Separation of form from orientation in 3D measurements of aspheric surfaces with no datum

Abstract

Measurement and characterisation of 3D form to maintain manufacturing quality has particular problems in cases such as lenses which do not generally have a clear measurement datum. A 3D-form measurement includes information about the form, the orientation and the position of the surface under test. Orientation and position can be design parameters or may result from misalignment of the test specimen on a measurement table. In either case, it is necessary to separate form from orientation and position if the data-set is to be fitted and compared with an “ideal” surface. In this paper two pre-processing algorithms are presented and examples given of the separation of form from orientation and position. The algorithm is applied to simulated data-sets consisting of up to 26,000 discrete points on a square grid, simulating the measurement of an aspheric lens in 3D. The rotationally symmetric data-set is translated for a distance x 0, y 0 and z 0 and rotated about two axes, x and y, to simulate misalignment. To simulate inaccuracies from a manufacturing process, normally distributed random noise is superimposed on the ideal surface. An application of pre-processing using a real data-set is also shown. Furthermore, form fitting is addressed and the interpretation of form by decomposition of the data into error types is discussed.