We have developed a frequency-comb spectrometer that records 35-nm (4 THz) spectra with 2-pm (250 MHz) spectral sampling and an absolute frequency accuracy of 2 kHz. We achieve a signal-to-noise ratio of ~400 in a measurement time of 8.2 s. The spectrometer is based on a commercial frequency comb decimated by a variable-length, low-finesse Fabry Pérot filter cavity to fully resolve the comb modes as imaged by a virtually imaged phased array (VIPA), diffraction grating and near-IR camera. By tuning the cavity length, spectra derived from all unique decimated combs are acquired and then interleaved to achieve frequency sampling at the comb repetition rate of 250 MHz. We have validated the performance of the spectrometer by comparison with a previous high-precision absorption measurement of H13C14N near 1543 nm. We find excellent agreement, with deviations from the expected line centers and widths of, at most, 1 pm (125 MHz) and 3 pm (360 MHz), respectively.
© 2015 Optical Society of America
Molecular absorption spectroscopy has many applications, including: environmental monitoring [1–3], measurement of contaminants in industrial processes [4, 5], human breath analysis [6–8], detection of contraband and warfare agents  and fundamental science . There are several mature competing techniques for measuring molecular absorption spectra, including tunable laser spectroscopy, cavity-ringdown spectroscopy (CRDS) and Fourier-transform infrared spectroscopy (FTIR). The best approach depends on the requirements of the application and there is usually a trade-off between measurement parameters such as spectral coverage, sensitivity, spectral resolution, spectral accuracy, measurement speed, simplicity and cost.
In recent years, frequency combs have been demonstrated to be ideal sources for absorption spectroscopy because they combine broad spectral coverage, dense spectral sampling, high ac curacy and fast measurement . Frequency combs allow simultaneous interrogation at thousands of precisely known optical frequencies and – as they are coherent sources – resonant enhancement within a high-finesse cavity can be employed for high sensitivity .
Several methods have been developed to measure absorption spectra using frequency combs; most notably: multiheterodyne detection using two frequency combs with slightly different repetition rates [13–17]; vernier detection using a resonant optical cavity to scale the comb’s repetition rate [18–21]; and using dispersive elements such as a diffraction gratings and virtually imaged phase arrays (VIPAs) [7, 22]. These three methods offer similar performance in terms of spectral coverage, spectral sampling density and measurement time. The figure of merit introduced by Newbury et al.  (the product of the SNR, normalized by the square root of the acquisition time, and the number of resolved frequency elements) is typically ~ 106 – 107 for these spectrometers.
The combination of a VIPA, a diffraction grating and an imaging array is attractive because it requires only a single frequency comb and it minimizes the number of moving parts. To date, however, VIPA-based spectrometers have only been able to resolve decimated comb modes [22, 24] or have been unable to resolve comb modes at all [3, 7, 25]. For the latter, the spectrometer cannot take advantage of the inherent accuracy and stability of the comb mode frequencies, negating that benefit of using a comb.
We have developed a quantitative frequency-comb absorption spectrometer that delivers broad spectral coverage (~4 THz) and utilises the full spectral sampling and frequency accuracy available from a stabilised optical frequency comb. It is based on a commercial frequency comb in conjunction with an imaging system consisting of: VIPA, diffraction grating and near-IR camera. The imaging system has a resolution of 1.2 GHz, so, in order to fully resolve the 250-MHz-spaced comb modes, an external resonant optical cavity with a free spectral range (FSR) of ~9.5 GHz is used as a tunable spectral filter to decimate the frequency comb modes, producing a 2-dimensional array of well separated bright spots when imaged by the camera. A fully automatic control system dynamically locks the filter cavity to the frequency comb and sequentially measures all unique decimated comb subsets, which are interleaved to produce complete spectra with 250-MHz spectral sampling over ~4 THz in a total measurement time of 8.2 s. The comb is locked to an ultra-stable laser that gives stability and accuracy of the frequency axis of <10 Hz and <2 kHz, respectively, for measurement times of 1 – 10 s.
The spectrometer requires only one frequency comb, unlike similarly performing dual-comb spectrometers, and its only moving part is a PZT-scanned filter-cavity mirror, making it a useful tool for applications requiring fast, quantitative spectra. In conjunction with new portable high-performance frequency combs , this automated system may easily evolve into a useful tool for field applications and is consistent with world-wide efforts to bring frequency-comb applications out of the metrology laboratory.
The spectrometer’s performance was evaluated by measuring the 2ν3 vibrational overtone band of H13C14N centered at ~1543 nm. The measured line centers and widths are in excellent agreement with a previous high-precision measurement.
2.1. Optical system
Figure 1 shows the experimental setup. The frequency comb (Menlo Systems FC1500) has a repetition rate of 250 MHz and spans ~1500 – 1600 nm. Its carrier-envelope-offset frequency (fCEO) and repetition rate (fRR) are locked to a cesium beam clock and a cavity-stabilized continuous-wave reference laser (NKT Koheras BoostiK E15), respectively. The resulting stability of each comb mode is ~10 Hz for an observation time of 1 – 10 s (set by the reference laser) and its absolute frequency is known to ~2 kHz (set by our ability to measure fRR).
The frequency comb is combined with the reference laser, which provides a marker for calibrating the frequency scale. We use two optical paths alternately: a sample path that contains a H13C14N reference cell at 100 Torr, and an empty reference path for calibration. Light from the two paths is passed through an optical fiber to ensure they are colinear before introduction to the imaging optics. The light is line-focused into the AR-coated access window of the VIPA (Light Machinery). The VIPA is a specialized étalon with a free spectral range (FSR) of 50 GHz and a finesse of ~100 that disperses the comb light vertically . To avoid frequency ambiguity, it is used in combination with a 600 lines/mm diffraction grating (Thorlabs GR25–0616) oriented to disperse the light horizontally . The resulting beam is imaged on an InGaAs camera (Xenics Xeva-1.7-320). The camera captures just over one VIPA FSR in the vertical direction and ~35 nm (~4 THz) of spectral width in the horizontal direction. The algorithm used to extract the absorption spectrum from the image is described in detail in Section 2.3.
By measuring the vertical width of an imaged spot due to the reference laser, we estimated the resolution of the VIPA spectrometer to be ~1.2 GHz, which is significantly larger than the comb mode separation (250 MHz). In order to resolve the comb modes, we use a variable-length, low finesse (~200) Fabry-Pérot cavity to decimate the comb. We chose a cavity FSR (νFSR) of 9.5 GHz (transmitting every 38th comb mode) because it is significantly larger than the spectrometer resolution and produces the optimum two-dimensional distribution of imaged modes on the camera. A longer cavity would result in closer spacing of imaged modes, leading to cross-talk in the extracted spectra. Scanning the cavity length allows access to all unique subsets of 9.5 GHz-spaced decimated combs. However, as demonstrated in Fig. 2, when detuned from the best match between comb and cavity, the pass-bands of the cavity transfer function acquire an accumulating offset from the comb mode frequencies that reduces the transmitted optical power of modes far from the center of the camera image. The finesse of the cavity was chosen to provide enough selectivity to suppress unwanted comb modes, yet was low enough to transmit sufficient optical power (P > 0.1Pmax) for all imaged modes when maximally detuned from the best match.
2.2. Cavity locking and data acquisition
Figure 3 shows the integrated cavity transmission (measured by the photodetector positioned after the Fabry-Pérot cavity) as a function of cavity length. This curve is similar to previous observations [28, 29]. Local maxima occur when cavity resonances (separated by ~9.5 GHz) are optimally aligned with a 9.5 GHz subset of comb modes. The peak of the envelope corresponds to νFSR = 38 × fRR and, as the cavity is detuned from this optimum length, the increasing mismatch between fRR and νFSR leads to lower transmission of some modes and thus a reduction in the amplitude of successive maxima. The asymmetry of the envelope is due to dispersion in the mirrors combined with an asymmetric distribution of comb power around the central wavelength.
To measure a complete spectrum, we record two camera images (one for the sample and one for the reference path) for each of the central 38 adjacent peaks in the cavity transmission pattern in Fig. 3. A dither lock stabilizes the cavity length during the acquisition of each image to ensure that the cavity transmission intensity profile for each image pair is identical which allows accurate normalization. Coordinating the acquisition requires control of the cavity length, the dither locking electronics and the camera triggering. Our control system is based on an Arduino Due board, which provides sufficient flexibility to create a completely automated acquisition system.
Figure 4 shows a schematic of the cavity length control and dither locking system. The Arduino Due board has a program loop rate of 20 kHz. It generates a 10 kHz dither signal by toggling a digital output at each program loop. The signal is filtered, amplified and sent to a piezoelectric transducer (PZT) behind one filter-cavity mirror (also shown on Fig. 1). The amplitude of the resulting oscillation in the transmitted optical power is proportional to the local derivative of the pattern in Fig. 3 and its phase indicates the sign of the same derivative.
The signal from the photodetector (D) is band-pass filtered (BPF) and sampled by the Arduino, which performs digital demodulation and low-pass filtering (LPF) to generate an error signal with zero crossings at cavity transmission peaks. The error signal is passed to a digital proportional-integral (PI) loop filter in the Arduino, the output of which is passed through an on-board 12-bit digital-to-analog converter (DAC), attenuated to give fine control, and summed with the dither signal. A second 12-bit DAC coarsely controls the cavity length to ensure the servo control stays within its range. It is also used to step between cavity resonances. The dither locking servo has a closed loop bandwidth of order 1 kHz, which is dependent somewhat on the peak to which it is locked. This gives a settling time of a few milliseconds after a step between adjacent peaks.
The Arduino board also controls the automatic acquisition of the 38 consecutive pairs of camera images. Digital outputs are used to cycle the position of the shutter between the sample and reference paths (shown in Fig. 1) and trigger the camera. Sample and reference images are acquired alternately using a camera integration time of 8 ms. Successive images are separated by intervals of 100 ms, dominated by the shutter settling time. The measurement time for a complete spectrum (38 image pairs) is 8.2 s. By using a high-speed shutter, we expect the measurement time would be reduced to less than 2 s.
2.3. Image analysis
The modes of each decimated comb subset are dispersed vertically (by the VIPA) and horizontally (by the diffraction grating) before being focused onto the InGaAs camera, yielding images similar to that shown at the top left of Fig. 5. For the sample-path images, each bright spot corresponds to a cavity-resolved comb mode with brightness dependent of the degree of absorption by the gas sample. The reference path image is required to normalize common-mode brightness variations in the optical system. For visualisation purposes, a sample image normalized by its corresponding reference image is shown on the top right of Fig. 5 with the characteristic absorption fingerprint clearly visible. The intensity profile of each spot extends some distance from the centroid before diminishing below the camera noise floor. Spot separation was less than this distance, so, in the ratio image, we would expect to see solid regions of a single shade wherever a given spot was dominant, giving rise to the distinctive diamond shapes, with sharp boundaries forming where the intensity arising from each competing spot is equal. Each image pair (sample and reference) is analyzed to extract a traditional one-dimensional absorption spectrum.
The integrated power of each comb mode was determined by applying a matched filter to the raw images. This step can be understood as a cross-correlation of the images with a 5 × 5 pixel kernel based on a single imaged mode that best approximates the profile of all modes. The cross-correlation is a weighted integration at all possible kernel positions, and thus the amplitude of the maxima are proportional to the power of the respective comb modes. It can be shown that the matched filter is the optimal linear technique to detect the presence of a signal contaminated by white noise . Therefore, the spots that are only partially transmitted by the cavity and appear dimmer on the image are easily extracted from the image. The filter also serves to reduce cross-talk from adjacent spots. For each image pair, the ratio of corresponding cross-correlation maxima is computed to find the normalized transmittance of the corresponding comb mode.
The local maxima of the cross-correlation image closely correspond to the centroid positions of the spots, allowing a very accurate determination of the position of each comb mode in an image. Knowing the dispersion in both the vertical and horizontal directions, and keeping in mind that adjacent modes are separated by precisely 38 fRR, allows the relative frequency of each imaged mode to be determined and an absorption spectrum for a single frame to be constructed. Also, knowing that the subset of modes in each successive image pair is offset fRR from the last, allows us to interleave a set of 38 consecutive spectra to reconstruct a full absorption spectrum, as shown in the bottom panel of Fig. 5. Due to environmental fluctuations affecting the free-space beams, slight power fluctuations occur during the time interval separating the acquisition of the reference and sample images. A robust (bi-square), first-order polynomial fit was used to individually renormalize individual spectra before interleaving. Using a faster shutter or reducing alignment fluctuations would eliminate the need for this step.
Finally, within each set of 38 consecutive image pairs there is a single pair that also shows the reference laser (see Fig 5). If the position of the reference laser is used as a proxy for the nearest comb mode, and the optical frequency of this mode is known, then an absolute frequency can be assigned to every imaged mode. The optical frequency νref of the reference laser was independently measured using a wave meter (HighFinesse WS/7) (accurate to ~10 MHz) and the optical frequency of the nearest comb mode, νn, was deduced by minimizing |νref − νn| where: νn = n × fRR + CEO and n is the mode index. A measurement of fCEO and fRR using a frequency counter referenced to a Cs beam clock (Datum CsIII) allowed the optical frequency of each comb mode to be determined. This technique limits the measurement of the absolute frequency accuracy to that of the Cs beam clock, which, when multiplied up to optical frequencies by the mode index, gives an uncertainty of ~2 kHz. If the reference laser were to be locked to a well characterised optical transition, then absolute frequency accuracy could be improved.
The full reconstructed spectrum is shown in Fig. 6. It spans ~4 THz (35 nm) with 250-MHz (2 pm) spectral sampling and 2-kHz (10 am) absolute accuracy. The signal to noise ratio varies slightly across the interleaved spectrum primarily because individual modes have a range of intensities when imaged by the camera. Data points are therefore limited either by relative intensity noise for the brighter spots or by additive noise from the camera for dimmer spots. At all intensities the noise is white with an average signal-to-noise ratio across the interleaved spectrum of ~400. This gives a figure of merit  of , which compares well with other comb spectroscopy techniques.
3. Spectral analysis
The full spectrum presented in Fig. 6 was used to determine the line centers and the Lorentzian components of the linewidths of 48 2ν3 rotational-vibrational absorption lines of H13C14N. The sample was contained in a nominally 100±10 Torr, 50 mm long reference cell (Wavelength References; HCN-13-100) at room temperature (22.5 1°C).
Regions of the absorption spectrum were approximated ± by fitting functions of the form:31]), and Lorentzian component FWHM, 2γ.
An initial estimate of the parameter set was found by moving to peach absorption line, windowing the spectrum to include the immediately adjacent lines, and performing a linear least-squares fit using Eq. (1) with j = 2 and m = 3 (m = 2 for the edge cases). Parameters ν, σ and γ for the line of interest for each fit were retained. This initial parameter set was used to suppress the main absorption lines in the spectral data, revealing the residual broadband background structure. A robust (bi-square) fourth-order polynomial fit to this structure allowed it to be removed before performing a final linear least-squares fit of all lines simultaneously using Eq. (1) with j = 0 and m = 51, seeded by the initial parameter set. Figure 7 shows a closeup of the fitted spectrum around the P(16) feature.
To validate the quality of the spectrometer, line centers and widths derived from the fit were compared with those expected at 100 Torr (calculated from ). Significant deviation from the expected Lorentzian linewidth (up to ~8 pm or 1 GHz) suggested that the reference cell pressure was lower than the nominal pressure of 100 Torr. Least-squares optimization was used to minimize deviation from the expected linewidths, giving an estimate of 92.5±0.8 Torr, which is within the ±10% tolerance quoted by the manufacturer. Figure 8 displays a comparison of selected line centers and linewidths to expected values at 92.5 Torr. Measurement uncertainties are the 2σ confidence intervals obtained from the least-squares fit.
We find good agreement with the expected values predicted by . Line center and width measurements using this analysis exhibited repeatability consistent with the 2σ confidence intervals derived from the fit. Repeatability also corresponded well to the uncertainty in these parameters predicted by a modelled spectrum with added Gaussian noise of SNR = 400. We do, however, see deviations from calculated expected values of up to ~1 pm and up to ~3 pm, respectively – exceeding the 2σ confidence intervals and thus presenting a strong indication of underlying systematic errors. One source of such errors are the smaller hot-band features visible in the spectrum. These were not included in this analysis and, consequently, some of the main absorption lines experienced small shifts from the expected line centers. This was particularly noticeable for the P(2), P(7) and P(20) features, which was also noted by . We also observe broader structure that may indicate pressure shifts and pressure broadening introduced by a buffer gas in the reference cell. We are confident that a more detailed analysis will result in closer agreement with previous work.
We have demonstrated a quantitative frequency comb spectrometer with 35-nm (4 THz) bandwidth around 1543 nm, 2-pm (250 MHz) spectral sampling and an absolute frequency accuracy of 2 kHz. We achieve a signal-to-noise ratio ~400 in 8.2 seconds, giving a figure of merit of , which compares favourably with other comb spectroscopy techniques. We have validated the performance of the spectrometer by comparing our measurement of the 2ν3 vibrational overtone of H13C14N to a previous high-precision measurement; finding excellent agreement with line centers and Lorentzian linewidths exhibiting deviation of, at worst, 1 and 3 pm, respectively.
Our approach has demonstrated a practical spectrometer that harnesses the full potential of a stabilized frequency comb and can be easily deployed for a range of high-precision spectroscopic measurements.
The authors would like to thank the Australian Research Council for supporting this research through the LP120200605 Linkage Project grant. The authors also wish to acknowledge the South Australian Government for providing financial support through a Catalyst Research Grant and the Premiers Science and Research Fund.
References and links
1. S. Spuler, M. Linne, A. Sappey, and S. Snyder, “Development of a cavity ringdown laser absorption spectrometer for detection of trace levels of mercury,” Appl. Opt. 39, 2480–2486 (2000). [CrossRef]
2. F. Couto, M. Sthel, M. Castro, M. da Silva, M. Rocha, J. Tavares, C. Veiga, and H. Vargas, “Quantum cascade laser photoacoustic detection of nitrous oxide released from soils for biofuel production,” Appl. Phys. B 117, 897–903 (2014). [CrossRef]
3. L. Nugent-Glandorf, F. R. Giorgetta, and S. A. Diddams, “Open-air, broad-bandwidth trace gas sensing with a mid-infrared optical frequency comb,” Appl. Phys. B 119, 327–338 (2015). [CrossRef]
4. S. Y. Lehman, K. A. Bertness, and J. T. Hodges, “Detection of trace water in phosphine with cavity ring-down spectroscopy,” J. Cryst. Growth 250, 262–268 (2003). [CrossRef]
5. H. H. Funke, B. L. Grissom, C. E. McGrew, and M. W. Raynor, “Techniques for the measurement of trace moisture in high-purity electronic specialty gases,” Rev. Sci. Instrum. 74, 3909–3933 (2003). [CrossRef]
6. M. R. McCurdy, Y. Bakhirkin, G. Wysocki, R. Lewicki, and F. K. Tittel, “Recent advances of laser-spectroscopy-based techniques for applications in breath analysis,” J. Breath Res. 1, 014001 (2007). [CrossRef] [PubMed]
7. M. J. Thorpe, D. Balslev-Clausen, M. S. Kirchner, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy: application to human breath analysis,” Opt. Express 16, 2387–2397 (2008). [CrossRef] [PubMed]
8. T. H. Risby and F. K. Tittel, “Current status of midinfrared quantum and interband cascade lasers for clinical breath analysis,” Opt. Eng. 49, 111123 (2010). [CrossRef]
9. D. Moore, “Recent advances in trace explosives detection instrumentation,” Sens. Imag. Int. J. 8, 9–38 (2007). [CrossRef]
10. K. C. Cossel, D. N. Gresh, L. C. Sinclair, T. Coffey, L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, R. W. Field, E. R. Meyer, E. A. Cornell, and J. Ye, “Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment,” Chem. Phys. Lett. 546, 1–11 (2012). [CrossRef]
11. F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: Technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010). [CrossRef]
12. M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006). [CrossRef] [PubMed]
13. S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27, 766–768 (2002). [CrossRef]
16. A. Zolot, F. Giorgetta, E. Baumann, W. Swann, I. Coddington, and N. Newbury, “Broad-band frequency references in the near-infrared: Accurate dual comb spectroscopy of methane and acetylene,” J. Quant. Spect. Rad. Trans. 118, 26–39 (2013). [CrossRef]
17. G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Comm. 5, 6192 (2014). [CrossRef]
18. C. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007). [CrossRef]
19. F. Zhu, J. Bounds, A. Bicer, J. Strohaber, A. A. Kolomenskii, C. Gohle, M. Amani, and H. A. Schuessler, “Near infrared frequency comb vernier spectrometer for broadband trace gas detection,” Opt. Express 22, 23026–23033 (2014). [CrossRef] [PubMed]
21. M. Siciliani de Cumis, R. Eramo, N. Coluccelli, M. Cassinerio, G. Galzerano, P. Laporta, P. De Natale, and P. Cancio Pastor, “Tracing part-per-billion line shifts with direct-frequency-comb vernier spectroscopy,” Phys. Rev. A 91, 012505 (2015). [CrossRef]
24. L. Nugent-Glandorf, T. Neely, F. Adler, A. J. Fleisher, K. C. Cossel, B. Bjork, T. Dinneen, J. Ye, and S. A. Diddams, “Mid-infrared virtually imaged phased array spectrometer for rapid and broadband trace gas detection,” Opt. Lett. 37, 3285–3287 (2012). [CrossRef] [PubMed]
25. T. Johnson and S. Diddams, “Mid-infrared upconversion spectroscopy based on a Yb:fiber femtosecond laser,” Appl. Phys. B 107, 31–39 (2012). [CrossRef]
26. L. C. Sinclair, I. Coddington, W. C. Swann, G. B. Rieker, A. Hati, K. Iwakuni, and N. R. Newbury, “Operation of an optically coherent frequency comb outside the metrology lab,” Opt. Express 22, 6996–7006 (2014). [CrossRef] [PubMed]
28. A. Ferguson and R. Taylor, “Active mode stabilization of a synchronously pumped mode locked dye laser,” Opt. Comm. 41, 271–276 (1982). [CrossRef]
29. T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82, 3568–3571 (1999). [CrossRef]
30. G. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory , 6, 311–329 (1960). [CrossRef]
31. W. Demtröder, Laser spectroscopy: basic concepts and instrumentation, 2674 (Springer Science & Business Media, 2003).
32. S. L. Gilbert, W. C. Swann, and C.-M. Wang, “Hydrogen cyanide H13C14N absorption reference for 1530 nm to 1565 nm wavelength calibration–SRM 2519a,” NIST Special Publication 260, 137 (2005).