Ibrahim
Sadiek
a,
Tommi
Mikkonen
b,
Markku
Vainio
bc,
Juha
Toivonen
b and
Aleksandra
Foltynowicz
*a
aDepartment of Physics, Umeå University, 901 87, Umeå, Sweden. E-mail: aleksandra.foltynowicz@umu.se
bLaboratory of Photonics, Tampere University of Technology, Tampere, Finland
cDepartment of Chemistry, University of Helsinki, Finland
First published on 27th October 2018
We report the first photoacoustic detection scheme using an optical frequency comb—optical frequency comb photoacoustic spectroscopy (OFC-PAS). OFC-PAS combines the broad spectral coverage and the high resolution of OFCs with the small sample volume of cantilever-enhanced PA detection. In OFC-PAS, a Fourier transform spectrometer (FTS) is used to modulate the intensity of the exciting comb source at a frequency determined by its scanning speed. One of the FTS outputs is directed to the PA cell and the other is measured simultaneously with a photodiode and used to normalize the PA signal. The cantilever-enhanced PA detector operates in a non-resonant mode, enabling detection of a broadband frequency response. The broadband and the high-resolution capabilities of OFC-PAS are demonstrated by measuring the rovibrational spectra of the fundamental C–H stretch band of CH4, with no instrumental line shape distortions, at total pressures of 1000 mbar, 650 mbar, and 400 mbar. In this first demonstration, a spectral resolution two orders of magnitude better than previously reported with broadband PAS is obtained, limited by the pressure broadening. A limit of detection of 0.8 ppm of methane in N2 is accomplished in a single interferogram measurement (200 s measurement time, 1000 MHz spectral resolution, 1000 mbar total pressure) for an exciting power spectral density of 42 μW/cm−1. A normalized noise equivalent absorption of 8 × 10−10 W cm−1 Hz−1/2 is obtained, which is only a factor of three higher than the best reported with PAS based on continuous wave lasers. A wide dynamic range of up to four orders of magnitude and a very good linearity (limited by the Beer–Lambert law) over two orders of magnitude are realized. OFC-PAS extends the capability of optical sensors for multispecies trace gas analysis in small sample volumes with high resolution and selectivity.
Broadband detection of PA signals has so far been performed mostly with incoherent infrared radiators (e.g., lamps, blackbodies, etc.) modulated by conventional Fourier transform infrared (FT-IR) spectrometers.15,17 When broadband radiation is passing through a scanning Michelson interferometer, each wavenumber component, ν (in cm−1), is modulated at its characteristic Fourier frequency, f = V × ν (in Hz), where V is the optical path difference (OPD) scan velocity (in cm s−1). Absorption at each ν is manifested as an acoustic wave at the corresponding modulation frequency that can be measured with the microphone. First broadband FT-IR-PAS instruments used electret microphones and were not widely applied because of the low spectral irradiance of broadband IR sources and the low sensitivity of the microphones.12,13,15 The implementation of cantilever-enhanced detectors significantly increased the detection sensitivity and FT-IR-PAS setups with detection limits of methane of 1.5 ppm (3σ, 100 s, spectral resolution 4 cm−1),18 and 3 ppm (2σ, 168 s, spectral resolution 8 cm−1)15 have been reported. In a very recent demonstration, Mikkonen et al.19 used a supercontinuum (SC) light source for broadband cantilever-enhanced PA detection and reported a limit of detection for methane of 1.4 ppm (3σ, 50 s, spectral resolution 4 cm−1). Although the brightness of SC sources exceeds that of thermal emitters by orders of magnitude, the noise level is also increased, which is the reason for the relatively small improvement of the detection limit.
The spectral resolution of all broadband PAS demonstrations has so far been limited by the nominal resolution of the FT-IR spectrometer, given by the inverse of the maximum delay range.20 Conventional FT-IR spectrometers provide a resolution of 0.1 cm−1 (i.e., 3 GHz), and higher resolutions, up to 0.002 cm−1, have been achieved with large instruments (OPD = 4.5 m) and long measurement times (30 min).21 In addition, care has to be taken to select a proper apodization function in order to minimize the instrumental line shape (ILS) distortions. Using an optical frequency comb (OFC) as a light source for Fourier transform spectrometers (FTS), in the so-called comb-based FTS, allows much faster acquisition (of the order of seconds) of spectra with high signal-to-noise ratio (S/N),22 and resolution down to kHz range with no ILS contribution.23
Here, we report the first demonstration of photoacoustic spectroscopy using an optical frequency comb. We call the technique: optical frequency comb photoacoustic spectroscopy (OFC-PAS). OFC-PAS combines the wide spectral coverage and high resolution of comb-based FTS with the small sample volume and wide dynamic range of photoacoustic detection. In this first demonstration, we measured high resolution PA spectra of the fundamental C–H stretch band of methane, CH4, in nitrogen, N2, at different pressures, in good agreement with simulations based on the HITRAN database.24 Spectral resolution up to 400 MHz, limited by the pressure broadening and 75 times better than the best reported using a SC source (30 GHz),19 has been accomplished. These capabilities open up for new insights for high resolution multicomponent trace gas analysis in small sample volumes.
S(ν)PA = α(ν) × ϕ(SmCcellP(ν)η) | (1) |
The intensity of the measured PA signal at a given total pressure changes linearly with gas density under the assumption that (i) the density of the absorbing gas is relatively low, so that Beer–Lambert law is linear, (ii) the input laser power is not high, so that absorption saturation effects can be neglected, and (iii) the relaxation rate from absorbed energy to heat is much faster than the rate of heating/cooling of the gas sample. However, the measured signal is also proportional to the scaling factor, ϕ, which is a function of the sample pressure, composition, and temperature. Therefore, the measurement conditions of pressure and gas matrix have to be optimized to accomplish the highest S/N according to the application requirements (vide infra).
The output of the DROPO, after long-pass filter in order to block the remainder of the pump power, is coupled into a home-built fast-scanning FTS. A general schematic of the tilt-compensated interferometer is shown in Fig. 1 (dashed box). A stable cw reference diode laser (λref = 1563 nm) is also coupled to the FTS and is used for the calibration of the OPD. The two retro-reflectors, mounted back-to-back, provide easier alignment and larger OPD range compared to conventional interferometers with one moving mirror. The maximum OPD range is 2.8 m, corresponding to a nominal resolution of 0.0037 cm−1, or 110 MHz. The OPD is scanned at V = 0.16 cm s−1, which implies that the signal comb is modulated at Fourier frequencies in the 470–510 Hz range. Two out-of-phase intensity interferograms are constructed at the two outputs of the FTS, with total power of 31.5% of the input power (16.5% in one output and 15% in the other). One of the output beams is directed to a cantilever-enhanced photoacoustic cell, while the other is directly measured with a HgCdTe detector (VIGO System) and used for normalization of the PA signal. For a typical input power of 50 mW, 8 mW out of the FTS is guided to the PA cell, of which 4.8 mW and 3.2 mW are contained in the signal and idler combs, respectively.
The photoacoustic cell (Gasera, PA201) with a cantilever-enhanced detector is used. The output beam of the FTS has a diameter of 5 mm and the PA cell has an input inner diameter of 4 mm. Therefore, a focusing lens (f = 50 cm) was placed 25 cm in front of the PA cell to reduce the beam diameter to 2.5 mm. The PA cell is made of gold-coated aluminium with a length of 100 mm and a sample volume of 8 mL. A double-path configuration is implemented using a gold-coated mirror on the back side of the cell resulting in power spectral density of the signal comb of 42 μW/cm−1. The displacement of the cantilever as a result of pressure changes due to absorption is measured via an integrated spatial-type interferometer in the photoacoustic cell.13,16 The PA cell is also equipped with a vibrational noise damper to attenuate external acoustic noise.
Two mass flow controllers (Bronkhorst, F-201CV) and a pressure regulator (Bronkhorst, P-702CV) are used to flow the gas sample and regulate the pressure in the line leading to the PA cell. The PA cell has an internal pumping and gas exchange system that draws the sample from the supply line using micro pumps and automatic valve system. This gas supply system allows for changing the pressure inside the PA cell in the range between 300–1000 mbar. All measurements were performed at 23 °C, as controlled by the PA cell thermostat. The test gas methane (100 ± 10 ppm CH4 in N2, air liquide) was used. Pure N2 was available for flushing the cell and diluting the methane sample.
To obtain broadband OFC-PAS spectra, three interferograms are acquired simultaneously using a National Instruments hardware (PCI-6221, 250 kS/s, 16 bit) and home-written LabVIEW™ program: the PA and the comb interferograms, as well as the cw laser interferogram for OPD calibration. Afterwards, the PA and the comb interferograms are resampled at the zero-crossings and extrema of the cw laser interferogram using home-written MATLAB® program. The absolute value of the Fourier transform of the OPD-calibrated interferograms yields the frequency-calibrated PA spectrum and the comb intensity envelope. Finally, the PA spectrum is divided by the comb intensity envelope to yield a normalized PA spectrum. The spectra of the C–H stretch band of CH4 were measured at different working pressures of 1000 mbar, 650 mbar, and 400 mbar. At each pressure, the nominal resolution of the FTS was adjusted to yield 3 points per full width at half maximum (FWHM) of the methane lines, which resulted in a resolution of 1000 MHz, 650 MHz, and 400 MHz for the three pressures, respectively. The acquisition times of single interferograms with these resolutions were 200 s, 308 s, and 500 s, respectively.
We have observed that the entire C–H stretch band is imaged with a much smaller amplitude at the lower and higher frequency sides symmetrically around the band origin. Such “ghost” imaging might be caused by modulation of the intensity of the light source or sampling errors of the interferogram in the PA cell, since the cantilever displacement is measured interferometrically. These artefacts account for the slight intensity mismatch between the measurements and the simulations in the higher frequency side and the unassigned lines in the lower frequency side. It should also be noted that the normalization of the PA signal by the comb envelope may introduce a slight intensity mismatch with respect to the simulations due to the absorption of molecular species (mainly interfering water lines) in the non-common beam path.
Since the three measurements shown in Fig. 4 were performed with the same input laser power, PA cell, and gas matrix (i.e., P, Ccell and η are constants), the change of the scaling factor is a direct measure of the change of cantilever sensitivity with pressure, attributed to the so-called gas spring and the effective mass that depend on the pressure and the molecular mass of the gas.
Table 1 summarizes the scaling factors, signal and noise levels as well as the S/N observed at the three different pressures. The noise, σ(CH4), is estimated as the standard deviation of the baseline of the CH4 spectra around 3021 cm−1. We note that the noise in the presence of CH4 absorption is higher than the noise level measured with pure N2 in the PA cell [σ(N2), also listed in Table 1]. This difference might originate from the small structures that exist on the baseline of the CH4 measurements due to the aforementioned sampling problems. We also note that background noise measurements with light on and off yielded similar levels. The S/N is calculated as the ratio of the line-centre PA signal at 3016.5 cm−1 (SPA) and the standard deviation of the noise on the baseline around 3021 cm−1.
Pressure [mbar] | Resolution [MHz] | ϕ [V/cm−1] | S PA [mV] | σ(CH4) [mV] | σ(N2) [mV] | Measured S/N | F α | Expected S/N |
---|---|---|---|---|---|---|---|---|
a Line-centre PA signal at 3016.5 cm−1. b Normalized line-centre absorption coefficient. | ||||||||
1000 | 1000 | 10.5 | 42.8 | 0.43 | 0.23 | 100 | 1.0 | 100 |
650 | 650 | 9.20 | 31.6 | 0.61 | 0.32 | 52 | 0.85 | 69 |
400 | 400 | 15.0 | 41.2 | 0.74 | 0.52 | 56 | 0.69 | 44 |
In conventional FT-IR the S/N decreases with the square root of the increase of the resolution,26 assuming constant signal and white noise. The change of S/N must also account for the change of the line-centre absorption coefficient with pressure and number density. The line-centre absorption, also listed in Table 1, denoted by Fα and normalized to 1 at 1000 mbar, is estimated for the line at 3016.5 cm−1 using the HITRAN database.24 The last column of Table 1 shows the S/N expected in conventional FT-IR, taking into account the change of resolution and the line-centre absorption coefficient (assuming S/N of 100 at 1000 mbar). The discrepancy between the measured S/N and that predicted for conventional FT-IR is attributed to the fact that our PA measurements are not purely white noise limited, and that the cantilever signal and noise are enhanced by different factors when the pressure changes.
In general one can conclude that the fundamental trading rule of measurement time, resolution, and sensitivity of conventional FT-IR must be modified to include also the cantilever response and applied according to the application need. For example, high-resolution spectral measurements, which are essential for better selectivity and multicomponent analysis, would preferably be performed at the pressure of 400 mbar rather than 650 mbar, since there is an indication of higher cantilever sensitivity that compensates the decrease in S/N due to increased resolution and lower Fα.
We evaluated the attainable limit of detection (LOD) based on the S/N of the strongest methane line at 3058 cm−1 (see Fig. 3) measured at 1000 mbar, equal to 120. This corresponds to a detection limit of 0.8 ppm in 200 s for an exciting signal comb power spectral density of 42 μW/cm−1 in the absorption band of methane. Table 2 compares our LOD with that of previous FT-IR-PAS and the recent SC-PAS experiments using cantilever-enhanced detectors (all normalized to 1σ and 100 s measurement time). As shown in Table 2, the LOD is comparable for the three methods, while the resolution of OFC-PAS is more than two orders of magnitude better. Moreover, considering the lower power spectral density and the higher resolution of OFC-PAS compared to SC-PAS,19 the attainable LOD of OFC-PAS becomes about a factor of five better than that of SC-PAS.
We also evaluated the performance of the system in terms of the normalized noise equivalent absorption, , where αmin is the minimum detectable absorption, equal to 4.2 × 10−5 cm−1 at 1000 mbar, Psp.el. is the power per single spectral component, and t is the measurement time. At a resolution of 1000 MHz (0.033 cm−1), the power spectral density of 42 μW/cm−1 corresponds to Psp.el. of 1.4 μW. Considering the measurement time of 200 s, we obtained a NNEA of 8 × 10−10 W cm−1 Hz−1/2, which is comparable to values reported with PAS based on cw lasers in the range of 2.7 × 10−10 to 18 × 10−10 W cm−1 Hz−1/2.7,27 The very low NNEA obtained here confirms that the comb source is not causing significant noise contribution. Moreover, the capability of OFC-PAS to record spectra over thousands of elements simultaneously is not fully reflected in the definition of NNEA.
In the measurements presented in the current work, the nominal resolution of the FTS was higher than the repetition rate of the comb source, frep, and sufficient to record the absorption lines with negligible ILS distortion. If needed, spectral features narrower than frep can be measured with no ILS distortion using the method of comb-based FTS with sub-nominal resolution, in which interferograms with length matched precisely to c/frep are measured.23,28,29 OFC-PAS can also be realized using the dual-comb approach30–32 rather than the mechanical FTS. However, the main advantage of dual comb spectroscopy, i.e. the rapid data acquisition, cannot be utilized in OFC-PAS, since the frequency of the interferogram is limited by the cantilever response to the hundreds of Hz range.
The detection limit of OFC-PAS can be improved by several measures. First of all, a factor of 40 improvement can be expected using available high-power mid-IR OFC sources33 with an output power of up to 1.5 W, compared to 36 mW of the signal comb used in this work (assuming noise is not introduced). Secondly, using multi-line fitting routines instead of the single point S/N determination would decrease the uncertainty of the fitted concentration and yield improved LOD, where a factor of 11 improvement is expected for the C–H stretch band of methane addressed in our work.34 Using these two measures combined, a LOD of methane in the lower ppb range should be readily accomplished.
The high fidelity of the high-resolution broadband spectra measured with OFC-PAS holds the potential to extend the capability of optical spectrometers for multispecies trace gas analysis in very small sample volumes.
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