1. Introduction

Light sources which can be rapidly wavelength-tuned are necessary for real-time monitoring of various fast gas phase processes, like e.g. for diagnostics of combustion processes in engines, industrial process control, or environmental monitoring as well as atmospheric and stratospheric analysis (see e.g [1–3].). For multi-species detection approaches with several tunable diode lasers were used in many cases. However, measurement systems in which just one laser source is used to generate a broad spectrum of radiation at a high repetition rate, thus enabling time-resolved spectroscopy of multiple species and a retrieval of physical parameters of a gas-phase mixture in real time, are also favorable. A prototype single-pulse time-of-flight absorption spectrometer with a spectral resolution of a few nm, using a passively mode-locked laser generating 10 ps pulses with a spectral width exceeding 450 nm, was presented in [4]. The operation of a more advanced system, using high repetition rate 0.5 ps laser pulses with a 20 nm wide spectrum, was demonstrated in [5], with a spectral resolution of 0.3 cm ⁻¹. The experimental development of time-resolved spectroscopy in recent years [6–10] was based on employing a few hundreds of nm bandwidth supercontinuum (SC) radiation generated by short and intense laser pulses propagating in a highly nonlinear optical fiber [11,12]. The supercontinuum spectrum of the radiation at the fiber output results from various nonlinear optical processes which take place when a 10 ⁻¹⁴-10 ⁻⁹ s pulse propagates along the fiber. Particularly, in case of a nanosecond pulse the spectral broadening occurs mostly due to four-wave mixing and stimulated Raman scattering [11,12].

In [5–10] mode-locked lasers with a few MHz repetition rate were employed. Photonic crystal fibers (PCF) were used for generation of supercontinuum radiation in [6,7,9], while in [8,10] a conventional single-mode fiber (SMF) was applied. A short pulse of hundreds of nanometers spectral width was dispersed in a long dispersive single-mode fiber (DSMF). As a result, the wavelengths at the DSMF output are swept over time, since the spectral components travel with different group-velocities. This allowed an absorption spectrum to be recorded in the time domain by using a fast photo-detector and a fast digital oscilloscope. The influence of the dispersive element on the scan rate and the achievable spectral resolution was analyzed in [6]. In [9] a spectral resolution of about 0.14 cm ⁻¹ which is comparable to the line widths of H₂O and CH₄ under atmospheric conditions was achieved. Calculations of CH₄ column density and of observed standard deviations of this value as a function of the averaging count of consecutive laser pulses were also performed. In [13,14] sub-GHz spectral resolution has been demonstrated using distributed Raman amplification in a dispersive element (DSMF) which provided its virtually lossless operation. Hence, the capability of this experimental approach to derive species concentrations in gas mixtures at repetition rates which can resolve dynamics of turbulent flow or combustion phenomena was demonstrated by these investigations. A more detailed review of the time-domain spectroscopy using super-continuum radiation and its applications is given in [15].

In the work presented in this paper, these previous investigations are extended by using a simpler and more compact microchip nanosecond pulse Q-switched laser with a repetition rate in the kHz range, rather than a more complicated mode-locked picoscond-pulse laser. This Q-switched laser has been used for generation of supercontinuum radiation in a photonic crystal fiber, subsequent wavelength-to-time stretching in a dispersive single-mode fiber, and a high acquisition rate recording of absorption spectra of a gas medium. One advantage of this approach is a simpler arrangement of the wavelength-swept source based on a nanosecond-pulse laser, as there is no need to use a pulse-picker in order to increase the time interval between the light pulses to avoid temporal and thus, spectral overlapping and which would limit the achievable spectral resolution. Since a ns pulse with a higher pulse energy compared to ps pulses provides also a high spectral power density of the generated broadband radiation, there is additionally the advantage that DSMFs with higher values of dispersion can be used. Thus, the spectral resolution is enhanced which is limited in this case by the fiber losses. The aim of the present work was to assemble a Q-switched Nd:YAG laser based wavelength-swept system for millisecond scale real-time absorption spectroscopy in the near-IR range, to characterize it and to show its potentials and possible limitations. The system operational stability is demonstrated and the spectral resolution for the time resolved recording of absorption spectra from gas mixtures contained in a gas cell is evaluated. Algorithms of molar species concentration retrieval from spectra with non-overlapping bands of gas mixture components are developed and tested, and the uncertainties of the derived values due to spectral pulse-to-pulse fluctuations of the supercontinuum light source are investigated.

2. Experimental

The scheme of the spectrometer is shown in Fig. 1 . A τ = 2 ns pulse of 1064 nm radiation from a microchip Q-switched Nd:YAG laser with 25 kHz repetition rate (Fig. 1, pos. 1), is focused into a few tens of meters length of a single-mode PCF (SuperK Compact broadband source, NKT Photonics). There radiation in a broad spectral range specified to span from 450 nm to 1750 nm (supercontinuum) is generated within 2 ns in a quasi-CW regime [10,11] (Fig. 1, pos. 2). The average power of the supercontinuum is measured (Fig. 1, pos. 2) to be about 110 mW, which at a repetition rate of 25 kHz corresponds to 4.4 μJ/pulse.

 

Fig. 1 (a) Scheme of the spectrometer. (b) Optical spectrum and optical power over time at different points in the set-up.

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In order to transfer different spectral components of the supercontinuum into the time domain – to enable subsequent spectroscopic measurements using a fast photo-detector – the 2 ns light pulse from the PCF is guided through a fiber coupler into a 25 km long dispersive single-mode fiber with a total dispersion of D = 500 ps/nm and an attenuation of 0.19 dB/km at 1550 nm. The efficiency of mode coupling between the PCF and the DSMF is not exceeding 10% because of the difference in mode-field diameters, which results in a small value of the overlap integral. At the output of the DSMF the radiation is wavelength-swept over a time interval of about 140 ns (Fig. 1, pos. 3). It is collimated by a free-space fiber coupler using an aspheric lens and is passed through a long-wavelength transmitting interference filter with a cut-off wavelength of 1350 nm in order to avoid ambiguous temporal overlap of different wavelengths around the DSMF zero-dispersion wavelength (ZDW) at 1310 nm. As a result, the light source covers a broad spectral range from 1390 nm to 1740 nm, having a spectral width in wavenumbers of Δ ≈1450 cm⁻¹ (Fig. 1, pos. 4). The upper boundary is limited by increasing optical losses over wavelength in the DSMF.

A beam-splitter is used to divide the broadband radiation into two beams, one directed to the signal channel, with a gas-filled cell of 247 cm absorption length, and the other used as a reference beam. The wavelength dependence of the splitting ratio of the beam-splitter is taken into account and corrected by conducting calibration measurements with an evacuated gas cell. Thus, an almost flat base-line has been achieved.

Temporally-resolved data acquisition of the instantaneous power of the 140 ns wavelength-swept light pulses - one transmitted through the gas cell in the signal channel (Fig. 1, pos. 5) and the other reflected by the beamsplitter to the reference channel - is performed using two identical fast InGaAs photo-detectors (Electro-Optics Technology, EOT-3500 PIN photodiode, 10 GHz electrical band width and rise time <35 ps, spectral range 1000-1650 nm) and a fast digital oscilloscope (Tektronix, DPO 7254, 2.5 GHz bandwidth, up to 20 GS/s sampling rate with two channels used). The broadband radiation is focused onto a lens integrated with the photo-detector by a 250 mm focal length objective, achromatic in NIR. To minimize the influence of the oscilloscope quantization errors during the data processing the amplitudes of the waveforms are adjusted by using an iris diaphragm to have similar values in both channels. The spectral data are recorded in a single-pulse mode. The oscilloscope is triggered by the rising edge of the reference pulse. The trigger time jitter in the two channels has been measured to be of the order of 0.1 ns. Hence, averaging of subsequent waveforms can be performed to reduce the pulse-to-pulse noise of the recorded spectra without decrease of spectral resolution. The data from the oscilloscope is transferred to a portable computer, where further data processing is accomplished using a specially developed algorithm.

The spectral resolution of the spectrometer was estimated by measuring the pulse duration of a monochromatic component of the supercontinuum radiation at the output of the DSMF (Fig. 1, pos. 3). This monochromatic light was obtained when the supercontinuum radiation was reflected from a narrowband fiber Bragg-grating with a spectral width of 50 pm (or 0.2 cm⁻¹) at 1535 nm. The temporal shape of the reflected pulse was recorded using the oscilloscope at 40 GS/s sampling rate, and its width (FWHM) was measured to be τ_m = 0.21 ± 0.04 ns. The value of τ_m defines the limit of the spectral resolution (the width of the instrumental function) of the spectrometer estimated as δν ≈τ_m/D ≈1.8 cm⁻¹ at 1550 nm.

3. Absorption measurements

Broadband absorption spectroscopy measurements have been performed in a gas cell with pure CO₂ and CH₄, and with mixtures of these gases with N₂ at ambient temperature (293 K). Figure 2a shows an example of the reference I_r(t) and the signal I_s(t-t₀) intensity waveforms, averaged over 100 pulses. Here, t is the time delay related to the trigger time, and the parameter t₀ accounts for the delay between the two light pulses coming to the two different photo-detectors. This delay has been measured as a first step of the system calibration procedure (t₀ ≈9.4 ns). The signal waveform is obtained in a 0.42:0.21:0.37 CO₂:CH₄:N₂ mixture at 1 bar. Weak vibrational overtone and combinational absorption bands at 1425-1440 nm and 1560-1615 nm (CO₂), and 1620-1740 nm (CH₄) can be distinguished, rotational components of the CH₄ bands being partially resolved. An H₂O absorption band with a peak at 1405 nm appears in both waveforms due to a small amount of water vapor present in the parts of the optical paths through the open air.

 

Fig. 2a Reference, I_r(t), and signal, I_s(t-t₀), waveforms averaged over 100 pulses. The signal waveform contains some weak CO₂ and CH₄ absorption bands on its envelope. Both waveforms show absorption lines of H₂O present in the open air.

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Without an absorption in the gas cell, the differences in the envelopes of the signal and reference waveforms as seen in Fig. 2 are resulting from a considerable wavelength dependence of both the beam-splitter reflection/transmission coefficient and of the focusing efficiency onto the 32 µm diameter sensitive area of the PIN photodiodes. This difference can be described by a characteristic transfer function ε(t) which was determined at a second step of the calibration procedure as the ratio of the two waveforms, each averaged over a large number (800) of subsequent single-pulse measurements with an evacuated cell: $\epsilon (t)=〈{\tilde{I}}_s(t-t_0)〉/〈I_r(t)〉$, where the angular brackets denote averaging and ${\tilde{I}}_s(t-t_0)$ denotes the signal waveform in this case.

For a conversion of the recorded time delay into a wavenumber or wavelength scale, 30 spectral absorption lines with well-known reference wavelengths from the HITRAN database [16] were identified. The calibration curves ν(t) as well as λ(t) have then been obtained by fitting a third-order polynomial function to map these reference wavelengths to the respective points in the time-domain. Alternatively, a more accurate approach for time-to-wavelength calibration employing a thin air-spaced Fabry-Perot etalon could be used as it has been described in detail in [17].

If it is assumed for simplicity at first that the width of the spectrometer instrumental function in time (or frequency) domain is negligible, then the relation between thecorresponding signal and reference waveforms can be written as:

The absorption cross sections are calculated at a given total mixture pressure and absorbing species partial pressures using pressure-broadened Lorentzian line-shapes.

The transmission spectrum T_exp(t) of the gas in the cell can then be calculated, at the time delay scale t, as:

A part of a transmission spectrum recorded in the 0.42:0.21:0.37 CO₂:CH₄:N₂ mixture at 1 bar is presented in Fig. 3 as an example of a spectrum with non-overlapping absorption bands. Averaging over 800 pulses, or 32 ms, has been applied. The time delays have been converted into wavenumbers using the calibration curve presented in Fig. 2b . The transitions to the overtone and combinational vibrational states of CH₄ (the tetradecad, P₄) - in the range of 5800-6200 cm⁻¹, and of CO₂ - in the range of 6200-6400 cm⁻¹, are clearly noticeable. The observed absorption bands of CH₄ contain the strong narrow Q-branch at about 6005 cm⁻¹, and the resolved rotational components of the wide-spread P- and R-branches of 2ν ₃ transitions, as well as some unresolved features of ν ₂ + ν ₄ + ν ₃ transitions, with the sharp peak at 5873 cm⁻¹, and ν ₁ + ν ₃ transitions around 5820 cm⁻¹. Narrower and significantly weaker absorption bands of CO₂, corresponding to P- and R-branches of the transitions to the ν ₁ + 4ν ₂ + ν ₃ and 2ν ₁ + 2ν ₂ + ν ₃ (or 30013 and 30012 in notation of [16]) states at 6230 cm⁻¹ and 6350 cm⁻¹, respectively, with more dense rotational structure, appear as unresolved features. The noise of the spectrum at the applied high degree of averaging is quite low, except the noise in the initial range of 5800-5850 cm⁻¹. There, higher noise level is accounted for by the relatively small values of both reference and signal waveform amplitudes at the corresponding time delays (140-150 ns, see Figs. 2a and 2b). The presence of well-resolved rotational components of the 2ν ₃ band of CH₄, separated by about 2B ≈10 cm⁻¹ in P- and R-branches (B is the rotational constant), confirms the given above estimate of the achieved spectral resolution (approximately, 1.8 cm⁻¹).

 

Fig. 3 Calculated and measured (800 pulses averaged) spectra of CH₄ and CO₂ absorption bands. The calculated spectrum was convolved with a Gaussian instrumental function of 2.1 cm⁻¹ width.

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Fig. 2b Calibration function to convert time delays into wavenumbers and wavelengths.

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The experimental spectra can be compared with those calculated using center wavenumbers and intensities of the absorption lines, as well as pressure broadening and line shift coefficients provided by the HITRAN database. An appropriate calculation-fitting procedure has to be used in the analysis. If such spectra are recorded in a suitable broad range with an adequate spectral resolution, one can also evaluate parameters like gas temperature and pressure, especially if the species concentrations are known. An important role in this case plays the convolution of the calculated spectrum with the instrumental function of the spectrometer [18]. Therefore, the theoretically calculated transmission spectrum has been convolved with an approximated instrument function. First, the ideal transmission spectrum $T(\nu )=\exp (-k\cdot {\displaystyle \sum _i{c}_i\cdot {\sigma }_i{}^{calc}(\nu )})$has been calculated with known values of concentrations c_i, where the absorption cross section per molecule σ_i^calc(ν) has been computed by summation over all Lorentzian profiles of the rovibrational lines at the given total gas pressure. Then T(ν) has been convolved with an assumed Gaussian instrumental function providing a function

T_conv(ν) with the best similarity to the experimental observed data. The width of this best-fit Gaussian instrumental function was found to be 2.1 cm⁻¹ (FWHM), in good agreement with the previously estimated spectral resolution. This value characterizes the actual spectral resolution of the spectrometer.

This theoretically obtained transmission spectrum of the CO₂:CH₄:N₂ mixture is compared with the experimental data in Fig. 3, while their difference (residuum) is plotted in the lower part of the figure. The general agreement of measurement and theory is reasonably good. The noticeable difference in the amplitudes of the narrow Q-branches in the calculated and experimental spectra of the CH₄ band, with the similarity of the amplitudes of the P- and R-branches components, might be due to the fact that the collisional line-mixing effect [19,20] has not been taken into account in the calculation. This effect depends on the specific distribution of transition frequencies in a rovibrational spectrum and on the rate of rotationally inelastic collisions within a single vibrational state at a given molecular number density, as well as gas temperature, and may significantly influence the shape of observed spectral features, especially, that of narrow Q-branches. Hence, neglecting the line-mixing effect sets definite limitations on employing the simplified treatment of the absorption spectra while deriving species concentrations. Another reason for the mentioned difference in the calculated and experimental Q-branch amplitudes might be overestimated values of the pressure broadening coefficients for the components of the Q-branch, given in the HITRAN database employed. Some first estimates show that a 35% reduction of the Q-branch width due to these effects would be sufficient to result in the respective correction of the calculated Q-branch amplitude after it is convolved with the spectrometer instrumental function of 2.1 cm⁻¹ width.

The spectrum of this CO₂:CH₄:N₂ mixture with known composition has been used for testing the evaluation of CH₄ and CO₂ concentrations. The concentrations were found by least-squares (LSQ) fitting of the experimental spectrum T_exp(t), integrated for reduction of the noise contribution over a definite time delay interval (or the respective spectral range), to the corresponding integral of the spectrum T_conv(ν). The latter is a convolution of T(ν), calculated using the HITRAN database, and the instrumental function as described above. Conversion of wavenumbers to time delays t was performed using the calibration curve presented in Fig. 2b. The LSQ fitting was accomplished by minimizing the functional F:

The accuracy of the determined concentrations is affected by the number of pairs of waveforms used for averaging, which is directly related to the signal-to-noise ratio (SNR). The spectrum acquisition time, at a given laser pulse repetition rate (25 kHz), is also defined by the number of averaged pulses. Hence, the concentration measurement rate is limited by an SNR value which ensures quantitative measurements with a desirable accuracy: the rate decreases with the number of averaging of the consecutive waveforms, while at the same time the SNR grows. Thus, in the case of weak bands like those of the CO₂ spectra in the range of 6200-6400 cm⁻¹ (see Fig. 3), one has to find a tradeoff between the accuracy and the rate of the measurements. The SNR was calculated as a ratio of the integral of (1 - T_exp(ν)) over the respective transmission band, normalized by the width of this band, to the integral of the standard deviation of (1 - T_exp(ν)) values in a closely allocated spectral interval with zero absorption, weighted by the interval width. For instance, for the R-branch of the 2ν ₃ overtone band of CH₄ the SNR is calculated to be equal to 4.52 at 0.8 ms acquisition time (i.e., averaging over 20 pulses). As a comparison, for the R-branch of the 2ν ₁ + 2ν ₂ + ν ₃ combinational band of CO₂ the SNR equals to 0.26 and 5.62 at the acquisition times of 0.8 ms and 30 ms (750 pulses averaged), respectively.

The least-squares fitting procedure allowed to evaluate the decrease of the magnitudes of the relative error of derived CH₄ and CO₂ concentrations and their standard deviations as a function of the spectrum acquisition time, or the number of averaged pulses, using long sequences of single-pulse measurements. The results, presented in Fig. 4 , show that for CH₄ concentrations the relative error becomes reasonably small already at sub-millisecond acquisition times (see Fig. 4). On the contrary, for CO₂, with significantly weaker absorption bands in the selected spectral range, the appropriate acquisition times are exceeding sub-millisecond values, being of the order of a few tens of ms (Fig. 4). In particular, the relative errors reach a 5% level at the acquisition time of around 1 ms for CH₄, and 30 ms for CO₂. It is worth noting that at acquisition times larger than 40-50 ms systematic errors in species concentration retrieval may appear because of, e.g., drifts of the transfer function ε(t), due to slow variations of the difference in the background absorption in the optical paths of the signal and reference channels in open air and/or of the parameters of spectral and spatial distributions of the supercontinuum radiation in the employed wavelength range. Changes in the homogeneity of the mixture composition along the large distance inside the gas cell may also result in the systematic errors. This point becomes especially important and should be taken into account in case of species which provide weaker absorption.

 

Fig. 4 Dependence of the accuracy of species concentration retrievals as a function of the spectrum acquisition time.

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4. Conclusion

The application of a wavelength-swept source of coherent radiation for a time-domain millisecond scale real-time absorption spectroscopy in the near-infrared range has been investigated. The spectrometric system, based on a compact nanosecond-pulse 25 kHz repetition rate Q-switched Nd:YAG laser, a photonic crystal fiber for supercontinuum generation and a dispersive single-mode fiber for wavelength-to-time conversion, with temporally-resolved detection of the transmitted light pulses, has been assembled. This system has demonstrated satisfactory operation stability and has been successfully applied to high measurement rate broadband absorption spectroscopy of gases in the range of 5750-7200 cm⁻¹ with a spectral resolution of about 2 cm⁻¹.

As an example, weak overtone and combinational vibrational spectra of CH₄ with partly resolved rotational structure, and spectra of CO₂ with unresolved features recorded in gas mixtures of CO₂:CH₄:N₂ have been used. It was shown that the quality of spectral information obtained is sufficient to derive concentrations of mixture components with non-overlapped spectral bands employing the proposed algorithms of data processing. At an appropriate signal averaging the relative error of the retrieved molar concentrations of the different species can reach 5% (at absolute volume concentrations of 20% to 40%). This error is mainly defined by the uncorrelated noise of the two photo-detectors and the intrinsic noise and pulse-to-pulse fluctuations of the spectral power density of the particular nanosecond super-continuum radiation source. This noise also limits the temporal resolution to some ms, as averaging over many pulses is required.

It should be also noted that the spectral data are accurate enough to observe the manifestations of the collisional line-mixing effects in the recorded spectra. Further improvements of the data treatment procedure, providing higher accuracy of concentration retrieval, can be achieved by taking into account the influence of these effects on the spectral shape by, e.g., including models of the relaxation matrix formalism into spectra calculation procedure.