A method for measuring a structure that contains overlying and underlying films in a region where the overlying film's thickness rapidly decreases until the underlying film is exposed (e.g., an edge-exclusion structure). The method includes the steps of: (1) exciting acoustic modes in a first portion of the region with at least one excitation laser beam; (2) detecting the acoustic modes with a probe laser beam that is either reflected or diffracted to generate a signal beam; (3) analyzing the signal beam to determine a property of the structure (e.g., the thickness of the overlying layer) in the first portion of the region; (4) translating the structure or the excitation and probe laser beams; and (5) repeating the exciting, detecting, and analyzing steps to determine a property of the structure in a second portion of the region.