Methods are provided for estimating a surface profile of a sample in an interferometer having a broad bandwidth light source. The interferometer detects interference pattern intensity data over a series of frames of a relative scan between the sample and a reference surface. Particular methods comprise, for each location (x,y) of interest on the sample: determining an envelope of the detected interference pattern intensity data corresponding the location (x,y) of interest based on amplitudes of the detected interference pattern intensity data; determining a rough estimate zrough of the surface profile of the sample at the location (x,y) of interest based on the envelope; estimating a phase offset θ of the detected intensity data using a curve fitting optimization process to fit the detected intensity data to a broad bandwidth interference model; and refining the rough estimate zrough of the surface profile using the phase offset θ to obtain a fine estimate zfine of the surface profile of the sample at the location (x,y) of interest, the fine estimate zfine having improved resolution over the rough estimate zrough. Similar methods are used for characterizing films applied to substrates.