Research On Specular 3D Shape Dynamic Measurement Method Based On Fringe Reflction

With the rapid development of science and technology,optical mirrors are increasingly used in the fields of space optics and precision manufacturing,which places higher demands on the surface shape processing and inspection technology of optical mirrors.As a noncontact measurement method,the fringe reflection mearurement method does not cause damage to the mirror surface during measuremen and also has the advantages of full-field,high accuracy and economic stability,and has become a very mature three-dimensional(3D)shape measurement method after extensive research by scholars in recent years.Measurement accuracy and measurement speed are two indicators for evaluating measurement methods.At present,the fringe reflection measurement method is capable of achieving high accuracy and fully satisfies the requirements of static measurement scenarios.However,if it is to be applied to the dynamic measurement,the study needs to focus on improving the measurement speed.This paper focuses on the method that using singleframe fringe image to measure 3D shapes,and presents a detailed study of the encoding of fringe,the demodulation of phases from single-frame stripe image,the reconstruction of 3D shape and the errors caused by multiple optical channels.Firstly,the paper introduces the basic principles and system arrangement of the fringe reflection measurement method.the calibration involved in the measurement process is analyzed and summarized.The calibration is divided into the calibration of camera,the calibration of reference plane and the calibration of monitor.The classical Zhang’s calibration method is used to calibrate the internal and external parameters of the camera;the reference plane is calibrated using a checkerboard grid target,which is done simultaneously with the calibration of the camera;the monitor is calibrated using a codegenerated dot target.After calibrating the position of the virtual monitor in the camera coordinate system,then obtains the position of the real monitor in the camera coordinate system through the symmetry relationship.Secondly,a phase demodulation method and a 3D reconstruction method suitable for dynamic measurements are presented.Combining the Hilbert transform and the Lissajous ellipse fitting to solve the folded phase,which can meet the requirements of solving the phase of a single frame image without the process of pre-filtering so that the phase is solved with high accuracy and fast.Expanding the phase at the highest quality pixel with a highreliability value at first,and finally expanding the phase at the lowest quality pixel with the lowest reliability value to prevent error propagation.And the key of 3D shape reconstruction is to convert phase information into gradient information,and convert gradient information into height information.In this paper,the regional wavefront reconstruction method is used to reconstruct 3D shape.Otherwise,a dynamic measurement method based on multi-optical channels is proposed,in which all phase information of the surface to be measured can be obtained by taking only one image of the stripes encoded in red and blue channels.A compensation scheme is proposed to address the problems of color aberration and crosstalk associated with color coding.The root-mean-square value of the phase deviation caused by the color difference is reduced from 0.200 rad to 0.016 rad after compensation;the crosstalk causes intensity leakage between different colors,and the coupling coefficient from the red channel to the blue channel is reduced from 0.023 to 0.005,and from 0.018 to 0.007 for the blue channel to the red channel after compensation.Finally,a color orthogonal fringe reflectometry system was built according to the measurement principle and the 3D surface shapes of concave spherical reflector,planar reflector and the real-time positions of silicon wafer are measured.After least-squraes fitting of the results of 3D surface shapes,the residuals’ peak-to-valley value and root-mean-square value of the concave spherical mirror are 803.3 nm and 89.7 nm,respectively,the PV value and RMS value of the planar mirror are 652.4 nm and 72.8 nm.The distribution of the fitted residual diagram is similar to that obtained by the Zygo interferometer,which proved that the system and measurement method in this paper could meet the accuracy requirements.In addition,the real-time positions of the silicon wafer at different times are measured,and the results showed that the system and measurement method can achieve dynamic measurements.