An absorption spectroscopy instrument with a light source for providing a beam of light, a modulator to produce a modulated beam of light, a high finesse optical cavity, means for injecting the modulated beam of light off-axis into the high finesse optical cavity and a detector positioned to receive and measure light exiting through said optical cavity. The detector may be a highly sensitive and high bandwidth detector. The modulator may be a one or two-tone modulator having means, such as a plurality of RF synthesizers, for modulating the light source by one or two tones. If one tone of applied modulation is used, the frequency is larger than the absorption bandwidth of the target chemical. In the case where two tones are used, the first frequency is larger than the absorption bandwidth of the target chemical and the second frequency is small relative to the first frequency.