The Research On The Application Of Chebyshev Polynomial In Computer-aided Alignment Of The Cylindrial System

The focal power of the cylinder surface in meridian section and the sagittal section are different.This optical characteristic makes this optical element widely used in kinds of optical systems,but also restricts the use of the traditional computer-aided adjustment scheme in the cylindrical optical system.Zernike polynomials are used to fit the wavefront aberration that represents the system quality in the traditional computer-aided adjustment scheme.Since the Zernike polynomials are orthogonal in the circular domain and also have correlationship with the aberrations caused by misalignment and the Seidel aberration,the model of the obtained fitting coefficients and misalignments can be built to help adjust the optical system.But for the optical system which contains such optical lens with rectangular aperture and single-direction focal power as cylinder surface,it is necessary to find polynomials to replace the Zernike polynomials for fitting the wavefront aberration,a polynomial which can separate aberrations in two orthogonal directions.In this paper,based on the computer-aided adjustment of the cylindrical surface test with computergenerated hologram method,the Chebyshev polynomials are chosen to replace the traditional Zernike polynomials to fit the wavefront aberration in view of the problem that Zernike polynomials do not suitable for the rectangular wavefront aberration fitting.And a computer-aided adjustment model is established to guide the cylinder surface adjustment.The specific research contents are summarized as follows:1.The existing testing methods and characteristics of cylindrical surfaces are introduced,and the development of computer-aided alignment technology at home and abroad is described.We investigate the use of wavefront fitting methods in non-circular aperture system,which set a foundation for future research.2.The principle of computer aided adjustment is expounded.After comparing the way Chebyshev polynomials and Zernike polynomials represent the wavefront aberration,the Chebyshev polynomial is selected to establish the computer aided adjustment model.And the scheme is applied to the numerical simulation of the adjustment of a cylindrical surface testing system.The simulation results verify the feasibility of the scheme.3.Corresponding to a cylinder surface with certain parameter,we design cylinder surface testing system with computer-generated hologram method.According to the phase parameters of the hologram designed,the detection and calibration parts of the hologram are drawn,and the amplitude-type CGH in the case system is produced by using the laser direct writing technique.4.Setting up the experimental platform for cylinder test.A cylindrical surface testing system is built with the computer-generated hologram and Zygo interferometer.The experimental results show that using the computer-aided adjustment model with Chebyshev polynomials can make the adjust process easier and more smooth.