Methods and apparatus for controlling the removal of material from microfeature workpieces in abrasive removal processes. An embodiment of such a method comprises irradiating a periodic structure of the workpiece and obtaining an intensity distribution of radiation returning from the periodic structure. The workpiece can be irradiated with a wide spectrum of wavelengths (e.g., white light), or the workpiece can be irradiated with a laser or lamp at specific wavelengths. The intensity distribution can be an image or other signal from which a dimension or other physical parameter of the periodic structure can be determined. For example, the intensity distribution can be an intensity signal of radiation returning from the workpiece in a selected bandwidth (e.g., 200 nm-900 nm) or an image of a diffraction pattern of radiation that has been scattered by the periodic structure. The method further includes outputting a control signal based on the obtained intensity distribution. For example, the control signal can be an endpoint signal indicating the actual endpoint of the abrasive removal process.