A process for planarizing, polishing, or providing other modification of a wafer surface or other workpiece. The process includes using an abrasive article having a textured abrasive coating affixed to a backing. The abrasive article includes a monitoring element, such as a window, to allow transmission of radiation therethrough. The radiation level is monitored throughout the planarization process to determine the approach of the desired endpoint. The window in the abrasive coating can be an area devoid of abrasive coating or having minimal or a thinned abrasive coating.