Co-Phasing Error Extraction Technology Of Optical Synthetic Aperture System Based On Interference Pattern

As an imaging system for observing long-range targets,telescope has played an important role in space exploration,remote sensing imaging,aerospace and other fields since its birth.Especially in today’s world,exploring the vast universe is the common dream of all mankind.However,due to factors such as production cost,transportation,technology and load volume,single aperture telescopes have been difficult to meet people’s demand for large aperture and high resolution in the above fields.The optical synthetic aperture imaging system can achieve equivalent large aperture through multiple sub-imaging systems,which is an effective means to achieve high-resolution imaging.Based on its advantages of low cost and flexible shrinkage and layout,the concept of optical synthetic aperture has attracted much attention since it was proposed in the 1980 s.The premise for optical synthetic aperture imaging system to achieve high resolution imaging by combining multiple imaging units is that each imaging unit needs to achieve the correction of co-phasing error.Co-phasing errors are mainly tilt and piston phase errors,and tilt phase error detection is more simple,which can be detected by traditional Shack-Hartmann sensor in adaptive optics.It is more difficult to detect the piston phase error between imaging units.Therefore,the piston phase error detection technology has been a research hotspot in the field of optical synthetic aperture imaging.For optical synthetic aperture imaging and piston error detection,the main contents of this dissertation are summarized as follows:Based on the advantages of Fourier optics in modelling optical systems,a unified mathematical model is established for optical synthetic aperture imaging systems using Fourier optics.Compared with the existing models based on physical optics,the Fourier optical model based on coordinate transformation and shape splicing proposed in this dissertation uses a combination of special functions with fixed forms and the corresponding Fourier transform to model the optical synthetic aperture imaging system,which is simpler and more scalable.Based on the above model,the analytical point spread functions of optical synthetic aperture systems with different arrangements and submirror shapes under ideal conditions and with co-phasing errors are derived,and the above analytical solutions are verified by numerical simulations.The simulation results show that the established Fourier optical analytical mathematical model can correctly characterize the optical synthetic aperture system and the corresponding point spread function under ideal conditions and with co-phasing errors,and also verify the feasibility of coordinate transformation and shape splicing methods in the modeling of optical synthetic aperture imaging systems.For the detection of co-phasing errors in optical synthetic aperture imaging systems,the piston error detection method of interference pattern based on optimized Hartmann sensor is investigated and three existing methods of piston error extraction,namely the correlation coefficient method,the peak ratio method and the peak shift method,are analyzed.The three methods were compared and investigated using simulation and experiment respectively.The results show that the peak shift method has the highest accuracy under ideal conditions,but it is sensitive to noise.The correlation coefficient method is robust to noise and can perform high accuracy piston error detection under different signal-to-noise ratio conditions.However,when the lens is offset,the detection performance of the three methods will drop sharply,and the maximum detection error of the three methods will reach 0.4 wavelengths.Therefore,the above three methods require the lens to be strictly aligned with the sub-aperture edge or develop a new piston error extraction method that is robust to lens offset.Facing the dilemma that the previous three methods can’t detect piston error with high precision under the condition of lens offset,a method of piston error detection based on phase recovery is proposed.The original problem of piston error extraction is transformed into an optimization problem.By using the established mathematical model and optimization algorithm,the reconstructed interference pattern generated by the mathematical model can approach the collected interference pattern continuously.This method takes both piston error and lens offset as optimization variables,so it is robust to lens offset.The proposed method is verified by simulation and experiment,and the piston error detection with high precision is realized.In order to overcome the limitation of 2π ambiguity and expand the detection range of piston error,a large range piston error extraction method based on dual wavelength is proposed.A new evaluation index is established to evaluate the similarity between the measured interference pattern and the reconstructed interference pattern at two different wavelengths,and the original single wavelength optimization problem is upgraded by using this evaluation index,which expands the measurement range of the original method.The proposed method is verified by simulation.The results show that the proposed method can not only achieve large capture range and high precision piston error detection,but also has robustness to lens offset.Moreover,the detection range can be further extended by introducing more wavelengths,so the method has the advantage of strong scalability.This dissertation provides new ideas and methods for modeling and piston error extraction of optical synthetic aperture imaging system,and provides theoretical and practical guidance for the subsequent development of optical synthetic aperture imaging systems.