Abstract: A system comprising a plurality of methods for measuring surfaces or wavefronts from a test part with greatly improved accuracy, particularly the higher spatial frequencies on aspheres. These methods involve multiple measurements of a test part. One of the methods involves calibration and control of the focusing components of a metrology gauge in order to avoid loss of resolution and accuracy when the test part is repositioned with respect to the gauge. Other methods extend conventional averaging methods for suppressing the higher spatial-frequency structure in the gauge's inherent slope-dependent inhomogeneous bias. One of these methods involve averages that suppress the part's higher spatial-frequency structure so that the gauge's bias can be disambiguated; another method directly suppresses the gauge's bias within the measurements. All of the methods can be used in conjunction in a variety of configurations that are tailored to specific geometries and tasks.