Theoretical Research And Analysis Verification Of Coherent Imaging Aberration In Interferometry

With the development of ground-based and space remote sensing detection technology,the performance demand of high-resolution and large field of view advanced optical imaging system is increasing.The high demand for diagonal resolution and light collecting ability makes the aperture increase continuously,and presents the development trend of complex surface shape and high-precision scale ratio,which makes the manufacturing and detection of large aperture optics face unprecedented challenges.As a detection method of large aperture aspheric surface,interference compensation detection can achieve nano precision.It has the advantages of high sensitivity,high measurement accuracy,non-contact measurement and so on.After high-precision compensation by zero compensator(null lens,CGH,etc.)or compensation optical path,the test beam returned from large aperture aspheric surface interferes with the reference beam returned from small aperture spherical reference mirror.However,with the increase of aperture and asphericity,the imaging aberration caused by wavefront degradation can not be compensated by the depth of field and focal depth of the system.This kind of aberration will be coupled with the surface error in the process of propagation,and then affect the detection results.Based on the scalar diffraction theory,the interference coherent imaging aberration model theoretically deduces the non rotational symmetric wavefront degradation,which makes up for the deficiency of the wavefront propagation theory in the case of non rotational symmetry.Based on the propagation theory and the principle of differential geometry,an interference coherent imaging aberration model is established,which can quantitatively describe the influence of aberration on the final imaging results.In this paper,the theory of interference coherent imaging aberration is studied,and its model and algorithm are verified by experiments combined with cylindrical mirror interference detection.The research content of this paper mainly includes the following three parts:1.Characterization Theory of degenerate transmission of non rotational symmetric wavefront With the increase of the aperture of the optical element,the inspected mirror expands towards more complex non rotational symmetrical surfaces such as cylindrical surface,off-axis aspheric surface and free-form surface.In order to better explore the interference compensation detection of non rotational symmetrical surface,based on the scalar diffraction theory,the transfer function of non rotational symmetrical secondary wavefront degradation is deduced,and the theory of non rotational symmetry is improved by establishing a mathematical and physical model.Combined with the principle of differential geometry,the influence of imaging aberration on interference compensation test is studied by establishing a mixed mode of fine beam tracking and wavefront evolution.The rotationally symmetric wavefront transfer function in scalar diffraction theory is modified to make the wavefront transfer function meet the situation of non rotationally symmetric.It also provides a necessary means to analyze the influence of imaging aberration on detection accuracy2.Establishment of convolution kernel imaging and its numerical aberration detection modelBased on the transfer function of wavefront degradation and the idea of point source perturbation,the coupling process of surface information and imaging aberration is transformed into a convolution process.The neighborhood approximation method of regional layered sampling is used to digitize the frequency modulation function(convolution kernel).By comparing various sampling methods and selecting the form of Gaussian sampling,the convergent convolution kernel matrix expression is obtained.Combined with the numerical calculation model and simulation model,the model of interference detection imaging aberration is obtained.Based on this model,the analytical form of the degraded image surface can be obtained,and the analytical expression of its phase distribution and instrument transfer function can be obtained to evaluate its imaging quality.3.Experimental verification of interference coherent imaging aberrationThe aberration model of interference coherent imaging is analyzed quantitatively,the experimental optical path of interference compensation detection of cylindrical mirror is designed,and the positions of meridional and sagittal image planes are calculated by Gaussian formula.The cross diaphragm is introduced into the detection optical path.By changing the position of the CCD image plane of the interferometer,the meridian(sagittal)direction is focused,and then the defocus in different directions is changed.The degradation of the diaphragm edge is observed.The detection results in different cases are compared with the model simulation results,so as to quantitatively analyze and verify the correctness of the interference detection imaging aberration model.