Analysis of absolute testing based on even-odd functions by Zernike polynomials

Abstract

Recently most of modern absolute measurement methods rotate the flat or sphere in the interferometer. So it is very important to exactly know how some errors such as angle rotation error, center excursion error influence the metrology. This paper analyses these errors how to influence testing accuracy by Zernike based on Even-Odd functions. We review traditional absolute testing of flats methods and emphasize the method of even and odd functions. The flat can be expressed as the sum of even-odd, odd-even, even-even and odd-odd functions. Through six measurements the profile of the flat can be calculated. We use 36 Zernike polynomials in polar coordinates to analysis the method. The polynomials can be separated by even-odd, odd-even, even-even and odd-odd parts. We substitute polynomials for surface data and change the arithmetic. Then we can analyze the every surface error data and exactly know the calculate accuracy of every term through the arithmetic. The results of errors analyze by means of Matlab are shown that how the angle rotation error to influence the accuracy. The errors analysis can also be used in other interferometer systems which have the motion of the coordinate system.