1. A method of optically monitoring a substrate during polishing, comprising: receiving an identification of a selected spectral feature and a characteristic of the selected spectral feature to monitor during polishing; measuring a first spectrum from the substrate during polishing, the first spectrum measured within an initial time following initiation of polishing; measuring a sequence of second spectra from the substrate during polishing, the sequence of second spectra measured after the initial time; for each second spectrum in the sequence of second spectra, removing the first spectrum from the second spectrum to generate a sequence of modified third spectra; determining a value of a characteristic of the selected spectral feature for each third spectrum in the sequence of third spectra to generate a sequence of values for the characteristic; and determining a polishing endpoint or an adjustment for a polishing rate based on the sequence of values.