Research On Random Phase Shifting Technology In High Accuracy Interferometry

In optical shop testing,phase shifting interferometry is widely accepted with itshigh accuracy and high repeatability.However, in conventional phase shiftingalgorithms,the phase shifts between interferograms should be a special constantvalue,or at least should be equal,so phase shifting interferometer is very sensitive tovibration in the environment. To reduce the rigorous requirements for environmentstability and the performance of phase shifter in phase shifting interferometry, randomphase shifting technology is researched in this paper,and figure information of the testpart can be calculated with unknown phase shifts and with high accuracy.The maincontents of this paper are concluded as follows:1、A random phase shifting experiment system is established,and in order toextract the measurement errors that uncorrelated with phase shifting procedure,theimplementation of accurate equal-step phase shift technology is studied atfirst,including the selection of ways to change the reference phase,the calculation ofphase shifting speed and the calibration of phase shifter,and the system is verified atlast.From the result,we can see that the rms repeatability of this system isλ/5670(2σ).The measurement accuracy of this experiment system is calibrated with aZygo interferometer,and the measurement errors that uncorrelated with phase shiftingprocedure are obtained,so we can carry out experiments with this system later.2、 Least-square-based random phase shift algorithms are studied,and the drawbacks of existing algorithms are analyzed, since the nonuniform distribution ofbackground intensity and modulation will affect the calculation of phase-shift plane inrandom and tilt phase shifting interferograms，an intensity normalized iterative phaseshift algorithm is proposed in this paper, the acquired interferograms are normalizedfirst, and phase-shift plane is determined with the processed interferograms, so thecouple effect of background intensity and modulation on the calculation of tiltcoefficients can be eliminated, and tilt phase shift errors during phase shifting can becompensated effectually. Compared with other methods, the proposed method hashigher accuracy, and the convergence time is shortened to a half, so it is more suitablefor real application.3、Random phase shift algorithm based on principal component analysis(PCA) isstudied, and formulas to get phase distribution from randomly phase-shiftedinterferograms are derived. The accuracy of this method and factors that mayinfluence the result are discussed with computer simulation.In order to lower therequirements for the number of frames and fringes,the principal component analysis(PCA) method is combined with the least squares method effectively in this paper,andwe call this new method Extended PCA method.Simulation result shows that theExtended PCA method can obtain the phase distribution from only5interferogramswith higher accuracy,and the fringe number in these interferograms is less thanone.We also carry out optical experiments to compare the measurement result usingthe Extended PCA method with that of a Zygo interferometer,and the rms of residualfigure between two results is1.05nm，experiment results show that with ExtendedPCA method we can get nano scale measurement accuracy from randomly phaseshifted interferograms,so it is practically valuable.4、Since there are needs to calculate figures from less interferograms with time asshort as possible,we make a comparative study among three representative two-stepphase shifting algorithms,they are frame average method、histogram method andSchmidt orthonormalization method.During computer simulation,the accuracy andprocessing time of these three method are compared using the sameinterferograms,and four major factors that may influence the accuracy of these three memthod are discussed,they are the phase shift values,the fringe number in theinterfergram, the number of frames used to normalize the intersity and the visibility ofinterferograms. Finally,we compare the results of these three method with that of aZygo interferometer,and the rms of the residual figure are all about3nm.So we cansee,such two-step phase shifting algorithms can also be used in routine measurement.With the research results in this paper,it is helpful to lower the requirement forenvironment stability and the proformance of the phase shifter in phase shiftinginterferometry,and it provides technique foundations for the wider use of phaseshifting technology in scientific and production applications.