Study On The Influence Of Intensity Distribution On Wavefront Reconstruction By Quadri-Wave Lateral Shearing Interferometers

As high accuaracy wavefront sensor,lateral shearing interferometers need wavefront derivatives in at least two althogonal directions to reconstruct wavefront.So the usual lateral shearing interferometers need split light spatially or temporally to obtain wavefront derivatives in at least two orthogonal directions which breakes the instantaneity and stability of system in some extend.Quadri-wave lateral shearing interferoters?QWLSI?split the incident light wave into four replicas with a grating and the replicas superpose coherently and form interferogram at the viewing screen.By dealing with the interferogram,the wavefront of incident light wave can be obtained.QWLSI is composed with just a grating and an image sensor and the system is simple and compact.Since the diffracting replicas transverse along the same optical path,the system is non-sensitive to the environment vibration.QWLSI can obtain wavefront derivatives in sevral directions from one interferogram and is realtime.Now,QWLSI is being used in an increasing number of fields,such as optical testing,laser beam evaluation,adaptive optics control and so on.However,when programming and experimenting QWLSI system,we find that when intensity distribution of incident light wave is non-uniform,the wavefront reconstruction accuaracy decreases.In the traditional researches about QWLSI,we can not find the research of influence of non-uniform intensity distribution on wavefront reconstruction.However,in the researches of eliminating the influence of non-uniform intensity distributions on other interferometers,people focused on the picture processing of interferogram that is making the background be uniform and inhancing the contrast by image enhancement and image filtering.However,our analyze show that when the intensity distribution of incident light wave is non-uniform,the discrete sampling of interferogram with image sensor will cause error of argument interferogram which can not be reduced by picture processing.In this paper,we do research of QWLSI system in theory,simulation and optical experiment under the conditions that when intensity distributions are uniform and non-uniform,propose the problem and the corresponding algorithm.The result of our research show that the three algorithms that we proposed can effectively reduce and even eliminate the influence of non-uniform intensity distributions on wavefront reconstruction and the algorithms have their own merit and demerit.The main research contents and achievements are as follows:Programming the QWLSI system.At first,we simulate the diffraction of light with the theory of angle spectrum and obtain the interferogram.Then by taking Fourier transform and inverse Fourier transform of interferogram,we obtain the wavefront derivatives.At last,with the least square method,we reconstruct the wavefront.Simulation results show that when intensity distribution is uniform,the reconstruction accuaracy of 3rd³5^th Zernike polynomial satisfy the engineering request and when intensity distribution is non-uniform,the wavefront reconstruction accuaracy decrease.Analyzing the process of that how non-uniform intensity distribution affects wavefront reconstruction.When intensity distribution is non-uniform,every order of frequency spectrum of interferogramspread which causes the mixture of frequency information and then wavefront reconstruction error.Except for that,another more important reason is that,when intensity distribution is non-uniform an additional error exists in the argument of interferogram which is caused by the discrete sampling with an image sensor and is the function of intensity distribution,size of photosensitive area and pitch of amplitude grating.Theoretical derivation indicated that discrete sampling error has no matter with incident wavefront distribution.When interferogram divding the reconstructed intensity distribution,the influence of spread of frequency spectrum on wavefront reconstruction can be evaluated.To evaluate the sampling error when intensity distribution is non-uniform,we propose“reconstructed amplitude distribution?RAD?”and“collected amplitude distribution?CAD?”algorithm.The idea of the RAD algorithms is that modeling the QWLSI system at first and then reconstruct the wavefront of plane wave whose intensity distribution is the reconstructed intensity distribution of actual system.The reconstruction result of the modeling system is the wavefront reconstruction error caused by the non-uniform intensity distribution.When wavefront reconstructed from the actual system subtracting the wavefront reconstruction error obtained from the modeling system,the influence of intensity can be decreased.Simulation and optical results show that RAD algorithm can effectively decrease the influence of non-uniform intensity distribution on wavefront reconstruction.To avoid the main error source of RAD algorithm,CAD algorithm uses the intensity distribution collected by another image sensor to replace the reconstructed intensity distribution.Simulation results show that CAD algorithm can almost evaluate the influence of non-uniform intensity distribution on wavefront reconstruction.According to the derived expression,sampling error can be calculated with the reconstructed intensity distribution and known system parameters.Simulation and optical experiment results show that the algorithm can effectively decrease the influence of non-uniform intensity distribution on wavefront reconstruction.Discussing the relative merits and error source of every algorithm.