Research On Surface Error Measurement Of Quadratic Cylinder Mirrors

The quadratic cylinder refers to the cylinder whose section curve is a quadratic curve,including cylindrical surface,elliptical cylindrical surface,hyperbolic cylindrical surface,and parabolic cylindrical surface.Due to the dual curvatures of quadratic cylinder,it is often used for correcting astigmatic aberration,line focusing,and line imaging,and has become a typical component in systems such as synchrotron radiation systems,laser shaping devices,and X-ray telescope systems.The machining of such ultra-precision optical elements requires the support of ultra-precision measurement.The null compensating test is a common method for ultra-precision measurement of cylindrical optics.It requires the use of a computer generated hologram(CGH)or a cylindrical lens to produce a standard cylindrical wavefront.However,the null compensating test can only achieve a “one-to-one” test,which is less flexible and less efficient.Moreover,limited by the production aperture of compensator and the relative aperture of the wavefront,it cannot meet the requirements for large aperture cylinders.The long production cycle and high production cost of the compensator also results in a huge waste of time and economic costs.In this paper,the cylindrical sub-aperture stitching testing method is studied to realize measurement of large aperture or large numerical aperture cylinders.At the same time,in order to explore the general test of the quadratic cylinder surface measurement,methods of sub-aperture stitching for large aperture acylinders based on near-null testing and quadratic non-cylindrical partial compensation testing method are proposed.The research content of the thesis includes the following three parts:1.Sub-aperture stitching testing for cylindrical mirrors.Based on the principle of cylindrical sub-aperture stitching test,a sub-aperture stitching testing system is designed and built to realize the measurement of large-aperture cylindrical mirrors.The improved aspherical subaperture stitching algorithm is suitable for cylindrical stitching,which realizes the sub-aperture stitching of the cylindrical mirrors under the sagittal direction and the tangential direction.The stitching result comparison verifies its correctness and precision.The testing capability of the sub-aperture stitching testing system is analyzed,and verified by simulation and measurement experiment.The test results were used to guide the machining,and the surface shape error gradually converges.This shows that the sub-aperture stitching testing system has good repeatability and accuracy.2.Subaperture stitching test for large aperture mild acylinders.In order to realize the economical and fast test of the large-aperture mild cylindrical surface error with small deviation from the cylindrical surface,a method of subaperture stitching for large aperture acylinders based on near-null test is proposed.The wavefront generated by the cylindrical CGH is used to compensate most of the normal aberration of the acylindrical surface,and then the residual wavefront aberration is corrected by ray tracing and simulation,so as to realize flexible measurement of acylindrical surfaces with different parameters.It solves the problems of high cost,long production cycle and limited applicability to a single surface.The cross test experiment shows that the proposed method is flexible,and has high precision.3.Partial compensation testing for quadratic non-cylinders based on cylindrical lens.In order to explore general quadratic cylinder test and realize the test of the quadratic acylinder with large deviation from the cylinder,partial compensation testing for quadratic acylinder based on cylindrical lens which has high flexibility,wide applicability and low cost is proposed.Plano-convex cylindrical lens compensator can convert parallel beams into acylindrical wavefronts changing with the propagation distance along the optical axis,which can be used for the test of different acylinders.Simulation and experimental results verify the correctness and accuracy of the proposed method.