Research On Fringe Reflection Technology For Surface Shape Of Free-form Surface

Free-form surface optical elements have become a research hotspot at home and abroad because they have more design freedom,which can enhance the system property and facilitat its structure.At the same time,however,many surface degrees of freedom make the surface shape detection very difficult.At present,most of the precision optical free-form surface detection methods still use the aspheric surface detection method.As an effective optical detection method,the fringe reflection has simple structure,fast measurement speed and is not limited by the geometrical shape of the optical element under test,which provides a new idea for the measurement of aspheric surface and free-form surface.In this dissertation,the fringe reflection detection of free-form surface topography is taken as the ultimate goal.The current research status of free-form surface detection and fringe reflection mirror surface detection is described,and the fringe reflection method is deeply studied.Firstly,the physical model of the detection system is established by deducing the mapping relation between phase and gradient,then the theoretical calculation formulas of each parameters of the system are given.It has a high resolution of nm and a dynamic range of up to one million.Secondly,the calibration technology of fringe reflection detection system is studied.Based on the calibration principle of 2D plane calibration target,the internal and externalparameters of the CCD camera are calibrated.The re-projection error RMS is 0.06 pixel.According to the calibration result of the camera,the spatial position calibration of the reference plane and the LCD display screen are carried out respectively,and the calculation method of the system geometric parameters is given.Then,three commonly used gradient data integration methods,cross-path integration method,Fourier transform integration method and regional wavefront reconstruction method,are analyzed.A surface reconstruction method based on Zernike orthogonal polynomial is studied.The effects of different items and sampling points on the reconstruction results are analyzed,then select the first 36 coefficients of Zernike and 300 sampling points for simulation measurement.Take hyperboloid as an example to verify the validity of the algorithm and analyze the change of noise level.The simulation results show that the PV value of the fitting surface residual is 2.6645e-15 mm,the RMS value is 4.6616e-16 mm,and when the noise is less than 15%,it has good applicability.Finally,an experimental system is set up with a transverse resolution of 107 um and a field of view of about 132 mm × 98 mm.The system is used to measure a planar mirror,a concave spherical mirror and a free-form surface respectively.The PV and RMS values of the planar mirror reconstruction result are about 332 nm and 74 nm respectively,which are close to the measured values of Zygo interferometer.The measurement error between the PV of the concave spherical mirror and its nominal height is about 10%.At the same time,the measurement system built in this paper can recover the surface of the free-form surface.The results show a feasibility of the fringe reflection method for free-form surface topography detection,which provides a reference for the processing and evaluation of higher precision free-form surface optical elements in the future.