Dual-comb Fourier-transform spectroscopy takes advantage of an interferometer without moving parts. Interferences pattern between two femtosecond frequency combs, broadband laser sources whose spectra consist of evenly-spaced narrow lines, is measured. The measurement time and the spectral resolution are significantly improved compared to traditional Fourier spectrometers. However, the required short-term stability of the combs cannot be achieved by classic locking methods. Until now, no high-quality spectra could be recorded within a very short acquisition time. This thesis reports on the development of a real-time correction method able to compensate for the combs’ residual fluctuations and to restore non-distorted spectra. This analog technique does not require any locking system or a posteriori calculation. Its performance is demonstrated in the near-infrared (1.5 µm) and in the visible (520 nm) with fiber-based femtosecond lasers. Doppler-limited molecular spectra spanning 12 THz are measured within 500 µs. They are in excellent agreement with databases. For the first time, the full potential of dual-comb spectroscopy is demonstrated. The mid-infrared region is an attractive spectral range for molecular spectroscopy due to the molecules’ strong and characteristic absorptions. Therefore, extending dual-comb spectroscopy to this region is the next goal to achieve. Toward this goal, a comb emitting around 3 µm is characterized. It is based on the non-linear difference frequency generation from an erbium oscillator spectrally broadened with a highly non-linear fiber.
