Methods, systems, and apparatus for spectrographic monitoring of a substrate during chemical mechanical polishing are described. In one aspect, a computer-implemented method includes storing a library having a plurality of reference spectra, each reference spectrum of the plurality of reference spectra having a stored associated index value, measuring a sequence of spectra in-situ during polishing to obtain measured spectra, for each measured spectrum of the sequence of spectra, finding a best matching reference spectrum to generate a sequence of best matching reference spectra, determining the associated index value for each best matching spectrum from the sequence of best matching reference spectra to generate a sequence of index values, fitting a linear function to the sequence of index values, and halting the polishing either when the linear function matches or exceeds a target index or when the associated index value from the determining step matches or exceeds the target index.