Shape Measurement Of Thin Foil X-ray Mirror Based On Stereo Phase Measuring Deflectometry

X-ray thin foil mirror is the core component of the nested X-ray grazing incidence telescope and its surface shape accuracy directly determines the imaging resolution or energy concentration of the optical system.Although the surface shape of the X-ray thin foil mirror is usually a quadric surface of rotation symmetry,the surface shape gradient in the optical axis direction is large,so the traditional interference detection method is difficult to obtain high precision measurement results.Moreover,the lens structure is thin and easy to deform,and the optical surface becomes the inner surface of the lens structure during assembly.Due to this influence,contact and non-contact contour measurement methods are not suitable for the surface shape detection of thin foil mirrors.Therefore,it is necessary to propose an effective detection method of X-ray thin foil mirror.In this paper,a detection method based on stereo phase measuring deflectometry is proposed,which has the characteristics of large measurement angle,non-contact,high precision and fast speed.Theoretical analysis,optical simulation and experimental measurement results show that the method is feasible for the surface shape detection of X-ray thin foil mirrors.The detection principle of stereo phase measuring deflectometry is introduced,and the technical components involved in this scheme,such as phase shift technique,phase unwrapping algorithm,system calibration method,stereo matching scheme and surface reconstruction algorithm based on gradient data,are deeply studied.The suppression effect of step size of phase shift algorithm on nonlinear response error is analyzed.The advantages and disadvantages of various phase unwrapping algorithms are compared and an improved median filtering algorithm is used to eliminate the jump error in phase unwrapping.The camera imaging model,lens distortion model and binocular calibration technology are introduced,and the binocular camera image acquisition system is developed.Since the camera is collecting the virtual image reflected by the screen through the plane mirror,in order to obtain the pose relationship between the camera and the screen,the mirror calibration method based on the orthogonal constraint is used to solve the rotation matrix and the translation vector between them.Gradient data integration is used for surface reconstruction.The mathematical principles of direct integration,discrete Fourier transform integration,regional wavefront reconstruction and mode reconstruction are studied,and the reconstruction speed and accuracy of each algorithm are simulated and compared.To solve the problem of stereo matching accuracy and speed of smooth surface to be measured,a multi-step search algorithm based on polynomial fitting is proposed in this paper.The matching data is obtained by subdividing the search step near the initial position,and the vector height corresponding to the extreme point is calculated by polynomial fitting and derivation as the exact spatial coordinates of the measured point,so as to improve the matching accuracy and efficiency.To verify the effectiveness of the proposed method,a spherical mirror was measured using the Zygo interferometer(PV 0.245μm,RMS 0.026μm)as reference.The measurement results of the traditional matching method are PV 0.391μm,RMS 0.0596μm,163.51s.The accuracy of the multi-step search algorithm using polynomial fitting are PV 0.317μm,RMS 0.0403μm and 54.86s.The comparison results show that the proposed matching algorithm is faster,more accurate and has better application value.Based on the results of optical simulation,an experimental platform was built to measure the surface shape of the X-ray thin foil mirror.Firstly,the measurement optical path model is built in ZEMAX software,and the experimental device is built according to the optimized structural parameters.The system calibration and image acquisition are completed.Then,the twelve-step phase shift algorithm and the three-frequency heterodyne method are used to realize the absolute phase solution,and the improved median filtering algorithm was used to remove the phase "pull line" noise,and the multi-step search algorithm based on polynomial fitting was used for stereo matching.After calculating the gradient data,the model reconstruction method was used to restore the three-dimensional surface of the mirror to be measured.Compared with the design parameters of the lens,the measured surface residuals are PV 10.9μm and RMS 1.4μm.The experimental results show that the stereo phase deflectometry method based on multinomal-fitting multi-step search algorithm has certain feasibility and application value for the surface shape detection of X-ray thin foil mirrors.