Research On The Imaging Aberration In Interferometric Null Test And Optimization Of The Instrumental Transfer Function

With more and more achievements in the application of large optics in astronomy and remote sensing,our country has a growing demand for high-level advanced optical systems.As the only means of surface testing with nano accuracy,the interferometric null test is facing great challenges in testing large apertures,long optical paths,and high asphericity optical surfaces with high accuracy.In general,there are three typical kinds of errors affecting the accuracy of surface testing: direct measurement error,geometric tracing error,and the degradation of the test wavefront.For the direct measurement error and geometric tracing error,people have achieved massive results and applied these results in commercial productions for decades.However,the errors caused by diffraction effects in the interferometric null test are less reported because they are not significant in the test of small-aperture spherical mirrors in the past.Interferometric imaging aberration was first proposed by Zhou Ping and Zhao Chunyu et al.of Arizona,USA.They pointed out that both refractive and diffractive compensation elements will inevitably introduce imaging aberration while compensating the wavefront with high accuracy.Therefore,the imaging aberration makes the test wavefront degraded during long-distance propagation and produces unexpected mapping distortion,astigmatism,and field curve.With the development of optical elements towards larger-aperture and higher asphericity,the diffraction effect in the interferometric null test will be more and more significant.The test wavefront in the long optical path propagation will be degraded.The imaging aberration of the interference fringe attenuates the instrumental transfer function(ITF)of the interferometric null test in the high-frequency regime,which has become a significant constraint on the accuracy of the interferometric null test.This research addresses the significant impact of imaging aberration in interferometric null tests,which significantly restricts the accuracy of spatial band error tests.Then we study the characterization method of imaging aberration in the interferometric null test based on the differential geometric characteristics of the surface.We explore the method to model the propagation of wavefront degradation under the assumption of tiny beamlet theory.And we analyze the quantitative relationship between imaging aberration and test error.The details of the study are as follows.1.Establishing an elliptical Gaussian beam model for the optical field distribution in the optical path of the interferometric null test.Based on a hybrid geometric-diffractive optics approach,we decompose the incident wavefront into a series of Gaussian beam beamlets.According to the complex beam tracing theory,we approximate the propagation process of the wavefront in the optical system by the geometric optics theory.And the Gaussian beamlets will be distributed as an elliptical Gaussian beam in the imaging space of the optical system.By summing the elliptical Gaussian beamlets,we can obtain the light field distribution in the imaging space.We can characterize the degradation of the test wavefront in the optical system with high accuracy.2.Establishing the characterizing methods of imaging aberration for the interferometric null test of large optics.Since the design of compensation elements is usually optimized for wavefront characteristics,their imaging characteristics are often neglected.By combining the tiny beamlets tracing and phase plate imaging equation with the differential geometric properties of the surface shape,the imaging equation of the compensation element in the form of a Gaussian imaging equation can be derived.Such a model avoids the requirements for a large amount of ray tracing calculations in the simulation of the examined mirror imaging through the compensation element.Thus,it simplifies the calculation process.In addition,we can characterize the imaging aberration by a parametric formula.3.Optimization of the instrument transmission of the interferometric null test system is realized.After the quantitative characterization of the imaging aberration and the evolutionary propagation of the test wavefront,we establish a quantitative simulation model for the whole system parameterization from the mirror under test to the detector of the interferometer.Based on the simulation model,the instrumental transfer function of the whole optical path of the interferometric null test is used as an evaluation index to optimize the relevant parameters in the optical system.And based on the parametric simulation model,an optimized CGH(Computer generated hologram)is designed and prepared to reduce the imaging aberration and improve the instrumental transfer function of the optical system.4.Propose a method to measure the ITF of the interferometric null test of large optics.For the experimental verification of the above conclusions,we prepared a step-shape phase test plate.The ITF is defined by calculating the ratio of the power spectral density of the ideal and the test surfaces of the test plate.And we can verify the simulation model and the related theory by comparing the ITF before and after the optimization.This paper establishes a parametric and quantitative simulation model of the full optical path of the interferometric null test from the mirror under test to the detector of the interferometer.The simulation accuracy is 30 mrad with calculation time less than0.2s.Such a model provides a powerful guide for the design and optimization of the compensation element and the relevant parameters of the optical system.With the optimization,the ITF of the optical system is increased from 0.48 to 0.88 at 0.3Nyquist frequency.So,the accuracy and precision of the interferometric null test for large-aperture and complex surface optical mirrors are improved.