1. A method of operating a polishing system, comprising: polishing a substrate at a polishing station, the substrate held by a carrier head during polishing; transporting the substrate to an in-sequence optical metrology system positioned between the polishing station and another polishing station or a transfer station; measuring a plurality of spectra reflected from the substrate with a probe of the optical metrology system while moving the carrier head to cause the probe to traverse a path across the substrate and while the probe remains stationary, the path across the substrate comprising either a plurality of concentric circles or a plurality of substantially radially aligned arcuate segments; and adjusting a polishing endpoint or a polishing parameter of the polishing system based on one or more characterizing values generated based on at least some of the plurality of spectra.