Research On Robustness Of Surface Shape Measurement Based On Random Step Phase Shift Interference

In the measurement of the surface shape of optical components,the phase shift interference technique is widely used in research and production for its advantages of high measurement accuracy and repeatability.However,conventional phase shift algorithms require a fixed step of phase shift,therefore phase shift interference techniques are very demanding on the measurement environment.In order to reduce the requirements of phase shift interference technology on environmental stability and phase shifter performance,This paper has carried out the research of phase-shift interference surface shape measurement technology based on random step length.Through the research of phase demodulation technology of random two-step phase shift and random three-step phase shift,the high-precision phase extraction of the surface shape information of the optical element is realized,and the robustness of the random phase shift algorithm is analyzed.The main research in this paper is summarised in the following three points.(1)Existing random two-step phase-shift phase demodulation techniques almost always extract the measured phase information by calculating the tangent function of the measured phase.The technique requires the background light intensity of the interference fringe to be removed,so the accuracy of the background light intensity acquisition determines the accuracy of the phase calculation.A common method of removing background light intensity is to use a high pass filter to remove it,but too few stripes or an uneven phase distribution can result in the background light intensity not being accurately filtered out.For this problem,a random two-step phase shift algorithm based on polynomial fitting background light(PFBL-Polynomial fitting background light)is proposed.The algorithm combines a K-order two-dimensional polynomial with the least squares method to effectively improve the accuracy of the phase calculation by solving for the background light intensity of the interference fringe and removing it from the interference fringe.The simulation results show that when the order of the K-order two-dimensional polynomial is greater than or equal to 2,the PFBL algorithm calculates a surface shape residual of 0.001 A(RMS),which is better than the Schmidt orthogonal isation(GS)two-step phase shift algorithm and comparable to the Stoilov algorithm.Through the robustness simulation analysis of the PFBL algorithm,it can be known that the PFBL algorithm has good robustness to the phase shift amount,illumination non-uniformity and noise in the phase shift interferogram.(2)To solve the problem that the random two-step phase shift algorithm is affected by the accuracy of the background light intensity acquisition,a random three-step phase shift algorithm based on two dimensional polynomial combined with least square method(TDP&LSM-two dimensional polynomial combined with least square method)is proposed.The algorithm removes the background light intensity directly by the difference operation between the interferograms,then combines a K-order two-dimensional polynomial with least squares to extract the phase shift between two adjacent interferograms in turn,and thus solve for the measured phase.The simulation results show that when the order K of the K-order two-dimensional polynomial is 0 or 1,the calculation accuracy of the TDP&LSM algorithm and the PFBL algorithm with the value of K greater than or equal to 2 are equivalent;When K is taken to be greater than or equal to 2,the accuracy of the calculation is comparable to that of the four-step phase shift algorithm and the resulting surface shape residual is 6.74x10-4 λ(RMS).At the same time,it can be known that the TDP&LSM algorithm has good robustness to the phase shift amount,illumination non-uniformity and noise in the phase shift interferogram.(3)A Fizeau type random phase shift interferometry experimental apparatus has been constructed based on the principle of frequency phase shift interference.For the plane mirror with an aperture of 25mm,phase-shift interferograms were collected,and the surface shape distribution of the plane mirror to be measured was solved by PFBL algorithm and TDP&LSM algorithm respectively,and the measurement results were compared with the measurement results of Zygo laser interferometer.The effectiveness of the PFBL algorithm and the TDP&LSM algorithm was verified,as well as the relationship between the value of K and the accuracy of the algorithm in these two algorithms and the robustness of the algorithm.