Envelope functions for modulation spectroscopy

A spectrometer and spectrometry method comprising modulating a light source with a carrier waveform multiplied by an envelope function, directing light from the light source through a sample region and to a photodetector, and demodulating current from the photodetector at a reference frequency. Also a method for computing a modulation waveform comprising specifying a target detection efficiency in a Fourier space, computing a response of a waveform that comprises a carrier wave multiplied by an envelope function, and modifying the envelope function using nonlinear optimization means to minimize a difference between the computed response and a predetermined target gain spectrum.