Study Of Phase Retrieval Algorithm Based On Hybrid Unwrapping

In order to meet the requirement of high resolution observation,while considering factors of material,manufacturing,and weight,the segmented primary mirror has become the main approach of the large aperture telescope.A segmented primary mirror will bring phase errors,so,a wavefront sensor must be used to sense the error and then to correct it.Phase retrieval algorithm is one of the common methods for wavefront sensing.It is a wavefront sensing method that uses the intensity distribution of multiple defocus planes,and uses the iterative transformation algorithm based on Fourier transform to recover the pupil phase distribution.When the dynamic range of the wave front is greater than 1 wavelengths,it is necessary to introduce phase unwrapping algorithm into the iterative process.Phase unwrapping algorithm is the key factor to improve the dynamic range and phase recovery accuracy of wavefront sensing.In this paper,a phase retrieval algorithm based on hybrid unwrapping is proposed.In the early stages,a least-mean-square unwrapping algorithm is employed which has an advantage of robustness.In the later stages,a path-independent unwrapping algorithm is employed which has an advantage of high accuracy.The computer simulation of the phase retrieval algorithm is completed.In the simulation,the Zernike polynomial is used to produce the measured wavefront distribution for sensing,and the pupil model and the optical system model are established to obtain the intensity distribution of the defocused plane.Then,by using the intensity distribution information and the phase retrieval algorithm,the iterative equation is established to obtain the iterative phase value,and the iterative phase is wrapped to recover the phase.Finally,the weighted average of the phase recovered from each defocused surface is calculated to obtain the final recovered wavefront phase.First,simulations under large dynamic range and circular aperture are conducted.With a large dynamic range of wavefront as the research object,under the condition of two defocus plane and four defocus plane,the path independent unwrapping and least-mean-square unwrapping and hybrid unwrapping are used for comparative simulation study.The simulation analysis shows that the recovery accuracy of the hybrid unwrapping method is higher than that of the other 2 methods in the case of 2 defocused planes and 4 defocused planes,and the hybrid unwrapping of 4 defocused planes is higher than that of the 2defocused planes.Finally,simulations with the mosaic pupil of 18 hexagonal segments are conducted.Under the conditions of two defocus plane and four defocus plane,the path independent unwrapping and least-mean-square unwrapping and hybrid unwrapping are used for comparative simulation study.The simulation analysis shows that the hybrid unwrapping method has a higher recovery accuracy on complex pupils.In the same time,the dynamic range and SNR requirement of wavefront sensing algorithm for complex pupil are simulated with hybrid unwrapping algorithm.The simulation results show that when the PV value of the wavefront aberration is 3.5?,the accuracy of the algorithm is ?/43;when the noise RMS value is 10(the image is 12 Bit quantized),the accuracy of the algorithm is better than ?/40.