Absolute testing of optical flats using minimum norm least squares solutions

Abstract

A laser Fizeau interferometer measures surface form by comparing the wavefronts reflected from a reference surface and the surface under test. The measurement accuracy is limited by the unknown absolute form error of the reference flat. Absolute testing offers a strategy to break through the limitation. In this work, we propose a three-flat absolute testing method using minimum norm least squares solutions (MNLS). After acquiring three measurement sets from pairwise combinations among the flats, one flat is rotated by 90° or 180° for the fourth measurement. The simulation demonstrates the effectiveness of the proposed MNLS method and its robustness against rotational angle errors. Our absolute testing method is experimentally validated using a home-built and a commercial Fizeau interferometers. Correcting the absolute forms of the home-built Fizeau interferometer’s reference flat improves its measurement accuracy. The experimental outcomes of the MNLS absolute testing technique are compared with two alternative absolute testing methods. The MNLS method’s advantage is demonstrated.