A method for performing multi-heterodyne spectroscopy comprising the steps of: a) providing at least one multi-mode semiconductor laser comprising a first laser source (11; 12) and a second laser source (12; 11), further providing a detector having a detection bandwidth, wherein the first and second laser sources (12, 11) generate respective first and second laser beams, the first laser beam having multiple modes offset from a first offset frequency by integer multiples (n) of a first mode spacing (Δf 1) and the second laser beam having multiple modes offset from a second offset frequency by integer multiples (n) of a second mode spacing (Δf 2), wherein the first and second mode spacings are in the optical domain and almost equal to each other but differ by a difference frequency (Δf rep) in the radio frequency domain, b) passing at least one of the first and second laser beams through a sample, c) combining the first and second laser beams on the detector to generate a multi-heterodyne signal with a plurality of lines spaced by the difference frequency (Δf rep), d) setting the difference frequency (Δf rep) to lie within the detection bandwidth of the detector by tuning the first and second laser sources (12, 11) relative to each other, e) acquiring the multi-heterodyne signal from the detector by: (i) making a measurement of an individual spectrum; (ii) tuning the first and second laser sources (12, 11) to change the first and second offset frequencies by a fraction of the first and second mode spacings while keeping at least part of the multi-heterodyne signal within the detector bandwidth during said tuning; and (iii) making a further measurement of a further individual spectrum, and (iv) optionally repeating steps (ii) and (iii) a number of times, and f) combining the individual spectra into a combined spectrum, the combined spectrum having a resolution better than that of the individual spectra as a consequence of the individual spectra having data points that are offset from each other by less than the mode spacing, thereby to compensate for under-sampling. a) providing at least one multi-mode semiconductor laser comprising a first laser source (11; 12) and a second laser source (12; 11), further providing a detector having a detection bandwidth, wherein the first and second laser sources (12, 11) generate respective first and second laser beams, the first laser beam having multiple modes offset from a first offset frequency by integer multiples (n) of a first mode spacing (Δf 1) and the second laser beam having multiple modes offset from a second offset frequency by integer multiples (n) of a second mode spacing (Δf 2), wherein the first and second mode spacings are in the optical domain and almost equal to each other but differ by a difference frequency (Δf rep) in the radio frequency domain, b) passing at least one of the first and second laser beams through a sample, c) combining the first and second laser beams on the detector to generate a multi-heterodyne signal with a plurality of lines spaced by the difference frequency (Δf rep), d) setting the difference frequency (Δf rep) to lie within the detection bandwidth of the detector by tuning the first and second laser sources (12, 11) relative to each other, e) acquiring the multi-heterodyne signal from the detector by: (i) making a measurement of an individual spectrum; (ii) tuning the first and second laser sources (12, 11) to change the first and second offset frequencies by a fraction of the first and second mode spacings while keeping at least part of the multi-heterodyne signal within the detector bandwidth during said tuning; and (iii) making a further measurement of a further individual spectrum, and (iv) optionally repeating steps (ii) and (iii) a number of times, and (i) making a measurement of an individual spectrum; (ii) tuning the first and second laser sources (12, 11) to change the first and second offset frequencies by a fraction of the first and second mode spacings while keeping at least part of the multi-heterodyne signal within the detector bandwidth during said tuning; and (iii) making a further measurement of a further individual spectrum, and (iv) optionally repeating steps (ii) and (iii) a number of times, and f) combining the individual spectra into a combined spectrum, the combined spectrum having a resolution better than that of the individual spectra as a consequence of the individual spectra having data points that are offset from each other by less than the mode spacing, thereby to compensate for under-sampling.