Phase-controlled Fourier-transform spectroscopy

Abstract

Fourier-transform spectroscopy (FTS) has been widely used as a standard analytical technique over the past half-century. FTS is an autocorrelation-based technique that is compatible with both temporally coherent and incoherent light sources, and functions as an active or passive spectrometer. However, it has been mostly used for static measurements due to the low scan rate imposed by technological restrictions. This has impeded its application to continuous rapid measurements, which would be of significant interest for a variety of fields, especially when monitoring of non-repeating or transient complex dynamics is desirable. Here, we demonstrate highly efficient FTS operating at a high spectral acquisition rate with a simple delay line based on a dynamic phase-control technique. The independent adjustability of phase and group delays allows us to achieve the Nyquist-limited spectral acquisition rate over 10,000 spectra per second, while maintaining a large spectral bandwidth and high resolution. We also demonstrate passive spectroscopy with an incoherent light source.

Introduction

Fourier-transform spectroscopy (FTS) has provided solutions to countless chemical analysis problems in the fields of chemistry, pharmacy, medicine, biology, and physics including material science1,2,3. It enables the simultaneous identification of multiple molecular species via high-resolution broadband molecular spectra measured by a simple optical system consisting of a scanning Michelson interferometer and a broadband light source. The fact that this analytical method has long been widely used owes to the simple and robust autocorrelation-based working principle, enabling a variety of uses. For example, since it allows us to measure temporally incoherent light, FTS can be used as a passive spectroscopy technique with an external light source such as sunlight4,5. However, FTS has been mostly used for measuring static samples because of the low temporal resolution due to the low scan rate of mechanical delay lines. This is incompatible for investigating fast phenomena at a higher temporal resolution, such as combustion processes which often require a measurement rate over 10 kHz6,7. Rapid-scan FTS instruments typically operate at an improved temporal resolution only at a low spectral resolution, for example a scan rate of 1 kHz with a resolution of 120 GHz (4 cm−1)8 or 77 kHz with a resolution of 360 GHz (12 cm−1)9. For a higher resolution applicable to gas-phase analysis such as 15 GHz (0.5 cm−1), the available scan rate significantly drops down to less than 10 Hz10,11 due to the lack of a rapid-scan long-range delay line. Step-scan FTS12 is also known to improve the temporal resolution but it works only for measuring repeatable phenomena, which significantly limits applications. Another type of broadband absorption spectroscopy technique, called time-resolved frequency comb spectroscopy (TRFCS)13,14, has been used for analyzing transient chemical phenomena of gaseous molecules with high spectral resolution. The scan rate of this technique is 250 Hz, which is limited by the frame rate of the image sensor. The temporal resolution can be as high as 25 μs through repetitive measurements, but it also works only for measuring repeatable phenomena.

A recent development in dual-comb spectroscopy (DCS)15,16, a mechanical-scan-free FTS technique based on mutually coherent laser frequency combs with slightly detuned pulse repetition rates, has elegantly solved the problem and shown a tremendous improvement on the measurement scan rate17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34. The superiority of this technique is its highest scan rate, i.e., Nyquist-limited scan rate, enabled by fully utilizing the Nyquist range, determined by half a repetition rate of the laser. In other words, DCS has been a unique FTS that enables the highest measurement rate, spectral bandwidth and resolution to be achieved under the Nyquist-limited trade-off constraint. This capability is owed to the adjustable difference in both the repetition rate and carrier-envelope offset (CEO) frequency between the combs. The former determines the down-conversion factor from the optical to radio frequency (RF) to achieve the highest possible scan rate, while the latter adjusts the position of the RF spectrum within the Nyquist range for avoiding aliasing. The latter capability has not often been clearly appreciated in the previous reports on DCS, but we emphasize that it assures DCS to be an efficient FTS technique. In return for this superior capability, DCS requires a more elaborate and sophisticated system than the conventional Michelson-type FTS because DCS is based on the cross-correlation measurement between the two lasers, for which mutual coherence is usually fragile. Furthermore, it is an active-type spectrometer, which requires light sources in the instrument, and is not suitable to be used in a passive manner20,22.

In this work, we revisit conventional Michelson-type FTS and develop a Nyquist-limited highly efficient FTS, called phase-controlled FTS (PC-FTS), that allows us to arbitrarily adjust the scan rate, spectral bandwidth, and spectral resolution under a tradeoff relation among them. This approach uses a rapid-scan phase-control mechanism inspired by pulse shaping techniques35, that enables us to acquire interferograms continuously at a rate beyond 10 kHz. This is the highest scan rate achievable as a Michelson-type FTS, while avoiding spurious spectral distortions due to the aliasing effect. This is made possible by the arbitrary and independent adjustment of the group and phase delay added by the delay line, which can be understood as an analogy of the independent adjustment of the difference in repetition rate and CEO frequency in a dual-comb spectrometer. As a proof of concept demonstration, we measure broadband gas absorption spectra of hydrogen cyanide (H12C14N) and acetylene (12C2H2) in the near-infrared region spanning over 1.8 THz with a resolution of 11.5 GHz at an acquisition rate of over 12 kHz both with temporally coherent and incoherent light sources. Our system holds great promise for applications aimed at measuring non-repeating phenomena at high-temporal-resolution such as a transient combustion process, or a large number of events at high-throughput such as large-area environmental monitoring.

Results

Principle of PC-FTS

A schematic of PC-FTS is shown in Fig. 1a. It consists of a broadband light source, a scanning Michelson interferometer, a single photodetector and a digitizer. Since Michelson-type FTS is an autocorrelation-based measurement, there is no requirement on the temporal coherence for the measured light source. In our experiment, a coherent mode-locked laser or an incoherent amplified spontaneous emission from a super-luminescent diode (SLD) is used as a broadband light source. The scanning Michelson interferometer varies a time delay between the beams traveling along the reference and scan arms, so that an autocorrelation trace, called the interferogram, is obtained as a function of time by the photodetector. The digitized interferogram is Fourier-transformed to obtain a spectrum. By placing a sample in the optical path between the interferometer and the detector, its absorption feature can be encoded onto the spectrum. Our phase-controlled delay line consists of a dispersive element such as a diffraction grating, a focusing element and a scanning mirror, which are aligned in a 4f geometry such that each spectral component of the beam is focused at a different spot on the Fourier plane, where the scanning mirror is placed36,37. The reflected beam from the scanning mirror then passes through the optical elements in the 4f system and is retro-reflected by an end mirror. The 4f geometry ensures the beam travels back along the incident path for any facet-angles of the scanning mirror. Using a rapidly scanning mirror enables the system to function as a rapid-scan FTS. A detailed schematic of the PC-FTS is shown in Fig. 2 and the components used in the system are described in Methods section.

Fig. 1
figure1

Schematic and conceptual illustration of phase-controlled Fourier-transform spectrometer. a Schematic of the system. The system consists of a broadband light source, a scanning Michelson interferometer with the rapid-scan phase-controlled delay line, a sample gas cell, a photodetector, and a digitizer. The delay line consists of a dispersive element, a focusing element, and a scanning mirror aligned in a reflective 4f-configulation. The broadband light is focused at the Fourier plane in the 4f system after spectral separation by the dispersive element such that each spectral component is mapped on a different position at the Fourier plane. The scanning mirror changes its angle at an angular frequency of ω and reflects the light with angled directions. The beam traveling through the 4f system is retro-reflected with an end mirror and goes back along the same path. The corresponding optical frequency of the pivot position of the scanning mirror in the Fourier plane is indicated as ν0. b Concept of PC-FTS. The upper part shows how the interferogram is obtained in the time domain. For simplicity, the light fields are depicted as a pulse train with zero carrier-envelope-phase as shown in the pulses in the reference arm. Here, fs denotes the sampling rate, which may be determined by the pulse repetition rate or sampling rate of the digitizer. At each time frame, the light field in the scan arm acquires a linear spectral phase that is proportional to the angle of the scanning mirror in the delay line. The linear spectral phase ramp adds a group delay and phase delay to the light field. The pivot frequency ν0 is converted to the zero frequency in the down-converted RF spectrum after Fourier-transformation. Therefore, the down-converted spectrum can be positioned inside of the Nyquist range (0−fs/2) by adjusting ν0

Fig. 2
figure2

Detailed schematic of the phase-controlled FTS. a Detailed schematic of PC-FTS. HWP Half-wave plate, QWP Quarter-wave plate, PBS Polarizing beamsplitter. b Phase-controlled delay line with a galvanometric scanner. c Phase-controlled delay line with a polygonal scanner

The working principle of PC-FTS is depicted in Fig. 1b. A slight inclination of the scanning mirror placed at the Fourier plane adds a linear spectral phase ramp to the broadband light that travels through the delay line. Here, we describe the system with a galvanometric scanner. Assuming the scanning mirror rotates clockwise at a constant angular frequency ω, the added spectral phase ϕ(ν) and group delay τg may be described as:

$$\phi \left( \nu \right) \approx - 2{\mathrm{\pi }}c_{\mathrm{g}}\left( {\nu - \nu _0} \right)t$$
(1)
$$\tau _{\mathrm{g}} = - \frac{1}{{2{\mathrm{\pi }}}}\frac{{\partial \phi \left( \nu \right)}}{{\partial \nu }} \approx c_{\mathrm{g}}t$$
(2)

where t denotes time, ν optical frequency, ν0 the optical frequency corresponding to the pivot position of the scanning mirror in the Fourier plane, and cgω/ν0 the down-conversion factor, which is approximately a constant value in time. A full description of cg is described in Supplementary Note 1. The group delay is linearly proportional to time by a factor of cg, while the group velocity can be described as cgc, where c denotes the speed of light. This indicates that a high angular frequency of the scanning mirror makes possible a large bandwidth of the down-converted RF spectrum, leading to an efficient use of the Nyquist range. Adjusting the angular frequency of the scanning mirror, which determines the down-conversion factor of FTS, is analogous to adjusting the difference in repetition rate between the combs in DCS. Equation 1 tells us that a down-converted RF spectrum has a frequency of cg(ν − ν0), that can be shifted by changing the pivot position of the scanning mirror ν0. Adjusting ν0 allows us to fully utilize the Nyquist range while avoiding the aliasing, which is analogous function as that of the difference in CEO frequency between the combs in DCS. The Nyquist theorem tells us the trade-off relation among the scan rate fscan, spectral bandwidth Δν, and spectral resolution δν, which may be described as:

$$f_{{\mathrm{scan}}}{\mathrm{\Delta }}\nu \frac{1}{{\delta \nu }} < \frac{{f_{\mathrm{s}}}}{2},$$
(3)

where fs denotes the sampling rate. The detailed description of Inequality 3 is provided in Supplementary Note 2.

Phase and group delay correction

Since the down-conversion factor cg is not exactly a constant value in time, the phase-controlled delay lines generate temporally nonlinear phase and group delays, which must be corrected for FTS. The detailed description of the nonlinearity is provided in Supplementary Note 1. To linearize both the nonlinear phase and group delays, we use continuous-wave (CW) interferograms at two different optical frequencies and follow the correction procedure that is in principle the same as that of DCS19,38. Note that the fixed instrumental nonlinearities of the phase and group delays are corrected in the PC-FTS, while the random temporal fluctuations of the difference in repetition rate and CEO frequency are corrected in the DCS. Since the PC-FTS is an autocorrelation-based technique where random temporal fluctuation is inherently small, the correction interferograms are not necessarily measured for every measurement.

We measure the CW interferograms at two different frequencies with external-cavity laser diodes with a linewidth of less than 500 kHz lasing at 195.51 and 194.50 THz for the system with a galvanometric scanner, and 196.41 and 195.51 THz for the system with a polygonal scanner. The lasers’ frequencies are measured by an optical spectrum analyzer (AQ6317B, Yokogawa) with the accuracy of ±3 GHz. The measured CW interferograms are shown in Fig. 3a. The phase nonlinearity is seen especially in the data measured by the system with the polygonal scanner. The phase delays are extracted from the interferograms and plotted in Fig. 3b. The group delays are calculated from the phase delays at the two different frequencies as shown in Fig. 3c. The maximum group delay is about 100 ps, which corresponds to the spectral resolution of about 10 GHz.

Fig. 3
figure3

Characterization of the phase and group delays added by the delay lines. a Measured continuous-wave interferograms at the two different frequencies. b Phase delays of the CW interferograms. c Group delays evaluated from the phase delays at the two different frequencies

Broadband absorption spectroscopy

As a proof-of-concept demonstration of the PC-FTS, we measure broadband absorption spectra of gaseous HCN by the system with a galvanometric scanner. An Er-fiber mode-locked laser that generates femtosecond pulses at a repetition rate of 50 MHz is used as a light source. A full description of the system is provided in Methods section. The interferograms shown in Fig. 4a display the clear modulations of the molecular free-induction decay. By Fourier-transforming a single-sided interferogram with the aforementioned phase and group delay correction19,38 and the conventional phase correction methods39,40,41,42,43, a broadband spectrum spanning over 7 THz is obtained at a resolution of 10.1 GHz with a high signal-to-noise ratio (SNR) (Fig. 4b). Sharp absorption lines of the overtone vibrational bands of HCN are clearly observed. Note that the resolution of 10 GHz corresponds to the maximum optical path length difference of 30 mm in a conventional FTS, which is achieved only by tilting the scanning mirror in the PC-FTS. The scan rate is 300 Hz, which is not limited by the Nyquist range (0–25 MHz) determined by the pulse repetition rate of the mode-locked laser but the scan rate of the galvanometric scanner.

Fig. 4
figure4

Broadband spectroscopic measurement by PC-FTS based on a galvanometric scanner. a Continuous interferograms of H12C14N molecules measured with the mode-locked laser. The single-sided interferograms are continuously obtained at a scan rate of 300 Hz (the corresponding temporal interval is 3.3 ms). The inset shows modulations due to the free-induction decay. b A broadband spectrum obtained by Fourier-transforming a single interferogram. The non-averaged broadband spectrum covering 7 THz shows absorption lines of HCN molecules at a spectral resolution of 10.1 GHz with a high signal-to-noise ratio. The structured spectral profile comes from that of the mode-locked fiber laser

Nyquist-limited rapid-scan spectroscopy

To fully utilize the Nyquist range and achieve the Nyquist-limited highest scan rate, a polygonal scanner can be used instead of the galvanometric scanner. With the faster rotation speed of the polygonal scanner, a continuous measurement of interferograms at a rate of 12 kHz is demonstrated in Fig. 5a. Figure 5b shows the corresponding consecutive broadband C2H2 absorption spectra with a bandwidth of 1.5 THz at a spectral resolution of 11.5 GHz. The spectra are normalized and converted to transmittance by a baseline fitting with Savitzky–Golay filtering44. Note that the effective scan velocity calculated by (scan rate) × (maximum group delay) × c is 340 m s−1, which is orders of magnitude higher than those of conventional delay lines. The down-conversion factor, (effective scan velocity)/c = (scan rate) × (maximum group delay), is about 10−6. Figure 5c shows a 20-averaged spectrum compared to a computationally retrieved spectrum based on HITRAN database45. The SNR of a single spectrum is 54, which is limited by detector noise in this proof-of-concept demonstration. It could be improved by using a detector with better noise performance. The detailed discussion on SNR is provided in Supplementary Note 3.

Fig. 5
figure5

High-scan-rate broadband spectroscopic measurement by PC-FTS based on a polygonal scanner. a Continuous interferograms of 12C2H2 molecules measured with the mode-locked laser. The burst of the interferogram appears every 83 µs, corresponding to a scan rate of 12 kHz. Clear modulations of the molecular free-induction decay are observed. b Non-averaged transmission spectra corresponding to the interferograms shown in Fig. 5a. Each spectrum covers over 1.5 THz with a resolution of 11.5 GHz. The absorption lines of C2H2 are clearly observed. The noise in the spectra can mainly be attributed to the side-modulations of the sinc function caused by the rectangular Fourier-transform windowing. Apodization (not applied here) can reduce the side-modulations at the expense of the spectral resolution. c Comparison between a 20-averaged transmission spectrum and a computationally calculated spectrum based on HITRAN database. The standard deviation of the residual is 1.7%

PC-FTS with an incoherent light source

Since the PC-FTS is an autocorrelation-based technique, it functions as a passive spectrometer with a temporally incoherent light source. Furthermore, since a repetition rate is not usually defined for an incoherent light, the Nyquist frequency of the measurement is determined by an electronic sampling rate of a digitizer. This enables a higher scan rate with a larger Nyquist range.

To show the applicability of an incoherent light to the PC-FTS, we replace the mode-locked laser by a commercially available SLD and perform a proof-of-concept measurement. We acquire HCN absorption spectra over 1.8 THz with a spectral resolution of 11.5 GHz at a scan rate of 24 kHz, which is higher than that of the mode-locked laser by a factor of two. Note that the scan rate of 24 kHz is not achievable with the mode-locked laser at the repetition rate of 50 MHz because of the aliasing effect caused by the Nyquist constraint due to the pulse repetition rate. Measured continuous interferograms are shown in Fig. 6a, where free-induction decay of the molecules is clearly seen every 42 μs. A spectrum Fourier-transformed from a single interferogram and a 30-averaged spectrum are shown in Fig. 6b. The fringe observed in each spectrum is the ripple-noise due to the multiple-reflections between the facets of the SLD chip.

Fig. 6
figure6

Interferograms and spectra measured by the PC-FTS with the SLD. a Continuous interferograms of H12C14N molecules measured with the SLD at a scan rate of 24 kHz. b Spectra obtained by Fourier-transforming a single interferogram (left), and a 30-averaged spectrum

Discussion

To see how efficiently the PC-FTS uses the Nyquist range, it is helpful to estimate the bandwidth of the down-converted spectrum when measuring with a conventional FTS. Assuming a commercially available FTS system that can measure a broadband near-infrared spectrum spanning from 176 to 333 THz with a spectral resolution of 7.5 GHz at a scan rate of 1.9 Hz, the down-converted spectrum appears at 45–84 kHz, which is much narrower than the Nyquist range set by the sampling rate of a few tens of MHz. The down-conversion factor is 2.5 × 10−10, which is orders of magnitude smaller than that of the PC-FTS (10−6).

Comparing the two Nyquist-limited FTS (DCS and PC-FTS) is useful to see the characteristics of these methods. DCS is a mechanical-scan-free FTS, therefore the system can be robust. Additionally, this frequency comb based FTS can assure high frequency accuracy. On the other hand, PC-FTS works with a single light source, which can be an incoherent light source, making the system simple. Also, this autocorrelation-based FTS can be used as a passive spectrometer.

The concept of this technique can be applied for other wavelengths including the mid-infrared region, where the fundamental vibrational modes of molecules exist. The single-photodetector-operation of the FTS is especially advantageous in the mid-infrared region because of the lack of a high-quality mid-infrared detector-array required for a high-speed dispersive spectrometer. Furthermore, PC-FTS is useful not only for gas-phase molecules but also for liquid-phase or solid-phase materials. As discussed above, since we can arbitrarily choose a combination of the scan rate, spectral bandwidth and resolution, a broader spectral bandwidth, for example, can be measured by reducing the spectral resolution while keeping the scan rate. Finally, this highly efficient FTS technique can also be modified and applied to multi-dimensional FTS, which requires time-consuming scans of multiple delay lines32.

Methods

Phase-controlled delay line

Our phase-controlled delay line consists of a dispersive element, a focusing element, a scanning mirror, and a flat mirror. These components are aligned to form a reflective 4f configuration such that a spectrum of the incident light is focused onto the Fourier plane where the scanning mirror is placed. In our demonstration, a reflective ruled grating with 600 lines mm−1 and a curved mirror with a focal length of 150 mm are used as a dispersive element and a focusing element, respectively. The number of grooves of the grating and the focal length of the curved mirror are to be set for optimizing the system (See Supplementary Note 1 for details). A galvanometric scanner or a polygonal scanner with 36 facets are used as the scanning mirror. The mirror facets of both scanners are coated with gold. The facet size of the galvanometric scanner is 10 mm, and that of the polygonal scanner is 5.6 mm per each facet. The inner diameter of the polygonal scanner is 63.6 mm and its rotation speed is set to be 20,000 or 40,000 rpm (rotations per minute) in our experiments. Replacing these optical components to ones with different parameters allows us to choose different combinations of the scan rate, spectral bandwidth and resolution.

Phase-controlled FTS

A full description of our PC-FTS is shown in Fig. 2. A temporally coherent mode-locked Er-doped fiber laser (Femtolite CS-20-GS, IMRA) or an incoherent SLD (S5FC1005S, Thorlabs) is used as a broadband light source. The broadband light is delivered with a single-mode fiber to a fiber-collimator placed at the input port of the spectrometer. For a rapid measurement with the polygonal scanner, the light is optically band-pass-filtered with a span of 14 nm (corresponding to 1.8 THz) centered at 1533.5 nm (FBH1550-12, Thorlabs). The collimated light is split into two beams with a half-wave plate and a polarizing beamsplitter. The rotation angle of the half-wave plate is set to have a power ratio of 50:50 between the two output beams of the interferometer. While the beam in the reference arm is retro-reflected by a flat mirror, the other beam in the scan arm travels through the phase-controlled delay line and retro-reflected with a time delay. A quarter-wave plate inserted in each arm rotates the polarization of the reflected beam by 90 degrees, so that the recombined beams exit from the output port of the interferometer with orthogonal polarizations. The beams go through a gas cell containing either H12C14N (TT-HCN-1OOT-G-Q, triad technology) or 12C2H2 (TT-CH12-50T-G-Q, triad technology) in a two-way (round trip) geometry and detected by an InGaAs balanced photodetector (PDB415C-AC, Thorlabs). For balancing the photodiodes’ signals, a half-wave plate and a polarizing beamsplitter are used in front of the detector. The average power of the detected light is set to be 15 µW for each photodiode to avoid effects of detector nonlinearity. The detector signal is lowpass-filtered at 21 MHz when using the mode-locked laser. The signal is digitized by a data acquisition board (ATS9440, AlazarTech) at a sampling rate of 125 MS s−1. The digitized time domain data is segmented into independent interferograms and each of them is Fourier-transformed after the phase correction.

Code availability

The Matlab code used for analyzing the data of this study are available from the corresponding author upon reasonable request.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. 1.

    Griffiths, P. R. & De Haseth, J. A. Fourier Transform Infrared Spectrometry (John Wiley & Sons Inc., Hoboken, 2007).

  2. 2.

    Cossel, K. C. et al. Gas-phase broadband spectroscopy using active sources: progress, status, and applications. J. Opt. Soc. Am. B 34, 104–129 (2017).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Movasaghi, Z., Rehman, S. & Rehman, I. U. Fourier transform infrared (FTIR) spectroscopy of biological tissues. Appl. Spectrosc. Rev. 43, 134–179 (2008).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Geibel, M. C., Gerbig, C. & Feist, D. G. A new fully automated FTIR system for total column measurements of greenhouse gases. Atmos. Meas. Tech. 3, 1363–1375 (2010).

    CAS  Article  Google Scholar 

  5. 5.

    Gisi, M. et al. XCO2-measurements with a tabletop FTS using solar absorption spectroscopy. Atmos. Meas. Tech. 5, 2969–2980 (2012).

    CAS  Article  Google Scholar 

  6. 6.

    Kranendonk, L. A. et al. High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy. Opt. Express 15, 15115–15128 (2007).

    ADS  CAS  Article  Google Scholar 

  7. 7.

    Werblinski, T., Fendt, P., Zigan, L. & Will, S. High-speed combustion diagnostics in a rapid compression machine by broadband supercontinuum absorption spectroscopy. Appl. Opt. 56, 4443–4453 (2017).

    ADS  Article  Google Scholar 

  8. 8.

    Griffiths, P. R., Hirsche, B. L. & Manning, C. J. Ultra-rapid-scanning Fourier transform infrared spectrometry. Vib. Spectrosc. 19, 165–176 (1999).

    CAS  Article  Google Scholar 

  9. 9.

    Süss, B., Ringleb, F. & Heberle, J. New ultrarapid-scanning interferometer for FT-IR spectroscopy with microsecond time-resolution. Rev. Sci. Instrum. 87, 063113 (2016).

    ADS  Article  Google Scholar 

  10. 10.

    Häber, T., Schmitt, U. & Suhm, M. A. FTIR-spectroscopy of molecular clusters in pulsed supersonic slit-jet expansions. Phys. Chem. Chem. Phys. 1, 5573–5582 (1999).

    Article  Google Scholar 

  11. 11.

    Häber, T., Schmitt, U., Emmeluth, C. & Suhm, M. A. Ragout-jet FTIR spectroscopy of cluster isomerism and cluster dynamics: from carboxylic acid dimers to N2O nanoparticles. Faraday Discuss. 118, 331–359 (2001).

    ADS  Article  Google Scholar 

  12. 12.

    Manning, C. J., Palmer, R. A. & Chao, J. L. Step-scan Fourier-transform infrared spectrometer. Rev. Sci. Instrum. 62, 1219–1229 (1991).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Fleisher, A. J. et al. Mid-infrared time-resolved frequency comb spectroscopy of transient free radicals. J. Phys. Chem. Lett. 5, 2241–2246 (2014).

    CAS  Article  PubMed  Google Scholar 

  14. 14.

    Bjork, B. J. et al. Direct frequency comb measurement of OD + CO → DOCO kinetics. Science 354, 444–448 (2016).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Coddington, I., Newbury, N. R. & Swann, W. Dual-comb spectroscopy. Optica 3, 414–426 (2016).

    Article  Google Scholar 

  16. 16.

    Ideguchi, T. Dual-comb spectroscopy. Opt. Photonics News 28, 32–39 (2017).

    ADS  Article  Google Scholar 

  17. 17.

    Schliesser, A., Brehm, M., Keilmann, F. & van der Weide, D. W. Frequency-comb infrared spectrometer for rapid, remote chemical sensing. Opt. Express 13, 9029–9038 (2005).

    ADS  CAS  Article  PubMed  Google Scholar 

  18. 18.

    Coddington, I., Swann, W. & Newbury, N. R. Coherent multiheterodyne spectroscopy using stabilized optical frequency combs. Phys. Rev. Lett. 100, 013902 (2008).

    ADS  Article  PubMed  Google Scholar 

  19. 19.

    Deschênes, J. D., Giaccari, P. & Genest, J. Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry. Opt. Express 18, 23358–23370 (2010).

    ADS  Article  PubMed  Google Scholar 

  20. 20.

    Giorgetta, F. R., Coddington, I., Baumann, E., Swann, W. C. & Newbury, N. R. Dual frequency comb sampling of a quasi-thermal incoherent light source. In Conference on Lasers and Electro-Optics. paper CTuS3 (Optical Society of America, San Jose, 2010).

  21. 21.

    Bernhardt, B. et al. Cavity-enhanced dual-comb spectroscopy. Nat. Photonics 4, 55–57 (2010).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Boudreau, S. & Genest, J. Referenced passive spectroscopy using dual frequency combs. Opt. Express 20, 7375–7387 (2012).

    ADS  Article  Google Scholar 

  23. 23.

    Ideguchi, T. et al. Coherent Raman spectro-imaging with laser frequency combs. Nature 502, 355–358 (2013).

    ADS  CAS  Article  Google Scholar 

  24. 24.

    Rieker, G. B. et al. Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths. Optica 1, 290–298 (2014).

    CAS  Article  Google Scholar 

  25. 25.

    Ideguchi, T., Poisson, A., Guelachvili, G., Picqué, N. & Hänsch, T. W. Adaptive real-time dual-comb spectroscopy. Nat. Commun. 5, 3375 (2014).

    ADS  Article  PubMed  Google Scholar 

  26. 26.

    Villares, G., Hugi, A., Blaser, S. & Faist, J. Dual-comb spectroscopy based on quantum-cascade-laser frequency combs. Nat. Commun. 5, 5192 (2014).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    Millot, G. et al. Frequency-agile dual-comb spectroscopy. Nat. Photonics 10, 27–30 (2016).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Suh, M. G., Yang, Q. F., Yang, K. Y., Yi, X. & Vahala, K. J. Microresonator soliton dual-comb spectroscopy. Science 354, 600–603 (2016).

    ADS  CAS  Article  Google Scholar 

  29. 29.

    Link, S. M., Maas, D. J. H. C., Waldburger, D. & Keller, U. Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser. Science 356, 1164–1168 (2017).

    CAS  Article  Google Scholar 

  30. 30.

    Minamikawa, T. et al. Dual-comb spectroscopic ellipsometry. Nat. Commun. 8, 610 (2017).

    ADS  Article  PubMed  Google Scholar 

  31. 31.

    Dutt, A. et al. On-chip dual-comb source for spectroscopy. Sci. Adv. 4, e1701858 (2018).

    ADS  Article  PubMed  Google Scholar 

  32. 32.

    Lomsadze, B. & Cundiff, S. T. Frequency combs enable rapid and high-resolution multidimensional coherent spectroscopy. Science 357, 1389–1391 (2017).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  33. 33.

    Ycas, G. et al. High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm. Nat. Photonics 12, 202–208 (2018).

    ADS  CAS  Article  Google Scholar 

  34. 34.

    Muraviev, A. V., Smolski, V. O., Loparo, Z. E. & Vodopyanov, K. L. Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs. Nat. Photonics 12, 209–214 (2018).

    ADS  CAS  Article  Google Scholar 

  35. 35.

    Weiner, A. M. Femtosecond pulse shaping using spatial light modulators. Rev. Sci. Instrum. 71, 1929–1960 (2000).

    ADS  CAS  Article  Google Scholar 

  36. 36.

    Tearney, G. J., Bouma, B. E. & Fujimoto, J. G. High-speed phase- and group-delay scanning with a grating-based phase control delay line. Opt. Lett. 22, 1811–1813 (1997).

    ADS  CAS  Article  PubMed  Google Scholar 

  37. 37.

    Oldenburg, A. L., Reynolds, J. J., Marks, D. L. & Boppart, S. A. Fast-Fourier-domain delay line for in vivo optical coherence tomography with a polygonal scanner. Appl. Opt. 42, 4606–4611 (2003).

    ADS  Article  PubMed  Google Scholar 

  38. 38.

    Giaccari, P., Deschênes, J. D., Saucier, P., Genest, J. & Tremblay, P. Active Fourier-transform spectroscopy combining the direct RF beating of two fiber-based mode-locked lasers with a novel referencing method. Opt. Express 16, 4347–4365 (2008).

    ADS  Article  Google Scholar 

  39. 39.

    Forman, M. L., Steel, W. H. & Vanasse, G. A. Correction of asymmetric interferograms obtained in Fourier spectroscopy. J. Opt. Soc. Am. 56, 59–63 (1966).

    ADS  Article  Google Scholar 

  40. 40.

    Mertz, L. Auxiliary computation for Fourier spectrometry. Infrared Phys. 7, 17–23 (1967).

    ADS  Article  Google Scholar 

  41. 41.

    Porter, C. D. & Tanner, D. B. Correction of phase errors in Fourier spectroscopy. Int. J. Infrared Millim. Waves 4, 273–298 (1983).

    ADS  Article  Google Scholar 

  42. 42.

    Herres, W. & Gronholz, J. Understanding FT-IR data processing. Part 2: Details of the spectrum calculation. Intell. Instrum. Comput., Appl. Lab. 3, 10–19 (1985).

    Google Scholar 

  43. 43.

    Davis, S. P., Abrams, M. C. & Brault, J. W. Fourier Transform Spectrometry (Academic Press, San Diego, 2001).

    Google Scholar 

  44. 44.

    Savitzky, A. & Golay, M. J. E. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627–1639 (1964).

    ADS  CAS  Article  Google Scholar 

  45. 45.

    Gordon, I. E. et al. The HITRAN2016 molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transf. 203, 3–69 (2017).

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank Makoto Kuwata-Gonokami and Junji Yumoto for letting us use their equipment. We are grateful to Faris Sinjab, Venkata Ramaiah Badarla, and Miu Tamamitsu for their critical reading of the manuscript. This work was financially supported by JSPS KAKENHI (17H04852, 17K19071), JST PRESTO (JPMJPR17G2), Advanced Photon Science Alliance (APSA), Research Foundation for Opto-Science and Technology, and The Murata Science Foundation.

Author information

Affiliations

Authors

Contributions

T.I. conceived the work. K.H. and T.I. designed the system. K.H. conducted the experiment and analyzed the data. T.I. supervised the work. K.H. and T.I. wrote the manuscript.

Corresponding author

Correspondence to Takuro Ideguchi.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hashimoto, K., Ideguchi, T. Phase-controlled Fourier-transform spectroscopy. Nat Commun 9, 4448 (2018). https://doi.org/10.1038/s41467-018-06956-x

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing