Cylinder surface test with Chebyshev Polynomial Fitting Method

摘要

Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface .Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7 , a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented . Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment , it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms .The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.