Non-null lateral shearing interferometric testing of aspheric surface and wavefront reconstruction

Three typical asphericities and their corresponding variation rate, adjustment error, retrace error and interferometer systematic error in non-null aspheric surface testing were analyzed in this paper to propose that the variation rate of asphericity is the main factor affecting testing error and then give the method of determining surface machining error. A comparative study on the least square method and the coefficient conversion method which were based on the Zernike polynomials fitting was made to analyze the influence of shear value and the polynomials fitting order on wavefront reconstruction accuracy, and give the numerical simulation results. In order to verify the feasibility and testing accuracy of the above methods, the non-null lateral shearing interferometric testing was performed on a parabolic reflector surface generated by single point diamond turning process. During the testing, a vertex sphere was used as a testing wavefront and the least square method was used for wavefront reconstruction. Experimental results show that the largest form error of 0.203 μm was located near the edge of the reflector where the variation rate of asphericity was at the maximum value. The study provides a very decisive technical support for the application of lateral shearing interferometer to in-situ testing aspheric surface during machining process.