The present invention relates to a method and an apparatus to perform frequency comb spectroscopy. The method includes: —Arranging a waveguide optical cavity (3) having a plurality of cavity mode frequencies with a cavity mode frequency spacing (FSR), said waveguide optical cavity being dispersive so that the frequency spacing of the cavity modes is wavelength dependent; —Arranging a sample (S) with respect to the waveguide optical cavity (3) so that the sample is capable of absorbing light travelling into the waveguide optical cavity; —Coupling pulsed light coming from a light source (1) into the waveguide optical cavity (3), the source light including source comb frequencies (OCF) with a source frequency spacing (RR), the coupled light including an interval of frequencies centered on a main frequency of said comb frequencies due to cavity dispersion; —Locking the waveguide optical cavity to the frequency comb at said main optical frequency; —Detecting transmitted cavity frequencies; —Determining absorption by said sample (S) of said main optical frequency from the detected transmitted frequencies, —Changing the cavity mode frequency (FSR) spacing or the source frequency spacing (RR); —Coupling the pulse light to the waveguide optical cavity (3), the coupled light including an interval of frequencies centered on a second main frequency of said comb frequencies due to cavity dispersion; —Locking the waveguide optical cavity to the frequency comb at said second main optical frequency; —Detecting transmitted cavity frequencies; —Determining absorption by said sample of said second main optical frequency from the detected transmitted frequencies.