A method for obtaining high-accuracy measurements of surfaces or wavefronts of a part with underlying symmetry in a design prescription, the method being performed using a metrology system including a part-positioning means and a wavefront measuring gauge, the method comprising the steps of: a) acquiring a plurality of measurements at different relative positions of said part and gauge, b) performing the following steps: i) determining said gauge's optimal focus position for each of said measurements using knowledge of the local curvature of each test wavefront in said design prescription and gauge calibration constants; and ii) calibrating systematic gauge wavefront error in said measurements, by averaging those of said measurements having the same test conditions of said gauge and the positions of said measurements follow said symmetry, such that those gauge measurements at all of said different relative positions would be identical if said part were perfectly matched to said design prescription; c) performing at least one of the following steps: i) reducing uncalibrated error by averaging said measurements obtained at the same nominal location of the part, but where two or more of said measurements have different orientations relative to said gauge; and ii) reducing uncalibrated error by stitching said measurements together, where low spatial frequency information in said measurements is explicitly filtered out or compensated implicitly with free compensators. a) acquiring a plurality of measurements at different relative positions of said part and gauge, b) performing the following steps: i) determining said gauge's optimal focus position for each of said measurements using knowledge of the local curvature of each test wavefront in said design prescription and gauge calibration constants; and ii) calibrating systematic gauge wavefront error in said measurements, by averaging those of said measurements having the same test conditions of said gauge and the positions of said measurements follow said symmetry, such that those gauge measurements at all of said different relative positions would be identical if said part were perfectly matched to said design prescription; i) determining said gauge's optimal focus position for each of said measurements using knowledge of the local curvature of each test wavefront in said design prescription and gauge calibration constants; and ii) calibrating systematic gauge wavefront error in said measurements, by averaging those of said measurements having the same test conditions of said gauge and the positions of said measurements follow said symmetry, such that those gauge measurements at all of said different relative positions would be identical if said part were perfectly matched to said design prescription; c) performing at least one of the following steps: i) reducing uncalibrated error by averaging said measurements obtained at the same nominal location of the part, but where two or more of said measurements have different orientations relative to said gauge; and ii) reducing uncalibrated error by stitching said measurements together, where low spatial frequency information in said measurements is explicitly filtered out or compensated implicitly with free compensators. i) reducing uncalibrated error by averaging said measurements obtained at the same nominal location of the part, but where two or more of said measurements have different orientations relative to said gauge; and ii) reducing uncalibrated error by stitching said measurements together, where low spatial frequency information in said measurements is explicitly filtered out or compensated implicitly with free compensators.