Research On Radial Shearing Interference Technology Based On Single Diffraction Element

With the continuous development of science and technology,interferometric wavefront measurement technology has been widely used due to the characteristics of non-contact,high sensitivity and high precision.The conventional interferometers which require external standard reference wavefront are devoted to the high precision surface shape measurement,and the self-referencing interferometers are mainly devoted to measure the continuous and transient wavefront.Among of them,the radial shearing interferometers are easy to be designed into common-path,which can greatly reduce the system error and has better wavefront detection property,they don’t need external reference wavefront and can realize the continuous and the transient wavefront measurement with high spatial resolution and high precision,they have been widely used in many fields,such as adaptive optics,high-power laser beam characterization and corneal topographic inspection.After the development of half a century,the radial shearing interferometry has been well developed in mathematical and physical principles,radial shearing structures,phase extraction algorithms,and wavefront reconstruction algorithms.However,almost every radial shearing interferometer requires 3 to 5 optical elements,in addition,the carrier frequency or phase shift needs to be introduced into the optical path in order to obtain the phase map,which make the system unstable,and the radial shearing rate is difficult to adjust,they limit the application of radial shearing interferometers.Apparently,it is highly desirable to do the research on radial shearing interferometer.In this paper,we try to solve these major problems above: complex structure,difficult processing of interferogram,difficult adjustment of radial shearing rate.Some research results are obtained,meanwhile,some innovative results are listed as follows:Firstly,a multiple-wave radial shearing interferometer based on a single Fresnel zone plate is proposed.This is the first time to put forward the multiple-wave radial shearing interferometer based on a single Fresnel zone plate.This radial shearing interferometer is very compact.We obtained the mathematical formula of the interferogram and put forward the phase extraction algorithm.Numerical simulation results and experimental results proved the feasibility of this method.The multiple-wave radial shearing interferometer is very compact and doesn’t need to introduce tilt or phase shift into the optical path for phase extraction.It is stable and immune for environmental disturbance.It has a simpler structure than other commonly used radial shearing interferometers.Next,based on the known Gabor zone plate,a cosinusoidal zone plate is designed,and a radial shearing interferometer based on a cosinusoidal zone plate is proposed.This cosinusoidal zone plate has only two foci.Based on this zone plate,it can realize radial shearing with double wavefronts.The radial shearing interferometer based on the cosinusoidal zone plate is compact,convenient to adjust,and has high spatial resolution.The numerical simulation results show that this method can effectively measure the wavefront distortion.In addition,we optimized the system parameters.The results show that the interferometer has a strong ability for wavefront measurement.Finally,the principle experiment system of radial shearing interferometer based on the cosinusoidal zone plate is designed and built.The production method of cosinusoidal zone plate is studied firstly.According to the ideal cosinusoidal zone plate transmission function,we have designed a randomly encoded cosinusoidal zone plate.The inherent system error of randomly encoded cosinusoidal zone plate,sidewall error,the etching depth error and the alignment error in the processing are analyzed.Then the experimental optical path is built,and the wavefront reconstruction is realized.The correctness of this method is verified,and the accuracy of this interferometer is verified by comparing the experimental results of the ZYGO interferometer.In addition,the experiment results show that the radial shearing intherferogram is so stable with the distance changes.And the experimental results are analyzed,which provides theoretical guidance for the parameter design of practical application system.