We report the first demonstration of a broadband trace gas sensor based on chirp-pulse terahertz spectroscopy. The advent of newly developed solid state sources and sensitive heterodyne detectors for the terahertz frequency range have made it possible to generate and detect precise arbitrary waveforms at THz frequencies with ultra-low phase noise. In order to maximize sensitivity, the sample gas is first polarized using sub-μs chirped THz pulses and the free inductive decays (FIDs) are then detected using a heterodyne receiver. This approach allows for a rapid broadband multi-component sensing with low parts in 109 (ppb) sensitivities and spectral frequency accuracy of <20 kHz in real-time. Such a system can be configured into a portable, easy to use, and relatively inexpensive sensing platform.
©2011 Optical Society of America
The terahertz frequency region has received increased attention recently as technological solutions have been found to overcome the challenges of generating and detecting THz radiation. Terahertz systems for imaging and spectroscopy for a number of applications are available commercially. Optical methods, utilizing photomixers to generate THz radiation at the difference frequency between two frequency-stabilized continuous-wave (cw) lasers or a femtosecond pulsed laser illuminating a non-linear device, are well established techniques. These laser based methods typically suffer from low output power and a complex experimental setup but have the significant advantage of broad tunability that typically extends over 3 THz. Alternatively, THz frequency generation based on amplification and multiplication chains (AMC) driven by microwave (MW) sources has become commercially available and has been shown to operate at frequencies up to about 2 THz with power ranging from mW to μW at the higher frequencies. AMC methods use robust solid state devices to generate THz radiation with extremely high frequency accuracy and phase stability due to the inherent precision of microwave sources. In addition to advances in source development, highly efficient room temperature heterodyne detectors (mixers) have also become available and cryogenic heterodyne systems have demonstrated performance near the quantum noise limit . Unlike power based detector systems, terahertz heterodyne systems are capable of detecting both amplitude and phase information of the field and thus are suitable for many applications where phase coherence plays a major role.
Spectroscopy in the (0.2 to 1) THz region is a highly sensitive technique for detecting the gas phase rotational spectrum of a vast number of small compounds that have permanent dipole moments. The terahertz region offers several distinct advantages: i) narrow spectral features for a wide range of species are accessible by the frequency coverage of a single source (50 GHz to 100 GHz of bandwidth), ii) complete selectivity is possible because of the small intrinsic spectral widths even in “noisy” or “dirty” environments, iii) optimal sensitivity is realized by probing near the peak of the thermal Boltzmann distribution, iv) absolute specificity is achieved since frequencies are traceable to the Rb atomic standard ( ±2 parts in 1010), and v) absorption signals reflect absolute concentration without need of instrument calibration factors. In particular, rotational spectroscopy is sensitive to molecular structure, and each molecule (even isotopically substituted molecules) has a unique rotational spectrum much like a finger print or bar code. For molecules with only a few heavy atoms, the spectral region at 0.5 THz is near the peak of the Boltzmann distribution at room temperature and therefore, is the most sensitive region for detection of rotational lines. Many of these simple molecules are key atmospheric species (N2O, H2O), volatile organic compounds (formaldehyde, methanol), or indicators of disease states (NO, acetone). For direct absorption studies, the resolution is Doppler limited at room temperature to (1 to 5) MHz at 500 GHz for small molecules because of the thermal velocity distribution. The clear sensitivity advantages together with recent technological advances in sources and receivers make this region well suited for developing an analytical instrument for trace gas analysis.
A number of spectroscopic sensing THz systems using different technologies have demonstrated trace gas detection of different components over the last decade or so [2–4]. Bigourd et. al.  reported a sensor based on photomixing techniques to detect and quantify small quantities of hydrogen cyanide, carbon monoxide, formaldehyde, and water. This work gives estimates of the detection limits for HCN, CO, H2CO, at 9 parts in 106 (ppm), 0.1% and 114 ppm respectively. Newer approaches with improved sensitivities include a broadband Fourier transform absorption spectrometer operating in the mid infrared region based on a frequency comb technique to cover the (63 to 111) THz frequency range at a comb teeth spacing of 136 MHz . The spectrometer was used to record the spectra and quantify the concentration of six gas phase molecules with concentrations ranging from (9 to 142) ppm with detection sensitivity better than 10 parts in 109 (ppb) for a 30 s integration time. Due to the large number of lines measured for each molecule, the relative uncertainty on the concentration measurement is remarkably low and the precision of the entire system is reported to be better than 0.2%. Another broadband spectroscopic sensor based on rotational signatures in the (210 to 270) GHz frequency range has been demonstrated as a quantitative analytical method for the detection of several small organic compounds . The spectrometer uses a heterodyne detection method to measure absorption signals at total pressures near 0.133 Pa (1 mTorr). The sensitivity of the spectrometer was shown to be on the order of tens of ppm in 20 seconds for each of 32 gases and was extrapolated down to a few ppbs for measurement times on the order of a minute for each gas in the mixture. In addition to improved sensitivity, chemical specificity and acquisition speed are also greatly improved relative to power detection schemes because of the phase coherence characteristics of the heterodyne technique.
The chirped-pulse THz spectrometer described in this work is an extension of methods recently developed in the microwave frequency range . Microwave spectrometers typically record an emission signal instead of direct absorption. Emission signals are obtained by applying a pulse of radiation (shorter than the dephasing time) to a gas sample and when the frequency of radiation is on-resonance, the microwave pulse induces a macroscopic polarization state in the sample. Coherent emission from the sample is recorded in zero background after the pulse. This process is termed free inductive decay (FID) and is similar to the detected signals in nuclear magnetic resonance (NMR) arising from the magnetic polarization of the sample. A cartoon depicting this process is shown in Fig. 1 . New techniques based on chirped-pulse microwave excitation and FID detection have been used to record a 12 GHz segment of the rotational spectrum between (6.5 and 18.5) GHz  during a single data acquisition step. These methods are shown to have the same sensitivity as the conventional cavity-enhanced frequency-scanning methods but with a factor of ≈50-fold improvement in acquisition speed (17 min vs. 14 h). The key advantages of this method are realized by rapidly recording phase coherent signals with as much bandwidth as possible and signal averaging the time domain waveforms to improve the signal-to-noise ratio. A significant advantage of chirped-pulse excitation is that the pulse duration is decoupled from the bandwidth. The use of a chirped pulse instead of a short transform-limited pulse effectively decreases the power requirements by a factor of 104 for species with a 3×10−30 C-m (1 Debye) dipole moment. The ultra-fast arbitrary function generators that operate at 12 GS/s (gigasamples per second) and large-memory high-speed oscilloscopes required for this spectrometer have only recently become commercially available.
Using the newly developed heterodyne terahertz technology, we have designed and constructed a novel chirped-pulse experimental spectrometer that is capable of generating and detecting precise arbitrary waveforms at THz frequencies with ultra-low phase noise. This approach allows for a rapid broadband multi-component gas sensor with low ppb sensitivities and spectral resolution of better than 20 kHz in real-time. The system is based on solid state sources to achieve rapid broadband detection in a portable and relatively inexpensive package.
2. Experimental setup
The experimental setup, shown in Fig. 2 , was used to generate chirped THz pulses and record both absorption and free induction decay (FID) signals in the (530 to 620) GHz spectral region with a bandwidth of 10 GHz. The chirped pulses were digitally generated in a 12 GS/s arbitrary waveform generator (AWG) (Tektronix, AWG7221C) . The AWG was programmed with a 25 ns long chirped pulse centered at 2.4 GHz that covers a bandwidth of 200 MHz. The initial and final 5 ns of the pulse were dampened to zero using a raised cosine function to minimize sinx/x modulation. The AWG signal was mixed with a microwave Synthesizer 1 at 9.075 GHz, filtered and then amplified before entering the ×48 amplifier multiplier chain (AMC) [8,9]. Filtering was achieved using a tunable bandpass yttrium iron garnet (YIG) filter to select only the upper sideband of the mixer output. The carrier and lower sideband were suppressed by approximately 40 dB. The output of the AMC was a chirped-pulse signal from (546 to 555.6) GHz. Any portion of the entire multiplier chain bandwidth from (530 to 620) GHz can easily be accessed by tuning the AWG and filter at a speed currently limited by the 1 GHz/ms sweep rate of the YIG filter. The THz chirped pulse was then coupled into 25 meter long absorption cell [10–12] and then into a sub-harmonic mixer AMC (Mix-AMC) for detection. The long path absorption cell (also known as a White cell ) is a scaled down version of the modified White cell design reported in . The Mix-AMC down-converted the signal with a fixed local oscillator (LO) set to 545.760 GHz (the frequency of Synthesizer 2 ×48) to produce an intermediate frequency (IF) signal from (0.2 to 9.8) GHz. The IF was amplified by 42 dB and digitized on the oscilloscope (LeCroy 8zi) at a sampling rate of 20 GS/s (2 times the Nyquist limit) for a duration of 500 μs (10 000 sample records). The 25 ns pulse was digitized and most of the remaining 475 ns of the interval was used to record the FID signals. The repetition rate of the waveform generator was set to 2 MHz.
A single data segment contained 80 million points or 8 000 individual records. The segment was transferred to a 3.3 GHz quad-processor computer in 3 s using a high speed serial interface card (360 MB/s) to give a sustained data throughput rate of 2 666 records/s. For real-time monitoring purposes, each data segment was signal averaged in the time domain and then fast Fourier transformed (FFT) to the frequency domain. The final data sets consisted of 80 000 records that were signal averaged over a 30 s interval, zero padded to 100 000 points and fast Fourier transformed (FFT). Only the time domain waveform consisting of 10 000 floating point numbers was saved to disk for later analysis. When compared to the time for minimal post-processing on the oscilloscope, this method gave a significant improvement in the total throughput (greater than 4-fold). It is further noted that the throughput rate is still nearly 750 times slower than the experimental repetition rate of the trigger source and is currently limited by the memory write speed of the oscilloscope.
A gas mixture containing five different components was made from premixed gas cylinders or from the pure vapor above liquid samples and mixed directly in the White cell. Table 1 lists the composition of the gas mixture as determined using a thermistor pressure sensor. The total pressure used for these measurements was 7.0 Pa (53 mTorr). Absorption signals were processed from the averaged time domain signals obtained with and without gas in the cell. A Tukey apodization function was first applied over segments at the edges of the interval (2% of the total interval). The time domain waveforms were Fourier transformed (FFT) over the full 500 ns sampled interval that included the 25 ns chirped pulse. The magnitude of the FFT waveform was calculated for the transmitted power through the cell with and without gas. The transmitted powers were obtained from the square magnitude of these signals and are shown in the upper panel of Fig. 3 . A portion of the direct absorption spectrum is shown in the lower panel. The spectrum was obtained by taking the log (base 10) of the ratio of these signals. The transmission spectra in the upper panel suffer from rapid variations in the transmitted power as a function of chirp frequency. These variations likely arise from imperfections in thelinear chirp waveform, power variations of the sources and detector across the chirped interval and standing wave patterns between the source and detector. Changes in the patterns between the sample and background scans are associated with phase shifts associated with dispersion of the gas and lead to baseline variations in the absorption spectrum that limit the sensitivity. Although efforts are underway to improve the sensitivity of this spectrometer for direct absorption by correcting for these phase shifts, the absorption features are sharp relative to the baseline variations and therefore, are easily distinguished.
The absorption spectrum is compared with spectral predictions from HITRAN database  for OCS, N2O, and methanol (MeOH) and with the JPL database  for ethanol (EtOH) and acetone (Ace). Since the HITRAN database contains the self- and air-pressure broadening, air-shift parameters and absorption coefficients, these three molecules were used to characterize the system. For these gases, gas concentrations were targeted to give fractional absorptions between 30% and 70% in order to obtain reliably direct absorption signals well above the baseline variations. OCS and N2O each have one strong feature in this region at 546.860 GHz and 552.487 GHz, respectively (we note the line frequency reported in HITRAN for N2O is in error by 3.1 MHz but accurately predicted in the JPL database). The absorption line widths for the three gases are in good agreement with HITRAN predictions (see insert in Fig. 3). Based on the integrated intensities, the calculated concentration by volume of OCS is 0.94(6) % (type B, k=1)  and that for N2O is 3.8(1) %. MeOH has a well-defined series of equally spaced strong lines across the 10 GHz region and provides for an assessment of the relative performance. The intensities are in very good agreement with the predictions and are of similar quality as those shown for the ≈1.3 GHz section in the lower panel of Fig. 3. However, the absorption based concentration is somewhat less than that measured during gas mixing. Since MeOH is a liquid and was the first vapor to be introduced, some decrease might be expected because of sample purity and/or cell wall absorption. The latter effect has been observed in previous water studies in our lab . Nevertheless, the absorption signal strengths provide the best measure of the gas composition in the cell. The concentrations determined from the absorption measurements are summarized in Table 1.
In absorption, the baseline variations limit the sensitivity of the method. From estimates of the signal-to-noise ratios of single lines shown in Fig. 3 and the measured gas concentrations, the detection limits for the five components are determined and specified in Table 1 as a noise equivalent concentration (NEC). The sensitivities range from the medium ppm levels (1 ppm=1 part in 106 parts) to fractions of a percent. However, because of the large spectral range covered, significant improvements in sensitivity are expected (especially for EtOH and Ace) if multiple lines are used for detection .
It is further noted that each 2 MHz interval in the chirp was scanned in ≈5 ps. For a Gaussian absorption line with this width, the time-bandwidth product (441 MHz∙ns) would predict an 88 GHz broadened line in absorption. However, because of the short 25 ns chirp used for excitation, the actual measurement time of an absorption line is across most of the 500 ns interval that includes the molecular response function or the free induction decay. The free induction decay adds destructively to the chirped pulse to deplete the field strength and to sharpen the line. The insert in Fig. 3 shows the line shape observed for MeOH compared to the Voigt profile calculated from HITRAN. The Voigt profile is in good agreement for all of the observed lines. However, the residuals (shown below the line in the insert) indicate the observed line is slightly broader. The best fit line shape gives a Gaussian component of ≈1.49 MHz compared to the HITRAN value of 1.20 MHz. The additional 0.9 MHz Gaussian width contribution is very close to that expected for the transform limit of the 500 ns interval. We also note that this method gives the imaginary part of the response function as commonly obtained in conventional direct absorption measurements (in contrast to the response function observed for the free induction decay signals alone as discussed below). Therefore, with some small refinements in the sampling interval and/or pressures used, this method can be used to provide accurate line shape parameters over broad spectral intervals in very short measurement times.
3.2 Free inductive decay (FID)
A separate set of measurements of the free induction decay (FID) signal was performed on the same gas mixture used in absorption. Although the FID signal is present in the absorption data, to obtain the best signal-to-noise (S/N) ratios, the dynamic range of the 8 bit digitizer at the oscilloscope is maximized for small signal detection by increasing the input sensitivity by 10-fold. As in absorption, the FFT was taken of the averaged time domain waveform with and without gas in the cell and the resulting magnitude was squared to give intensity. The FID spectrum obtained from the FFT of an 80 000 record average acquired in 30 seconds is shown in Fig. 4 . Since the FID signals are detected in the absence of chirp pulse, this method is no longer limited in sensitivity by phase variations in the ratio between the signal and background signals. The dominant source of noise following the chirp is a 200-fold attenuated copy of the chirp that is time delayed by 167.55 ns. This delay corresponds to a pathlength of 50.23 m or roughly twice the optical pathlength of the White cell. We believe a misaligned or scattered portion of the chirp is inadvertently coupled into the 50 m (80 pass) configuration of the White cell. Since the attenuated copy of the chirp is only a 25 ns portion of the 475 ns region available to the FID, this 25 ns region was apodized to zero using a Tukey filter prior to performing the FFT of the data. We believe that with some further spatial filtering of the input pulse, most of the 475 ns region available for FID detection can be recovered.
The FID spectral intensities shown in Fig. 4 are very different from those observed in the absorption spectrum (Fig. 3) although still in excellent agreement with predictions (shown inverted in Fig. 4). Two factors are responsible for these differences and have been applied to correct each of the simulated line intensities. Under the conditions used here, the most important correction is the normalization of the intensities to the power seen in the chirp (see Fig. 3). The second factor arises because of the short but finite duration of the chirped pulse and becomes increasingly important as the chirped pulse lengthens in time and/or the total gas pressure increases. A timing diagram of the decay process is shown in Fig. 5 . Depending on the time delay since absorption, the FID signals decay to different levels within the windowed region used to perform the FFT. For each spectral line, the amplitude of the FID decay depends on the collisional dephasing time and thermal velocity spread of the gases. The total attenuation of the line intensity, Aj, absorbing at frequency, νj, is given by the following,
All of these factors in Eq. (1) may be obtained from the measurements. The frequency of the line determines the precise time delay following absorption and the Gaussian width is determined from its average velocity at room temperature. For OCS, N2O and MeOH, the Lorentzian widths from pressure broadening were obtained from the HITRAN database. For EtOH and Ace, they were estimated from the lineshapes observed in absorption. The average width parameters, ΔνL and ΔνG, for these measurements are listed in Table 1.
We also note that the line width parameters may be obtained directly from the line shapes observed in the FID spectrum. The Voigt line widths of the squared magnitude spectrum includes contributions from absorption (imaginary part of the FFT) and dispersion (real part of the FFT) and will always be broader than the square of the absorption part alone. As is well known in NMR and Fourier-transform ion cyclotron resonance (FT-ICR), narrower line widths are achieved only after phase correcting the imaginary component of the Fourier transform. The phase correcting procedure has been applied to the line shape of OCS shown in Fig. 6 . Here, the square of the imaginary part of the FID provides an accurate measure of the Voigt line shape parameters reported in the HITRAN database.Significant narrowing is also expected for the phase corrected FID data shown in Fig. 4. However, at higher pressures, the effect of line narrowing will become more subtle as the Lorentzian line shape component becomes dominant.
The simulated spectra of the five components are shown as inverted traces in Fig. 4 after power normalization and correction of the simulated line intensities according to Eq. (1). For the 25 ns pulse used here, the corrections for the latter are very small (although for other data sets taken using 200 ns chirped pulses, this correction is much more significant). As evident from comparisons with the simulated intensities in Fig. 4, the overall agreement with the experimental data is very good. A single calibration factor for the instrument brings the relative intensities for MeOH, OCS and N2O into agreement with experiment. Therefore, the absolute concentrations of other gases may be determined directly from the FID intensities once the absorption coefficients are known.
The noise of these background-free FID measurements is shown as an insert in Fig. 4. The scale of magnification is 500-fold. Surprisingly, finding a region devoid of lines for a noise estimate was difficult. This becomes immediately apparent from comparison with the signal level observed for the empty cell, which is also shown in the insert (EC). We estimate a signal-to-noise ratio for MeOH near 100 000:1. Both N2O and OCS also have strong features in this region of the spectrum. The respective detection limits for these three molecules are 100 ppb, 170 ppb and 280 ppb and summarized in Table 1 Because of the large partition functions for Ace and EtOH, limits of detection are in the low ppm levels. Water present as an impurity also has a weak feature at 552.021 GHz (not shown). Its concentration is estimated at 0.04% based on the HITRAN parameters and has permitted a limit of detection of 2 ppb if the strong line centered at 556.936 GHz is monitored. Other trace gas impurities have also been identified including methyl formate and formaldehyde. For the later, detection limits are expected to be in the low ppbs.
To determine how the noise scales with signal averages, measurements of a gas mixture were acquired for 10 000, 40 000, and 80 000 average intervals. The results are shown in Fig. 7 . The noise values shown are measured as the root-mean-square (RMS) over a small region bracketed in the figure because of the high density of spectral lines. The noise reduction closely follows 1/n, where n is the number of time-domain averages. This is expected for phase coherent detection systems since the measured electric field, following Fourier transformation, is squared to obtain the power spectrum. Squaring the signal removes the n-1/2 noise scaling expected for power averaging.
We have described a new analytic tool for trace gas detection based on chirped-pulse Fourier transform THz spectroscopy. The spectrometer was used to acquire both the direct absorption and free induction decay emission signals of five gases simultaneously over a bandwidth of 10 GHz in 30 seconds of acquisition time and with a spectral resolution of 300 kHz before interpolation. The spectrometer has demonstrated performance for broadband trace level detection of a variety of species important in applications ranging from atmospheric monitoring for climate change to breathe analysis for biomedical applications. The spectrometer can be extended to any terahertz (< 2 THz currently) frequency interval by changing the multiplier sources and detectors. We have demonstrated high sensitivity for the detection of the FID signals and expect the signal-to-noise scaling to remain over a large number of time-domain averages as reported in the microwave region . The background free aspect of the measurement permits the observation of true noise scaling of phase coherent methods. The advantage of detecting the electric field using heterodyne methods results in a power spectrum that scales directly with the number of averages. Furthermore, heterodyne detection allows for a spectral measurement accuracy of better than 20 kHz in this frequency range on nanosecond time scales.
For direct absorption measurements of MeOH, N2O and OCS, the spectral line profiles, widths and intensities are in good agreement with predictions from the HITRAN database. The relative FID emission intensities are in excellent agreement once corrected for power fluctuation and FID delay. This technique can be used for absolute determinations of gas concentration once the instrument calibration factor and absorption coefficients are known. For molecules where the lineshape parameters are not well characterized, this THz spectrometer is well suited to making extremely precise and accurate measurements with unprecedented speed and sensitivity.
The results presented here demonstrate the initial configuration for this spectrometer with a variety of speed and sensitivity enhancements currently underway. Noteworthy, the speed and sensitivity of the spectrometer are severely limited by the acquisition time and not by the detection technique. Therefore, a number of straight forward changes to the acquisition configuration can bring significant improvements. Multi-line fitting is a second area of improvement as implemented by several trace gas detection systems . The current White cell can be realigned for a 50 m path length yielding a two-fold improvement in signal.
We have so far discussed the sensitivity and speed of our technique for broadband (10 GHz) trace gas sensing where we digitize the entire spectrum with one chirped pulse. In collaboration with the Brooks Pate’s group at the University of Virginia, we are currently exploring segmented scan methods for detection of specific lines at known frequencies and for broadband detection across the full range available to amplifier/detector systems by taking advantage of the rapid frequency response of both the AMC and the MixAMC systems. The segmented scan approach is expected to lead to significant improvements in acquisition speed and simplification of the digitizer electronics. Further simplification is currently underway by making use of low-cost single-frequency phase-locked dielectric resonance oscillators (PLDRO) to replace the two microwave synthesizers. The all solid-state instrumentation of such a system is portable and robust and therefore, will be attractive for the commercial development of novel non-destructive and non-invasive testing equipment.
We wish to thank Tektronix Cooperation for loaning us the AWG instrument used for these measurements. We would also like to thank Dr. Bradley K. Alpert (NIST, Boulder) for fruitful discussions regarding the phase corrections. This project is funded by the Upper Atmospheric Research Program of the National Aeronautics and Space Administration (NNH09AK47I) and the National Institute for Standards and Technology.
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