An algorithm for stitching together a set of individual phase measurements into a unified larger phase map is presented. The set of individual phase maps results from scanning a component over the interferometer aperture and acquiring a measurement at each position. The algorithm is based on an iterative approach, where singular value decomposition is used to solve the rigid body movement problem between the different phase maps. The algorithm has been tested in numerical experiments and has been successfully applied to real data. © 2002 Society of Photo-Optical Instrumentation Engineers.