A data conversion technique for accurate interferometric testing of spherical surfaces

This paper presents a Cartesian to polar conversion technique based on a polynomial interpolation. The method is used for the processing of data from the two-orientation method for measuring spherical surfaces with an interferometer. The interferometer output consists of points on a square-grid coordinate system, which are then converted to a polar-grid coordinate system. The profile height data of the points on the polar-grid are calculated from a polynomial neighborhood analysis of points on the square-grid. Since the converted point on the polar-grid does not need to be at the center of the points in the analysis, profiles along concentric circles near to the edge of the test surface can also be calculated. A simulation of the polynomial and conventional 4-point techniques is carried out to verify the process. The comparison shows that the polynomial technique has produce a higher data conversion accuracy. Experiments on a phase-measuring interferometer were also conducted to verify the approach.