Abstract: A method for characterising instrument error in a surface measurement instrument, comprising obtaining first calibration measurement data representing a known surface form of a first reference object and obtaining second calibration measurement data representing a known surface form of a second reference object. At least a portion of the second calibration measurement data represents a measurement range that overlaps with at least a portion of a measurement range of the first calibration measurement data. A common error function is obtained that characterises the instrument error.

Abstract: A computer implemented method of determining the surface shape of an aspheric object using a metrological apparatus includes positioning the object on a support surface of a turntable so that an axis of the object is tilted with respect to the axis of rotation of the turntable; using a measurement probe to make a first measurement of the object; rotating the turntable; after rotation of the turntable, using a measurement probe to make a second measurement of the object, diametrically opposite the first measurement, estimating a first angle based on fitting the first measurement data using a surface model including: a dependency on the axis tilt angle and a dependency on the radius of the base of the object; estimating a second angle based on fitting the second measurement data to the surface model; and determining the tilt angle based on the first angle and the second angle.