Interferometric radius of curvature measurement

Abstract

The current state-of-the-art for measuring the radius of curvature involves an interferometer, a slide rail, and a distance measuring interferometer or digital radius slide. Using these components it is possible to implement a noncontact spherometer. This technique involves positioning the optic under test at two positions: cat’s eye and confocal. First, the optic is placed so that the transmission sphere is focused on the surface of the part, the cat’s eye position. At the cat’s eye position, the distance is recorded using the distance measuring interferometer. Also, an interferometric measurement is made that will indicate the precision in determining the position of the element relative to the focus point of the transmission sphere. Next, the test optic is moved so that the focus of the transmission sphere is at the center of curvature, the confocal position. At the confocal position, the distance is recorded using the distance measuring interferometer once again. A measurement is acquired at this position that provides a sensitive indicator of where the radius of curvature coincides with the focus of the transmission sphere as well as information about the surface figure and irregularity. Once the optic is tested in both cat’s eye and confocal positions, the distance between the two positions may be calculated. Furthermore, nulling errors or the deviation of the test optic from its best focus at each position may be calculated by using the interferometer data. The sources of error using this technique include unmeasured or erroneous measured motion, alignment errors, nulling errors, and environmentally induced positional drift. However, since the wavefront at each position is known and the axial focus error at each position is calculated, knowledge of the numerical aperture at each position allows computation of a corresponding nulling error. This compensates for the error incurred by not precisely positioning the surface at the cat’s eye or confocal position. Using these techniques, measurement to a few parts per million can easily be made.