The knowledge of absolute number density of molecular samples plays an important role in many disciplines such as precision measurement,^[1,2] environmental pollutants monitoring,^[3] cold collision and cold chemistry.^[4] Among various molecules of environmental interest, nitrogen dioxide is very attractive.^[5,6] NO_x species (NO, NO₂) play a vital role in determining the photochemistry of troposphere, controlling the abundance of ozone (O₃) and OH.^[7] And they have strong influences on air quality, formation of acid rain, and thus affecting all living things on the Earth.

The importance of detecting absolute number density of worthy species results in the development of a number of successful methods, which can be roughly divided into two main groups. One is the absorption method, including the differential optical absorption spectroscopy (DOAS),^[8] cavity enhanced absorption spectroscopy (CEAS),^[9,10] tunable diode laser absorption spectroscopy (TDLAS),^[11] cavity ring down spectroscopy (CRDS)^[12–15] and cavity attenuated phase shift spectroscopy (CAPS).^[16] The above mentioned methods are just a few examples among the many absorption techniques. The other is the laser-induced fluorescence (LIF) method, including the single-photon LIF^[17,18] and two-photon LIF.^[19] Besides, sensitive measurements of NO₂ have also been achieved with the technique of photofragmentation-chemiluminescence (PF-CL).^[20] In recent years, a new method called cavity-enhanced laser-induced fluorescence (CELIF) has been described by Sanders et al.,^[21] and then used for measuring the absolute number density of SD radicals.^[22] This method combines the absolute absorption capabilities of CRDS and the sensitivity of LIF. The CRDS data are used for normalizing the LIF signal to remove the influence of the laser intensity fluctuation.

The fluorescence lifetime of NO₂ depends on the pressure of the gas sample. Collisions with other molecular species in the gas sample can quench the photo-excited NO₂ from fluorescing. The ratio of the radiative rate constant to the other quenching rate constant determines the real lifetime of the NO₂ fluorescence. For instance, the radiative lifetime of NO₂ excited at ∼ 440 nm is ∼70 μs, and the real lifetime is estimated at ∼5 μs at a pressure of ∼ 0.2 Torr (1 Torr = 1.33322 × 10² Pa).^[17]

The NO₂ number density fluctuates remarkably in various areas, ranging from less than 100 pptv (parts per trillion) in the rural area to more than 100 ppbv (parts per billion) in the urban atmosphere.^[8,23] This density variation covers a wide range of more than six orders of magnitude. The technique of CRDS typically can cover no more than three orders of magnitude in the dynamic range in terms of absorbance measurement. The technique of CELIF can, however, extend the dynamic range of absorbance measurements compared with a sole CRDS measurement by at least three orders of magnitude.^[21]

In this paper, we describe a newly-built CELIF setup with a pulsed laser source and use it as a high-sensitivity instrument for measuring the absolute number density of NO₂ samples in the laboratory. Some of the experimental details are first described. Then, the experimental results obtained with the CELIF technique are presented. Some discussion and a simple conclusion are given in the end.

Figure 1 shows a conceptual drawing of our experiment setup. Survey scans of NO₂ are performed with the fundamental output of a pulsed dye laser (SirahPrecisionScan, linewidth 0.04 cm⁻¹) pumped by the third harmonic of an Nd:YAG laser (Spectra-Physics, Quanta-Ray Lab-170-10, 355 nm, repetition rate f = 10 Hz, pulse width 8 ns–10 ns). The dye laser is operated with Coumarin 440 dissolved in ethanol. The central portion of the laser output is first selected and then passes through a spatial filter assembly consisting of a pair of lenses (the focal length of which are f = 150 mm and f = 75 mm, respectively) positioned at 225 mm apart from a standard telescope arrangement. A 50-μm-diameter (aperture) precision pinhole is located at the focus of the telescope. The filtered laser beam is then coupled into the optical cavity through one end mirror with the help of an f = 600-mm lens located, and thus making the laser focus at the center of the cavity. The pulse energy of the laser shot for the following experiment is measured to be about 0.1 mJ in front of the spatial filtering assembly.

Fig. 1.

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	Fig. 1. (color online) Schematic diagram of the experimental setup.

The high-finesse ring-down cavity consists of two identical plano-concave reflective mirrors (Layertec) with quoted reflectivity > 99.98% at a wavelength around 440 nm. The cavity mirror is O-ring sealed to a stainless steel flange by screws. Cavity adjustment is realized by rotating three other screws of ultrafine threads from outside. The mirror substrates each have a radius of curvature of 100 cm, and they are 84 cm apart. The whole cavity assembly is located in a home-built vacuum chamber. The vacuum chamber has various ports for pressure gauges and quartz windows with a central axis collinear to the cavity axis.

Light leaking through the opposite cavity mirror is detected with a photomultiplier tube (PMT) positioned behind. A two-lens LIF detection optical system is aligned perpendicular to the cavity axis and LIF photons are collected by another PMT (H3695-10, Hamamatsu). The LIF collecting optics has a field of view that restricts the probe volume to ∼ 1.0 × 10⁻³ cm³. Only 1 cm of the total 84-cm cavity length is detected. The wavelength of the NO₂ fluorescence extends from visible to infrared. To avoid interfering from the pump laser of 440 nm, such as chamber and Rayleigh scattering, a long-pass optical filter of λ > 495 nm is placed in front of the LIF PMT. The CRDS and LIF signals are simultaneously acquired via a digital oscilloscope and sent to a host PC for later processing.

Following the cavity alignment, a mechanical pump and a turbomolecular pump keep the pressure in the vacuum chamber typically below 4 × 10⁻⁶ Torr, which is measured by an ion gauge. Bellows are adopted to minimize the influence of mechanical vibration from both pumps on the system stability. Then the turbomolecular pump is closed and the gas sample is introduced into the chamber via a flange connected dosing valve. The gas sample enters into the chamber continuously and is pumped away by the mechanical pump. A gas flow of constant low pressure is maintained in the chamber by concerted work of the dosing valve and an angle valve in front of the mechanical pump. The temperature of the flowing gas sample is ∼ 293 K.

The total volume of our sample cavity is estimated at about 2500 cm³. The flow rate of the dry gas mixture controlled by the dosing valve (INFICON VDH040-U) is about 20 sccm. The gas flows through the sample cavity under essentially plug flow conditions that are distorted by the gas entering into and leaving from the cell at right angle to the cavity axis. The residence time of the gas sample is about 2 s inside the cavity with a pressure of ∼ 0.2 Torr. Compared with static samples, flowing gas samples have some prominent advantages. Firstly, the walls of the chamber will adsorb some NO₂ during the experiment, so the optical absorption of a static sample declines on a timescale of a few minutes, which is confirmed in our experiment. Secondly, a flowing gas sample provides sufficient fresh molecules to be excited by the 440-nm laser.

The gas mixture of NO₂ / Ar (each with a purity of ∼ 99.9%) is first prepared in a 1-L gas mixing bottle with a total pressure of ∼ 4560 Torr (i.e., 0.6 MPa with NO₂/Ar = 0.01/0.59 in pressure). Starting from this concentration, the mole fraction of NO₂ is lowered by sequential dilution. For each dilution, a fraction (∼ 2/3) of the gas mixture is pumped away and Ar is added to restore the total pressure back to the initial value. After each dilution, the gas mixture is fully mixed for about 20 min by using convection currents generated through heating two loops of pipe of unequal length connected to the gas mixing bottle. Both the chamber and the gas feeding pipeline to the dosing valve are fully evacuated prior to each dilution.

For quantitative gas-phase absorption measurement in cavity ring-down setup, the CRDS time constants of the cavity without and with the absorbing species can be expressed as τ₀ = l/[c(1 − R)] and τ = l/[c(1 − R + αl)], respectively. Here l is the length of the cavity, R is the reflectivity of the cavity mirror, c is the speed of light, α is the absorption coefficient of the sample in the cavity and given as α = ρ · σ with σ being the absorption cross section of the sample and ρ being the sample concentration. If the cavity is filled with absorbing molecules, then the relationship between the number density of the molecules and their absorption cross section can be given as

Fig. 2.

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	Fig. 2. (color online) Simultaneously recorded CRD [(a) and (c)] and LIF transients [(b) and (d)] at ∼ 440 nm. Panels (a) and (b) correspond to the NO2/Ar mixture; panels (c) and (d) correspond to pure Ar background. CRD time constants are (a) ∼ 5.239 μs and (b) ∼9.221 μs.

Figure 3(a) shows the corresponding absorption spectrum of NO₂ from CRDS, which agrees well with those studied before^[25,26] in profile but with better resolution. The absorption cross section (σ) of NO₂ has been intensively studied in previous work. The number density of NO₂ in the cavity chamber for this measurement is calculated to be ∼ 4.9 × 10¹² cm⁻³ from Eq. (1), with an absorption cross section of σ = ∼ 5.66 × 10⁻¹⁹ cm^2[27] used. To remove the influence of laser shot-to-shot fluctuation on the LIF signal, the product of A^CRD and τ, I^CRD = A^CRD·τ, is used to normalize the LIF signal. Here A^CRD and τ are, respectively, the amplitude and the time constant of the exponential fit to the CRDS trace in the presence of the gas sample. This time-integrated value of I^CRD contains the information about the laser intensity exciting the gas sample. The normalized LIF signal S^CELIF is given as S^CELIF = S^LIF/I^CRD, and is called CELIF signal later. The normalization ensures that neither any shot-to-shot instability nor long-term drift in the probe laser pulse energy can contribute to the noise in S^CELIF. The LIF signal in the presence of pure Ar is processed similarly and taken as the CELIF background. Thus, the CELIF signal originating from NO₂ molecules, , is obtained to be

Fig. 3.

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	Fig. 3. (color online) (color online) (a) Absorption and (b) LIF spectrum of NO2. Flowing gas sample keeps pressure in the cavity chamber at 0.2 Torr.

Since the LIF signal is normalized by the time-integrated CRD laser intensity to remove the influence of its fluctuation, the LIF measurement has to take place in a regime where the fluorescence of NO₂ is linearly proportional to the probe laser pulse energy. Figure 4 shows the linear dependence of the NO₂ LIF signal on the probe laser pulse energy as measured by the time-integrated ring down signal. The measurements are performed with the gas mixture diluted 7 times after first preparation. The solid squares are the experimentally measured results with the solid line being a linear fit. The arrow indicates the laser pulse energy selected for our CELIF measurements, which falls in the linear regime of the relationship.

Fig. 4.

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	Fig. 4. (color online) Dependence of averaged LIF signal per shot on probe laser pulse energy as measured by time-integrated ring down signal. Error bar indicates shot-to-shot fluctuation of laser pulse energy, which is measured to be ∼ 7%. Arrow indicates laser energy selected for our CELIF experiment.

As is well known, the CRDS method has the ability to determine the absolute density of trace gas by measuring its absorbance of the incident light, once the corresponding absorption cross section is known as can be seen from Eq. (1). Its limit to detection (LOD) is determined by minimizing the absorbance that can be reliably measured. As an absorption method, its LOD inevitably suffers the strong background laser signal that is always present. The LIF method, however, can work with a nearly background free situation, and thus offering even higher detection sensitivity and much lower LOD. The LIF signal depends on a number of experimental factors, like the number density of the absorbing sample, the laser intensity for excitation, the fluorescence quantum yield of the molecule, the efficiency of fluorescence detection, etc. Extracting the number density information of the absorbing sample from the sole LIF signal needs the knowledge of all other factors, some of which is usually difficult to obtain for a practical experiment. However, this problem with LIF measurement can be circumvented with the help of the CRDS information. Our idea to solve this problem is explained as follows.

For the CRDS measurement, equation (1) can be rearranged as

Figure 5 shows the relationship between the values of and Δτ / τ measured experimentally. The gas mixture is first diluted twice after preparation and before being put into use. The concentration of NO₂ molecules gradually decreases by consecutively diluting the gas sample 5 times more. For each dilution the measurement is averaged over 600 laser shots. The probe laser is fixed at 440 nm. As one can see, good linearity is obtained for the relationship between and Δτ / τ with the ratio (i.e. the slope) being ∼ 2.91 × 10⁴. According to Eqs. (3) and (5), the relationship between the molecule density and the value of the signal can be expressed as

Fig. 5.

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	Fig. 5. (color online) Relationship between Δτ / τ and . Concentration of NO2 molecules gradually decreased by consecutively diluting the gas sample 5 times. The statistical error bars for both the horizontal (x-axis) and vertical (y-axis) quantities are smaller than symbol size.

Fig. 6.

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	Fig. 6. Determination of LOD of our CELIF measurement of NO2.

The noise in is processed in the following way:^[22]

In this work, we measure in laboratory the absolute number density of NO₂ seeded in Ar with cavity-enhanced laser-induced fluorescence (CELIF) through using a pulsed laser beam at 440 nm. The cavity ring down (CRD) signal is acquired simultaneously and used for normalizing the LIF signal and calibrating the relationship between the measured CELIF signal and the NO₂ number density. With the decrease of the NO₂ concentration, the CRDS reaches its limit of detection and fails to provide reliable information but the CELIF proceeds to work well for a few more dilutions before approaching to its detection limit. In 60 s of acquisition time, the minimum NO₂ number density is measured by the CELIF method to be (3.6 ± 0.1) × 10⁸ cm⁻³, corresponding to a minimum detectable absorption coefficient of (2.0 ± 0.1) × 10⁻¹⁰ cm⁻¹ and a noise equivalent absorption (NEA) sensitivity of (2.2 ± 0.1) × 10⁻⁹ cm⁻¹ · Hz^−1/2 for the system. For our case here, the sample absorption length for CRDS is ∼ 84 cm and that for CELIF collection is only ∼ 1 cm. For equal sample absorption length, like in the cases of molecular beams, the sensitivity of the CELIF will be about 3–4 orders of magnitude better than that of the CRDS measurement. In fact, there is still much room for improving our experimental setup. For example, an even larger solid angle for better fluorescence collection and a blackened chamber wall for less scattered light of background will further reduce the limit of detection. In principle, the CRDS calibration method introduced here can be applied to the CELIF measurement of other trace gas mixtures of similar conditions. But for outdoor measurements in more complicated conditions, other methods are needed to reliably explain the trace gas concentration from the LIF signal. Compared with a CELIF experiment using a continuous wave laser, the pulsed CELIF experiment is easier in cavity alignment and more convenient to operate. The scheme experimentally demonstrated in our laboratory here can be further improved and used for environmentally monitoring the outdoor NO₂ pollution.