Study On Noises Of The Error Calibration Method For The Sparse Aperture Telescope

The sparse aperture telescope achieves the imaging resolution as a single large aperture system by coherence stacking of each sub-mirror,which provides one solution to solve the resolution restrictions of the single aperture system,and makes the whole system lighter and smaller.As each sub-mirror of the sparse aperture optical systems is independent from each other,it is easy for the systems to have piston errors and tilt errors and other wave-front errors caused by noises from the environment.The error calibration is one of key technique for the sparse aperture optical system.Noises have great affect on errors.It is very necessary to research noises of the error calibration for the sparse aperture optical system.The phase diversity based on the image wave-front sensor is simple and has fewer parts,and only needs two images acquired for wave-front sensor.These advantages meet the requirements of the error calibration,and the phase diversity is fitted to be used for the sparse aperture imaging optical system.The testing accuracy and iterative time of the phase diversity for the sparse aperture optical system is interrupted by noises during the image acquisition process.This paper researches noises on the error calibration of the phase diversity for the sparse aperture telescope.Firstly,this paper introduces the research background of ways used on error calibrations of sparse aperture optical systems,and research statuses both abroad and domestic,and introduces the research status of the error calibration of the phase diversity,Secondly it discusses the effects caused by piston errors and tilt errors on PSF,MTF and image quality of the systems using the Golay3 sparse aperture as an example.It is shown that the piston errors have a periodic effect on image quality of the systems.The Strehl ratio of PSF becomes lower because of piston errors and tilt errors,and the frequency transfer characteristic of the systems is changed.The improved phase diversity based on filter-apodization is proposed to increase the retrieving precision of algorithm and decrease the iterative time.Lastly,according to the Cramér-Rao lower bound,the fisher matrix both for Gaussian noise and Poisson noise is derived.Noises on the error calibration of the phase diversity is studied for the sparse aperture telescope,and Cram ér-Rao Bound for two different non-redundancy sub-mirrors structures is calculated.As a result,Golay6 Golay3 sparse aperture has higher sensor accuracy than that of Golay3 while the object is a point.For extend source,the sensor accuracy is related to the type of noises.Golay3 sparse aperture has a optimum fill factor under Gaussian noise.At the end the conclusion is given out and works for next step is listed.