Study Of Key Technology Of Random Phase Shifting Interferometry

With the rapid development of laser technic,micro-electronic technic and computer technology,the optic systems are gradually tending to “bigger” and“smaller” in two scopes.The “bigger” means diameter of optic system is bigger and bigger to achieve a higher spatial resolution.For example,the full diameter of ground-based telescope GMT is as large as 25 meters which is stitched by 7 single mirrors with a diameter of 8.4 meters.The “smaller” denotes the surface error of the optics should be as smaller as possible.For instance,the manufacture precision of EUV is controlled bellow sub nanometers in RMS value.It is crutial for manufacture to ensure a high efficient optical testing when the optics are “bigger” in diameter and“smaller” in surface error.As the final step for high accuracy testing,phase shifting interferometry meets tremendous challenges as the optics are becoming bigger in size and smaller in surface error.For high diameter optics testing,the vibration and air turbulence prevent the conventional phase shifting interferometry to give a credible result,thus dynamic interferometry is necessary.In high precision optic testing,phase shifting error that casued by non-linearity of phase shifter or high frequency vibration is always the foremost error source that should be concerned.The study in this paper,namely Generalized Phase Shifting Interferometry(GPSI)is just under this background that conventional phase shifting interferometry is incapable in the progress of optics manufacture.Based on the former studies,some key techniques and problems in GPSI are studied and resolved,and breakthrough progresses have been made in follow aspects:(1)The general error propogation of conventional phase shifting algorithms are studied based on Fourier Analysis.We first indicate that the phase shifting amplitude(sampling range)is crutial to the accuracy of GPSI based on the error sensitivity analysis of GPSI.The error propogation of GPSI is also deduced.ETC is proposed to calibrate the phase extraction error of phase shifting algorithms,which is a general method and can serve as a base for optimization of exsiting GPSI.(2)The advanced iterative algorithm(AIA)is studied,two assumptions that limit the application of AIA should be relaxed.ETCI is accordingly proposed which can simultaneously improve the accuracy and speed of AIA.Principle Component Analysis(PCA)is studied subsequently,and a enhanced PCA(EPCA)based on hyper-ellipse fitting technique is proposed to cope with the fringe number limitation in PCA.(3)The necessity of fringe preprocess is discussed and three kinds of fringe normalization techqiue is introduced,which can be used for fringe normalization in different occasions.Based on the spatial distribution of phase shift between two normalized interferograms,we proposed three phase shift extraction methods.For random piston phase shift,LEF is proposed which can simultaneously extract the phase shift and phase distribution from two interferograms.For random tilt phase shift that caused by vibration,a special points fitting method is proposed which is a full field,non iterative and high accuracy method.For inhomogeneously phase shift,the polynomial fitting method is studied and the application field is pointed out.(4)The dynamic application of GPSI is studied.The requirement for time-domian dynamic phase shifting is indicated,and a time-domain dynamic phase shifting method based on least squares fitting is proposed which can be easily implemented without a high speed CCD and phase shifter.The spatial-domain dynamic phase shifting technique is also studied,detuning error can be reduced dramatically by proposed Pixel Lissajous figure and Ellipse Fitting(PLEF).The findings in this paper have been successfully applied in a self made interferometer.The repeatbility of proposed ETCI is less than 0.05 nm in RMS value,and the double-requency fringe error that caused by vibration can be wipped off efficiently by proposed ETC.