Research On Phase Reconstruction Based On Model Of Single Interferogram

With the development of science and technology industry,all kinds of advanced equipment are developing towards Opto Mechatronics System.The optical system is the input or output port of these complex systems.The precision of the surface figure is the key requirement of optical element,and the accuracy of surface is determined by the precision of the measurement.The interferometer is the key equipment of the surface test of optics.In order to improve the adaptability to the environment,the random phase shifting interferometer,the dynamic interferometer and the single frame carrier fringe interferometer are used for on-line measurement.But these kinds of interferometers involved hardware upgrade,or example,using multi CCD or improving the imaging quality of large view field.In order to realize the phase reconstruction on the basis of the existing simple interferometer,this paper presents a phase retrieval technique from the single interferogram,and this technique does not need the special requirements of the hardware and the large tilt of reference mirror.At the same time,low cost and high precision dynamic phase interferometry can be realized.Interferometer is an integration system of optical mechanical and electrical optical component.The interferogram is formed by the reference beam and the test beam,and converted into digital information through the imaging system.The main works of this paper is interpreting the interferogram obtained by the detector,and converting the direct measurement(interferogram)to the final measurement information(phase information).This paper introduces the principle and basic theory of the interferometer,and studies the interference image filtering technology.The phase unwrapping algorithm and the polynomial fitting program are discussed,and the phase algrithm of the phase-shifting algorithm is realized,and the validity of the algorithm is verified by experiments.Based on the investigation of the hardware and the related algorithms of the interferometer,the mathematical model of the single interferogram and the optimization objective function are established.In this paper,the optimization principle of Newton iteration method and genetic algorithm are introduced,and two kinds of optimization methods to solve the optimization objective parameters are analyzed.The method of setting the optimal boundary is given.According to the advantages and disadvantages of the two methods,a hybrid optimization method including the genetic algorithm and Newton iteration method is proposed.The simulation results are given in the paper.The method can not only be used for the phase reconstruction of straight interferogram,but also can be used to recover the phase of closed fringe.The optimization of phase reconstruction of the two interferograms is carried out.Although there are intensity errors and residual phase errors in the detected interferogram,the experimental results show that the algorithm is insensitive to these errors.The results of phase optimiztion and phase shift method are compared with each other,and the results show that both of them have the same distribution of phase and zernke polynomial coefficients.In order to analyze the influence of residuals on the measurement results,the phase fitting residuals are referenced into the optimization objective function.The simulation results show that the optimized iterative algorithm can make the simulated interferogram more consistent with the measured interferogram.Considering to the obvious effect of phase residuals on the optimization results,the residual measurement of carrier phase method is proposed to compensate for the lack of residual figure.At the same time,the paper introduces the principle and error analysis of carrier frequency measurement technology,and realizes the phase extraction algorithm of the carrier phase.Based on the analysis of the interference fringe model,we consider more characteristics of the laser source.Three more unknown parameters are added into the model considering the angle between the optical axis and the normal of the detector.After the model is improved,the optimal contrast analysis with four different conditions is given.Finally,in order to verify the reliability of the method,the phase reconstructions are performed with two representative measured interferograms.The phase retrieval algorithm of single interferogram is suitable for the measurement of low order phase error.Through the work of this paper,the phase reconstruction of single interference fringe is realized,which can be used to solve the phase of the interferometer.