrections, the atmospheric kOH′ is expressed as 7kOH′=f×(kdecay-kzero), where f, given by f=fpressure×fflow, is the total dilution factor, which arises from the low operating pressure of 200 mbar and the additional small flow of humidified air containing a constant mixing ratio of O3. fpressure represents the pressure dilution factor given by the ratio of the ambient pressure to the operation pressure, equal to ∼ 5. fflow is the flow dilution factor calculated as the ratio of the total flow rate of 6.25 Lmin-1 to the sample flow rate of 6.0 Lmin-1, equal to 1.04. Therefore, the total correction factor (f) is 5.2.

The instrument zero is critical for calculating kOH′ from the observed OH decay rate and is usually assumed constant over a certain observation period. To evaluate instrument zero, OH decay rates were measured in zero air produced by a portable zero gas generator, yielding a kzero of 5.2 s-1. Several factors affect the instrument zero, including the self-reaction of OH, reaction of OH with O3, OH diffusion, and reaction of OH with residual reactive species in zero air. The self-reaction rate constant of OH is 1.48 × 10⁻¹² cm3molec.-1s-1 at 298 K (Atkinson et al., 2004), contributing to ∼ 1.5 % of the instrument zero at the current OH concentration. The reaction rate constant of OH with O3 is 7.3 × 10⁻¹⁴ cm3molec.-1s-1 at 298 K (Atkinson et al., 2004), leading to an OH loss rate of 0.3 s-1, which accounts for ∼ 6 % of the instrument zero. The OH loss rate due to diffusion (kdif) under laminar flow conditions can be calculated from (Ivanov et al., 2007; Liu et al., 2009) 8kdif=Kdif×DOHrtube2, where Kdif=3.66 (for a cylinder cell) is the dimensionless geometric parameter, rtube is the radius of the cell, and DOH = 1.3 cm2s-1 is the OH diffusion coefficient at 200 mbar and 298 K in air. The calculated OH diffusion loss rate was 0.8 s-1, giving a contribution of ∼ 15 % of the instrument zero.

To assess the measurement precision of the LP-FRS instrument, an Allan deviation analysis was conducted on time series of zero-air measurements. The measured values were processed by subtracting the instrument zero. As shown in Fig. , the averaging time of the kOH′ data point was 10 s, with a total measurement time of about 4000 s. The measurement precisions of kOH′ were 2.3 and 1.7 s-1 with an acquisition time of 60 s and 120 s, respectively. When the averaging time increased to 300 s, the atmospheric kOH′ measurement precision could be further improved to 1.0 s-1.

A comprehensive approach to evaluating the instrument's total uncertainty is measuring zero air. Figure  illustrates the kOH′ values obtained from zero air on different days. Each value was obtained from 1 h continuous measurements. The time intervals for these zero-value measurements are longer than 2 weeks. The error bars of the data points agreed well with the kOH′ measurement precision obtained from Allan deviation analysis. No significant drift was found during measurements, with a mean value close to zero at 0.2 s-1. The kOH′ measurement uncertainty of the developed LP-FRS instrument, which can be determined from the deviations of these measurements, was within 2 s-1. The uncertainty of the LP-FRS instrument arises from two main sources: the dilution factor and the instrument zero. The uncertainties associated with the mass flowmeters and the pressure controller used were ∼ 1 % and < 1 %, respectively, resulting in a total uncertainty of the dilution correction factor of less than 2 %. The uncertainty of the instrument zero primarily originates from various influencing factors, such as changes in O3 concentrations and residual reactants in zero air and water.