selfCorrectIGMs

This function corrects the timing and phase of dual-comb interferograms using information extracted from the interferograms only.

This function applies the self-correction algorithm described in [1] to a sequence of dual-comb interferograms (IGMs). It estimates and cancels both the time-varying frequency offset and frequency spacing of the resulting radio-frequency (RF) comb. This algorithm is best suited to correct slow fluctuations, i.e. slower than dfr/2. A discussion on the limits of the algorithm is given in [2].

The function expects an IGM sequence in the form of a pulse train, but it can be adapted to accept any form of quasi-periodic IGM sequence. It also expects that the IGM sequence was band-pass filtered such that a single RF comb alias remains. This comb alias should be fully contained in a single Nyquist zone, falling to zero at f=0 and f=fr/2.

At some steps of the algorithms, the function displays a figure and asks the user to make a verification and/or to enter a parameter to continue.

Inputs
IGMs: sequence of dual-comb interferograms to be corrected (band-pass filtered)
dfr: estimated repetition rate difference between the optical combs [Hz] (also corresponds to the IGMs' repetition rate)
fs: sampling frequency [Sa/s]
method: estimation method. Use either 'phase' or 'frequency'.
- Use 'frequency' if the carrier frequency noise PSD is at a high level and mostly bandlimited in f=[0 dfr/2]
- Use 'phase' if the carrier frequency noise PSD is at a low level and broadband

Outputs
correctedIGMs: corrected sequence of dual-comb interferograms
phi_f0: phase signal that was used to correct the RF comb's offset [rad]
phi_dfr: phase signal that was used to correct the RF comb's spacing [rad]
fs_new: new sampling rate after resampling [Sa/s]

References
[1] Hebert, N. B., Genest, J., Deschenes, J. D., Bergeron, H., Chen, G. Y., Khurmi, C., & Lancaster, D. G. (2017). Self-corrected chip-based dual-comb spectrometer. Optics Express, 25(7), 8168-8179.
[2] Hebert, N. B., Michaud-Belleau, V., Deschenes, J. D., & Genest, J. (2019) Self-Correction Limits in Dual-Comb Interferometry. Journal of Quantum Electronics, 55(4), 1-11.

Patent pending WO2018102915A1

Copyright 2019, Nicolas Bourbeau Hebert