A substrate may be loaded onto a chemical mechanical polishing (CMP) apparatus, which includes a polishing pad and a wafer carrier that holds the substrate. The wafer carrier includes a backside plate, a wafer carrier frame, and at least one optical vertical displacement measurement unit that includes a respective laser source and a respective pixelated image sensor. A total reflection geometry is used to reflect a laser beam off a top surface of the backside plate. A polish rate or a polish thickness of a polished portion of the substrate may be measured at each location underneath at least one reflection point during the CMP process.