We demonstrate balanced-detection dual-comb spectroscopy using two free-running mechanical sharing dual-comb fiber lasers assisted by an all-computational digital phase correction algorithm. The mutual coherence between the combs allows us perform mode-resolved spectroscopy of gaseous hydrogen cyanide by digitally compensating residual timing and offset frequency fluctuations of the dual-comb signal. Setting the repetition rate difference between the combs to 500 Hz (1.5 kHz) yields more than 2000 resolved radio frequency comb lines after phase correction in a 3-dB bandwidth centered at 1560 nm of wavelength. Through coadding the corrected interferograms, we obtain a single time-domain trace with a signal-to-noise ratio (SNR) of 6378 (13 960) and 12.64 (13.77) bits of dynamic range in 1 s of averaging. The spectral SNR of the coadded trace reaches 529 (585), corresponding to a figure of merit of SNR of 1.3 × 106 (1.4 × 106). The measured absorption spectrum of hydrogen cyanide agrees well with the HITRAN database.

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