1. Introduction

For the investigation and characterization of technical combustion systems such as internal combustion (IC) engines, gas turbines or industrial furnaces it is essential to measure scalar quantities like temperature and species concentrations with high temporal resolution, i.e., in the order of tens of microseconds for IC engines [1]. To that end measurement techniques based on near-infrared (NIR) diode laser absorption spectroscopy have often been used to infer species concentration and temperature from the intensity and shape of molecular absorption lines [2–8]. Tunable diode lasers offer the possibility of fast wavelength tuning over a small bandwidth, which is sufficient to cover single spectral lines of many molecules of interest for combustion process diagnostics (e.g., H₂O, CO₂, CO, C₂H₂, CH₄). Since tuning bandwidth is limited [1] and related to the temporal resolution [9] as well as spectral information, pressure induced line broadening and shifting often limit the range of these sensors [8]. The fact that simultaneous multi-species and temperature measurements require at least two different diode lasers complicates the experimental setup and data acquisition.

A novel and highly attractive alternative light source for spectroscopic applications is supercontinuum (SC) radiation [10] since, in short, the more spectral information is obtained the more accurate determination of the desired physical quantities becomes feasible [1]. SC light is generated by launching short, intense, and spectrally narrow light pulses of a pump laser into a nonlinear medium [11]. Through the interplay of various nonlinear optical effects, directed radiation with high brightness is generated, covering a wide spectral range from the ultraviolet, near-infrared up to the mid-infrared [12–16]. Typically combinations of passive mode-locked fiber lasers with repetition rates in the MHz regime and highly nonlinear waveguides, such as photonic crystal fibers (PCF) are used [1, 9, 17–19]. For ps- and ns-pump sources the nonlinear spectral broadening of the pump pulse is dominated by four-wave mixing, stimulated Raman and Brillouin scattering [20]. In other spectroscopic applications standard single mode fibers (SMF) are used for SC generation instead of PCFs [21–24]. Employing a strongly dispersive fiber, for example within a dispersion compensating module (DCM) for optical communication systems, the SC pulses can be dispersed into wavelength sweeps due to the group-velocity dispersion of the different spectral components. This offers the possibility of time-domain based broadband spectroscopy by detection of the dispersed SC pulses with a high bandwidth photodiode and oscilloscope. Wavelength sweeps lasting several hundreds of ns ranging from about 1100 nm to 1700 nm facilitate high-speed multi-species optical sensing at atmospheric conditions [1, 9, 17–19, 22–24]. The capability of SC spectroscopy for minor species (e.g., NO₂, NO₃) detection in the atmosphere by a cavity enhanced approach was presented in [25–28]. A spectral resolution sufficient to resolve individual absorption lines was achieved by using fast detection equipment and highly dispersive fibers [1, 17, 18, 22–24].

In this work the feasibility of SC absorption spectroscopy for quantitative temperature measurements is presented for the first time to the best of the authors’ knowledge. The detection of the broadband absorption spectrum and hence multiple absorption transitions offers the possibility to determine the temperature from the ratio of at least two absorption features, exhibiting a different temperature sensitivity according to Boltzmann statistics, which describes the population of energy levels as a function of temperature.

Another approach is to fit a broad span of the theoretical to the experimental spectrum as shown elsewhere [29]. In this case the species concentration has to be known and the computing time will increase significantly. Since the presented SC absorption spectroscopy investigation targets the design of a real-time sensor, the calculation of the peak ratio is superior regarding the computing time efficiency.

Water is the ideal species for absorption-based temperature measurements since it is a major combustion product of hydrocarbons, is ubiquitous in the environment and shows distinct absorption features in the NIR. Absorption based thermometry was shown for a multiplexed diode laser system in [6, 30]. In this paper, temperature and multi-species measurements were carried out in a high-temperature flow cell at a pressure of 0.22 MPa for a temperature range from 450 K to 750 K. The temperature information is obtained from the peak ratio of the absorption features at 7339.83 cm⁻¹ to 7047.68 cm⁻¹ corresponding to wavelengths of 1362.42 nm and 1418.91 nm. These transitions have been chosen to guarantee significantly different lower state energies E”, since the relative sensitivity of the peak ratio to temperature is proportional to the lower state energy difference of the two transitions [6, 30].

Water was vaporized and injected in a heated gas stream of air and carbon dioxide. The evaluated intensity ratios are compared with theoretical calculations based on current HiTran2008 data [31]. This feasibility study was performed with the aim to investigate the exhaust gas recirculation in SI engines in future experiments. Furthermore, a comparatively cheap passively Q-switched ns-based SC source was compared to the employed mode-locked ps-pumped SC source regarding their applicability for time-domain based SC absorption measurements. In general, the ns-pumped system features higher spectral power densities per pulse compared to the ps-system because of the lower repetition rate of 25 kHz [19]. However, the achievable spectral resolution must be also considered, which in turn influences the signal-to-noise ratio. Accordingly, both effects have to be balanced against each other.

2. Instrumentation

The experimental configuration used for SC high-speed multi-species and temperature measurements in a flow cell is depicted in Fig. 1.

 

Fig. 1 Supercontinuum absorption spectroscopy setup for temperature and multi-species measurements (PCF: photonic crystal fiber; DC: dichroic mirror; DCM: dispersion compensation module; AC: achromatic collimator; M: mirror; AL: achromatic lens; PD: photodiode; Osc: oscilloscope).

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The supercontinuum radiation of the ns-pumped system (SuperK COMPACT, NKT Photonics) with a total average output power of 100 mW in regard to the entire spectral span was generated by focusing a 2 ns pulse at 1064 nm from a microchip Q-switched Nd:YAG laser with a repetition rate of 25 kHz into a single-mode photonic crystal fiber with a length of few tens of meters. The corresponding SC radiation ranges from 450 nm to 1750 nm.

The employed ps light source (SuperK EXTREME EXR-15, NKT Photonics) generates SC radiation by launching pulses with a duration of 5 ps, centered around 1064 nm, into a PCF. The repetition rate was reduced by an opto-acoustic pulse picker from initially 80 MHz to 2.136 MHz to ensure that consecutive dispersed SC pulses do not overlap by dispersion in the subsequent DCM. The spectrally broad output of the SC source (480 nm to 2400 nm) was split into its short- (600–1100 nm) and long-wavelength (1280–2400nm) component by a dichroic mirror. Due to the employed split box and lowered repetition rate the initial output power of the ps SC source was reduced from 6 W to 160.2 mW for the long-wavelength component. This NIR part was then dispersed employing a DCM (Lucent Technologies), containing a 6 km long dispersive fiber featuring a zero dispersion wavelength above 1700 nm and a total negative dispersion of −668 ps/nm at 1550 nm. The dispersion in the absorption region of water was calculated by a polynomial fit of the absorption features in the time-domain to the theoretical ones in the frequency-domain. By this method the dispersion was determined as −479 ps/nm at 1430 nm and −390 ps/nm at 1330 nm, respectively, which is in good agreement with typical dispersion properties of dispersion-compensating fibers given in [32].

The resulting output from the DCM is a rapid wavelength scan, which sweeps from around 1300 nm to 1700 nm within a time span of approximately 250 ns. The coverage of the spectral region is limited by the optical attenuation characteristics of the dispersive fiber. The time-averaged power was up to 1.3 mW over the entire residual spectral range, resulting in a single pulse energy of 0.6 nJ. The dispersed SC beam was then collimated with an achromatic fiber port collimator (Thorlabs, NA: 0.22) and passed through the flow cell using a 3-step multi-pass setup composed of two broadband dielectric mirrors extending the total absorption pathlength to 30 cm.The pathlength was mainly limited by the interfering absorption of the employed fused silica windows with a thickness of 12 mm, featuring an OH content of 240 ppm. Therefore, the signal decreases drastically around 1380 nm with an increasing number of passes. Additionally, back reflection from the window surfaces, diffuse reflection from the dielectric mirror surfaces ( $\frac{\lambda }{10}$) and beam steering effects influence the beam propagation in the measurement region. The optical accessible high-temperature flow cell allows the investigation of flows up to 3 MPa and 900 K. A detailed description of the flow cell can be found elsewhere [33]. Downstream the heating units of the flow cell a defined evaporated water mass flow was injected into the heated air and CO₂-flows, resulting in volume fractions of 2.4 vol.-%, 4.9 vol.-% and 7.3 vol.-%, respectively.

The dispersed SC pulses were focused by an achromatic collective lens and detected by a 10 GHz bandwidth photodiode (EOT, ET-3500) in combination with a 3 GHz, 20 GS/s oscilloscope (LeCroy, Wavepro 7300A). The power of the detected SC pulses was sufficient to over-saturate the photodiode. Therefore, the position of the photodiode in respect to the focal point of the prior achromatic lens was adjusted to achieve high signal strengths while preventing saturation. In this experiment, with a temporal resolution of around τ_det = 330 ps a spectral resolution of Δλ = 0.69 nm was achieved at 1430 nm and a lower resolution of Δλ = 0.85 nm at 1330 nm. Since the resolution is insufficient to resolve individual narrow absorption peaks due to the instrumental function of the detection system only blended absorption features were detected. However, the resolution is satisfactory to infer temperature information from the under-resolved absorption features in the presented temperature range.

Data processing

The original repetition rate of the SC source was reduced by an opto-acoustic pulse picker to 2.136 MHz. For each measurement a sequence of 2500 consecutive pulses were recorded in real time, resulting in a total measurement time of 1.17 ms. The single shot pulses were averaged to cancel out fluctuations in the spectral emission profiles of the SC source. For the averaged spectrum the signal-to-noise ratio (SNR) of the sensitive water absorption feature located at 1362.42 nm at a temperature of 443 K is 20. The acquisition scheme was also used to record reference signals, which was done at each measurement point without water injection. Thereby intensity differences in the spectral profile of the SC pulses cancel out. The absorption spectra were calculated according to the Lambert-Beer relation [8]

 

Fig. 2 SC absorption spectra for a ns- and ps-pumped SC source.

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Fig. 3 Influence of the spectral resolution on the peak ratio and precision of the temperature evaluation. Extract of theoretical absorption spectra with different resolutions for a temperature of 443 K (left) and the relative standard deviations of 32 calculated peak ratios (1362.42 nm/1418.91 nm) as function of the spectral resolution (right).

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The data processing for temperature evaluation used in this study was carried out according to the following consecutive steps: 1. Acquisition of experimental spectra and normalization; 2. Calculation of theoretical spectra at experimental conditions; 3. Determination of the filter function; 4. Convolution of theoretical spectra with the filter function and normalization; 5. Comparison of experimental and theoretical peak ratios.

3. Results & discussion

Figure 2 shows two SC absorption spectra for the ns-pumped [19] and ps SC source for a water volume fraction of 4.9 vol.-%, both averaged over 2500 consecutive single pulses.

The spectral resolution Δλ of a dispersion-swept SC spectrometer is given by Δλ = τ_m/|D|, where D is the total group-velocity dispersion of the employed dispersive element [9]. τ_m is the temporal resolution of the setup, determined by the optical pulse-width of the light source or the response time of the detection system, consisting of photodiode and oscilloscope, respectively. With a limiting impulse response width of the oscilloscope of τ_det = 330 ps, in the case of the Q-switched SC ns source the spectral resolution is limited by its pulse width in the order of 1 ns. Here, most of the spectral components are present within the whole pulse duration. In contrast, the ps SC source used has a specified output pulse width of ∼600 ps. As typical for most ps SC sources, the output has a wavelength chirp itself so that the temporal width of small wavelength packets is much shorter, comparable to the pulse width of the seed laser [38]. In this case, the temporal response of the oscilloscope limits the resolution in our experiments with the ps SC source. Assuming an average dispersion of D = −435 ps/nm in the spectral region of interest a spectral resolution of Δλ = 0.76 nm is obtained with the ps-pumped source as compared to Δλ = 2.3 nm in the case of the ns system. The better resolution of the ps-pumped system in contrast to the ns-pumped system can clearly be seen in Fig. 2. Here, the peak amplitudes are 0.049 and 0.024 at 1362.42 nm and 1418.91 nm, respectively, for the ns-pumped source and 0.074 and 0.031 at 1362.42 nm and 1418.91 nm, respectively for the ps-pumped system. Accordingly, the ps-pumped source has been used for temperature and multi-species measurements further presented in this manuscript.

In Fig. 3 the influence of spectral resolution in regard to quantitative temperature evaluation from the peak ratio of two transition features is illustrated. In the left part of Fig. 3 excerpts of theoretical absorption spectra are plotted for various spectral resolutions ranging from 18 pm, which corresponds for instance to a slow but high-resolution optical spectrum analyzer (OSA) to 2.3 nm representing the resolution achieved with the ns-pumped SC source. Each spectrum represents the average of 32 simulated absorption spectra, each of which was superimposed by an arbitrary white Gaussian noise with a noise level comparable with noise of the averaged experimental spectra presented here. In Fig. 3 the blending of neighboring absorption transitions can be clearly seen, consequently the SNR decreases with lower spectral resolution. Furthermore, one can infer that the peak ratio of the individual and blended absorption features varies with the spectral resolution. The peak ratio of the selected transitions for temperature evaluation (1362.42 nm/1418.9 nm) increases with decreasing spectral resolution which can be explained with the intensity and distance of the neighboring absorptions lines. Next to the absorption line located at 1362.42 nm two other strong transition lines are located within the next 2 nm whereas the line at 1418.91 nm has a larger distance to its neighboring transitions which are comparatively weaker as well. As a consequence, the peak intensity of the transition at 1418.91 nm is more affected by smoothing the spectrum with a filter function. Hence, for the temperature evaluation by peak ratios the spectral resolution of the setup needs to be characterized.

In the right part of Fig. 3 the relative standard deviation (rel. std. dev.) of the peak ratio is plotted for the different spectral resolutions investigated. The relative standard deviation was determined from the peak ratios of 32 individual spectra for each spectral resolution. It can be clearly seen that the relative standard deviation decreases with enhanced spectral resolution which is equivalent to a higher precision of the measurements. However, the effect declines towards higher resolutions. It can be seen that with the ps source employed, the relative standard deviation of the peak ratio decreases significantly compared to the ns setup. A further improvement is favorable and could be achieved with a longer dispersive ber and a faster detection equipment, which is, however, associated with higher costs. The spectral resolution is of particular importance for high-speed or even single-shot applications, where noise cannot be decreased by averaging a large number of spectra. In this case the spectral resolution, hence the SNR influences the precision of the measurement technique.

Figure 4 illustrates the experimental (top) and theoretical (bottom) normalized absorption spectra of water in a CO₂-flow at 633 K and 0.22 MPa and a volume concentration of water of 4.9 vol.-%.

 

Fig. 4 Experimental (top) and theoretical (bottom) normalized absorption spectra for 633 K.

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In addition, the residual which is defined as difference between experimental values and theory is plotted. The experimental spectrum is the average of 2500 consecutively recorded spectra at a repetition rate of 2.316 MHz. For the calculation of the theoretical spectrum, the different broadening coefficients of air and CO₂ have not been taken into account for simplicity. The theoretical spectrum was convolved with a Gaussian filter representing the instrumental function of the detection system which allows the direct comparison of both spectra [23]. The real apparatus function of the detection system is a complex shaped function which can typically not be expressed by a Gaussian, Lorentzian or Voigt profile. A possibility for its determination is the analysis of ultra short fs pulses with the detection setup used and measure the resulting response function [1], which was not carried out in this feasibility study. However, if the full width half maximum (FWHM) of the surrogate function is sufficiently small and is comparable to the FWHM of the true filter function, a very good match to theory is achieved by convolving the experimental data with the Gaussian surrogate function. The filter parameters were determined by matching the spectral resolutions of the experimental and theoretical spectra.

Figure 4 evidences that the theoretical convolved spectrum is in good agreement with the experimental one in the wavelength span of interest from 1360 nm to 1430 nm. First significant discrepancies appear in the region below 1350 nm, which can be attributed to a decreasing dispersion. However, this region is not consulted for the evaluation of the temperature depending intensity ratio used in this study. The labeled peaks are well represented by the theoretical spectrum regarding their line shape and intensity. The blended absorption feature of CO₂ at 1431 nm is also distinctive comprising the under-resolved 3ν₃ overtone bands. Figure 4 shows that SC absorption spectroscopy is applicable for multi-species detection at a detection rate as high as 2.136 MHz in a heated flow cell at a pressure of 0.22 MPa. For the investigation of exhaust gas recirculation, multi-species and temperature measurements comprising the majority species water and CO₂ are of special relevance.

To show the ability of SC absorption spectroscopy for quantitative temperature evaluation, the measurements were carried out in an air flow to guarantee comparability with the theoretical calculations based on HiTran data which is exclusively for air. Figure 5 shows the experimental (top) and theoretical (bottom) normalized absorption spectra for 763 K with a volume concentration of water of 4.9 vol.-% (left) and 443 K (right) with a volume concentration of water of 2.4 vol.-% in the wavelength span of 1360 nm to 1366 nm and 1416 nm to 1430 nm. All spectra are normalized to the temperature insensitive peak at 1418.91 nm. For better comparison of the peak values from theory and experiment these are highlighted by vertical lines in Fig. 5. Additionally, the lines can be found in the residual plot.

 

Fig. 5 Extract (1360 nm to 1366 nm and 1416 nm to 1430 nm) of the experimental (top) and theoretical (bottom) normalized absorption spectra for 763 K (left) and 443 K (right).

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It is obvious that the intensity of the absorption features in the range from 1360 nm to 1366 nm decreases with increasing temperature. For the most pronounced line at 1362.42 nm the experimental and theoretical peak ratios are ∼2.9 at 443 K, whereas at a temperature of 763 K the intensity ratio is only ∼1.2. At both temperatures the experimental spectra match the theory. In Fig. 6 the experimental data (quadratic boxes) and a theoretical curve (solid line) representing the peak ratio with an increment of 5 K, calculated with HiTran data for the investigated temperature range, are shown.

 

Fig. 6 Experimental data points and theoretical curve obtained from the peak ratios at 1362.42 nm and 1418.91 nm.

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Additionally, the maximum error based on line strength uncertainty according to the error codes listed in the HiTran database is depicted as dashed lines, since the line strength is an important source of error regarding peak ratio evaluation. Other parameters listed and afflicted with high inaccuracy for the two lines are the temperature exponent of the air broadening coefficient and the pressure shift coefficient. Their influence was neglected due to the broad instrumental function and the insensitivity of the technique to pressure induced line shifting. For both lines an uncertainty of 5 % to 10 % is specified in the database [31]. The maximal error of 10 % for each line strength causes a maximum error of the peak ratio of about 14 % considering both line strength errors to be independent from each other and applying a Gaussian propagation of uncertainty.

The theoretical curve fits well with the experimental peak ratios. Based on the results of this study it may be stated that the uncertainties for the two lines listed in HiTran were not reproduced by the measurements and are considered to be exaggerative. In the feasibility study three different volume concentrations of water, namely 2.4 vol-%, 4.9 vol.-% and 7.3 vol.-% are probed at temperatures only ranging from 603 K to 763 K. The standard deviations of the peak ratios for the probed volume concentrations are represented by vertical error bars. As a consequence of condensation problems at the window surfaces for water volume concentrations higher than 2.4 vol-% no error bars can be shown occurring at cell temperatures below 603 K. The standard deviation comprises three individual data points, i.e., one for each water concentration at a given temperature while every data point is obtained from 2500 consecutive real-time spectra. In the theoretical assessment of temperature, the peak intensity ratio is independent of water concentration. In this study a higher water concentration has the effect that the peaks used for temperature evaluation are more pronounced and therefore a higher accuracy can be achieved. The average absolute deviation between the theoretical curve and the experimental data points is 17 K. Part of this deviation is due to the spatial temperature gradient in the flow cell, which is ±7 K at 663 K [33]. Since the present study is a proof-of-concept investigation the data processing procedure was not automated, accordingly only few data points were recorded.

In future experiments the accuracy of the technique can be improved by employing a setup with a higher spectral resolution using a longer dispersive fiber or faster detection equipment. In this regard, the calculation of two theoretical spectra with two different instrumental functions suggests that an increasing spectral resolution leads to a higher SNR and therefore higher accuracy.

The accuracy in the evaluation of the peak ratio decreases significantly at temperatures above 800 K where the theoretical curve shows an asymptotic behavior which is the result of the exponential decay related to the Boltzmann statistics. The presented concept is applicable for quantitative temperature measurements with SC absorption spectroscopy in the range from about 400 K to 800 K, which is sufficient for measurements of the exhaust gas recirculation rate of IC engines during suction and compression stroke. For the evaluation of higher temperatures, e.g., in flames, other absorption lines than those used in the this study with a different temperature dependence must be evaluated. A further increase in spectral resolution would allow for an improved evaluation of the spectral features. It would also make the selection form a larger number of lines possible facilitating the optimization of the sensitivity in different temperature ranges. Alternatively, the temperature information can be extracted from transitions of different species.

4. Conclusion

The presented paper demonstrates for the first time to the authors’ knowledge the capability of time-domain based SC absorption spectroscopy for quantitative temperature measurements. The temperature information is inferred in a range from 450 K to 800 K by evaluating the peak ratio of blended temperature sensitive and insensitive transition features in the ν₁ + ν₃ overtone bands of water located at 1362.42 nm and 1418.91 nm. The experimental results are in very good agreement with theoretical intensity ratios calculated from absorption spectra based on HiTran data. However, the HiTran values are afflicted with comparatively high uncertainties a comprehensive calibration of the measurement technique is intended. Additionally, the clear advantage of ps-pumped SC sources over ns-pumped SC sources for time-domain based SC spectroscopy due to the distinct pre-chirped pulse emitted by the ps-system has been shown. In combination with the ability for multi-species measurements at high detection rates the measurement technique offers unique possibilities for combustion research, e.g., for the investigation of the exhaust gas recirculation in IC engines. Furthermore, in addition to the NIR light part, the visible region can be used for simultaneous absorption measurements of O₂. Future studies will use the advantages of broadband spectroscopy at process conditions where pressure broadening and line shifting effects become significant. By improving the spectral resolution of the SC absorption technique, temperature and multi-species measurements at combustion conditions become accessible. In IC engines this technique, through its potential to record data at high detection rates, will then allow for temporally resolved measurements of temperature and species concentration within a cycle.