In this series:

While working on my master’s degree

[1], I developed a real-time processing system for a dual-comb spectrometer [2]. Due to the high-speed and continuous nature of the data, the system used an FPGA board and an analog-to-digital converter (ADC) card for processing.

In this blog post, I briefly explain the application and the high-speed processing solution. In my next post, I’ll discuss the interfaces and codes required to achieve the solution and how Nutaq’s platforms can speed up the development time.

Dual-comb spectroscopy

The use of two frequency comb lasers (pulsed lasers) with slightly different repetition rates creates a linearly increasing delay between each pulse pair. In a dual-comb spectrometer, one comb can probe an optical sample (a gas cell or an optical cavity, for example) and the result is then probed by the second laser.

Figure 1: The dual-comb spectroscopy setup

Figure 1: The dual-comb spectroscopy setup

This mixing generates an interferogram (IGM) at the detector’s output. The IGM envelope represents the impulse response of the optical sample cross-correlated with the lasers’ pulse envelopes. The setup enables the retrieval of the impulse response of the optical sample even if it is at a much higher frequency than the analog-to-digital converter recording the IGM. For example, the optical sample impulse response can be in the THz spectral region while the ADC can operate in the MHz range to digitize the IGM.

This setup is comparable to the approach used in a high-speed oscilloscope. Known as Equivalent Time Sampling, it uses different time delays to sample a repetitive signal.

Figure 2: Equivalent time sampling [3]

Figure 2: Equivalent time sampling [3]

In dual-comb spectroscopy, the first comb probing the optical sample generates the repetitive signal and the second comb samples the signal at different delay corresponding to the first comb’s pulse.

Figure 3: Equivalent time sampling in dual-comb spectroscopy

Figure 3: Equivalent time sampling in dual-comb spectroscopy

Unfortunately, the frequency combs are not perfect and their instability can affect the resulting IGM. The laser repetition rate can vary as well as the phase of the pulses. These parameters will have an effect on the resulting IGM. To correctly reconstruct the impulse response of the optical sample using the Equivalent Time Sampling approach, the signal must be repetitive. If there are variations, the quality of the resulting IGM will deteriorate.

One way to alleviate the frequency comb instability is to track the parameters using stable continuous wave (CW) lasers and then applying a post-processing algorithm on the recorded IGM based on the reference signals [4]. Two CW lasers are required. The CW lasers are mixed with each frequency comb to generate a total of four reference signals, as shown in Figure 4.

Figure 4: Equivalent time sampling in dual-comb spectroscopy

Figure 4: Dual-comb spectroscopy system referenced by CW lasers

All five of the analog signals can be digitized using an acquisition card. The ADC nominal operation frequency in this setup was 100 MHz. At this sampling speed, the internal memory of the acquisition card (several gigabytes) was filled within a few seconds. A few hours can be required by a general-purpose computer to process the amount of data taken within a few seconds.

This post-processing solution has some drawbacks, namely the limited record time and the long delay before a user can see the impulse or spectral response of the optical sample. To eliminate these drawbacks, the data can be processed in real-time by an FPGA and the IGMs continuously averaged to increase the measure quality. This results in a turnkey system that instantaneously provides corrected IGMs with a high signal-to-noise ratio due to the absence of boundary on the measurement time.

Conclusion

This real-time processing and averaging system was my master’s degree project. In my next blog post, I will explain how it was successfully developed using Nutaq’s MI250 and the ML605 FPGA development board from Xilinx.

1. J. Roy, “Correction et moyennage temps-réel pour mesures interférométriques par peignes de fréquence”, Maître ès sciences (M. Sc.) (2013) http://www.theses.ulaval.ca/2013/30065/
2. S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27(9), 766–768 (2002).
3. Tektronix, http://www.cbtricks.com/miscellaneous/tech_publications/scope/sampling.pdf
4. J.-D. Deschênes, P. Giaccarri, and J. Genest, “Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry,” Opt. Express 18(22), 23358–23370 (2010).