Phase-correction algorithm for Fourier transform spectroscopy of a laser frequency comb

Fourier-transform spectrographs (FTS) are among the most important tools for high-resolution spectroscopy over a broad spectral bandwidth. Usually, the frequency axis of an FTS is calibrated with relatively few atomic lines and an absolute wavelength reference, which is often a stabilized He–Ne laser. Normally, the phase-spectrum is measured using a continuous light source to enable phase correction. Laser frequency combs (LFC) provide a much higher stability. Their spectrum consists of closely spaced narrow lines, which are very well suited for the characterization and calibration of an FTS. Due to the pulsed nature of the LFC, however, the phase spectrum cannot be measured in the same way as for continuous light sources. We show how a proper phase spectrum from an FTS measurement of an LFC can be obtained and how the strongly varying phase spectrum noise can be filtered. We analyzed a narrow spectral band 10.200–12.500  cm−1 in which we detected ∼60.000 lines with sufficient intensity. Only with an accurate truncation of the interferogram and a proper shifting, the complex structure of the phase spectrum is revealed. For phase filtering, we adapted Mertz’s algorithm and show how the instrumental line shape is significantly improved.