Research On Direct Wavefront Reconstruction Method Based On Transformer Structure

In modern times,with the further development of astronomy research,the requirement for the observation ability of ground-based optical astronomical telescope is gradually increasing,which promotes the emergence and development of adaptive optics（AO）technology.The main function of AO system is to overcome the influence of atmospheric optical turbulence,so as to restore the imaging performance of the telescope close to the diffraction limit as much as possible.It is generally composed of three parts:wavefront sensor,wavefront controller and wavefront compensator.The wavefront sensor,as the front-end device for sampling,is capable of rapidly detecting non-stationary aberrations,and its detection accuracy and capability directly affect the effectiveness of the system in compensating for turbulence-induced aberrations in the wavefront.The Shack-Hartmann Wavefront Sensor（SHWFS）is one of the most widely used wavefront sensors today.However,the SHWFS is a wavefront detection system that splits the received wavefront of the telescope through a sub-aperture.To improve the detection accuracy,the SHWFS requires a large number of microlenses,which weakens its ability to detect faint targets and thus reduces the operating range of the AO system.At the same time,the conventional wavefront reconstruction algorithm,which uses the slope of the microlens of SHWFS as the eigenvector,is affected by mode coupling and mode confusion errors,yet no method can be applied to various complex observation conditions and achieve stable and high accuracy wavefront reconstruction.Therefore,this work will further adapt the traditional SHWFS and SHWFS-based wavefront reconstruction methods and explore new possibilities to combine the Transformer neural network structure in deep learning with SHWFS to achieve direct high-precision wavefront reconstruction.The main research work and innovations of this paper are as follows:Firstly,considering the high actual cost of optical astronomical telescopes and AO systems,and the fact that actual data cannot be collected due to limited conditions,the choice of system design and effective simulation can effectively save costs and optimize the solution.The theoretical and simulation part of the AO system starts with the simulation of atmospheric turbulence,which consists mainly of modeling the turbulent phase through the atmospheric turbulence structure function combined with the power spectral density inversion method and the Zernike mode method.Finally,the introduction of Transformer structure is introduced to lay a theoretical foundation for the subsequent work content.Then,the first application of Transformer structure to high-precision wavefront reconstruction is realized,and the SH-U-Transformer network model is proposed,which is a network model combining Transformer and U-shaped network,based on the advanced Swin-Transformer adjustment improvement,to achieve direct high-precision under various complex observation conditions Reconstructing wavefronts.The simulation dataset generated by the OOMAO toolkit is fed into the constructed SH-U-Transformer model for training.The resulting network model can reconstruct aberrated wavefronts directly from spot array images acquired by SHWFS with a large-scale microlenses array with high accuracy and without additional steps.The SH-U-Transformer model is experimentally tested to achieve a stable,high-precision wavefront reconstruction task under a variety of complex observational conditions.Firstly,the residual wavefront RMS error of the SH-U-Transformer model is in the range of 0.010μm to 0.024μm,which exceeds the accuracy of conventional methods by nearly two orders of magnitude even for the strongest turbulence,i.e.atmospheric coherence length r₀=5 cm,and exceeds that of the SH-Net network model by 50%.The accuracy of the wavefront reconstruction of the SH-U-Transformer model remains stable,and this paper tests the gradual increase of the magnitude of the observed target or guide star from 3rd to 8th magnitude,with very little difference in the reconstruction wavefront accuracy when the magnitude is 3rd to 7th magnitude,and the residual wavefront RMS error value is between0.006μm and 0.024μm,while when the magnitude is 8th magnitude,the reconstruction The accuracy decreases but remains between 0.025μm and 0.040μm.Third,the turbulence structure is changed as a whole.In this paper,the turbulence model was changed to the generally accepted Hufnagel-Valley turbulence model to test the SH-U-Transformer’s ability to cope,and with a small retraining strategy,it was able to quickly adapt to the new turbulence situation and the reconstruction accuracy remained stable with a residual wavefront RMS error value of 0.012μm to 0.026μm.At the same time,the SH-U-Transformer model can reconstruct the wavefront at a very fast speed of 15ms.Finally,drawing on the characteristics of the quadrilateral cone wavefront sensor,the SHWFS was adapted to a 2×2 microlenses whole-row wavefront sensor,and a matching CSwin-Transformer-based neural network model SH-CSwin-UT was built by itself,and the wavefront reconstruction system composed of these two parts was named SH-SWCS.This system greatly improves the detection capability of the wavefront sensor for faint targets,reduces the processing cost,and increases the sensitivity of the sensor with a small number of microlenses,and the subsequent wavefront reconstruction is done directly by the SH-CSwin-UT,which breaks the limitation of the number of microlenses and enables the wavefront reconstruction with high accuracy.Compared to the conventional SHWFS-based wavefront reconstruction method,SH-SWCS can work at a higher magnitude than the conventional SHWFS-based wavefront reconstruction method.For a telescope of the same aperture,the conventional SHWFS wavefront reconstruction method can only reconstruct wavefronts for targets brighter than 5th magnitude,whereas SH-SWCS can reconstruct wavefronts for magnitudes up to 8th magnitude.In contrast to the conventional SHWFS-based modal method,SH-SWCS can reconstruct the wavefront of the first 200Zernike modes with just four effective microlenses.At the same time,SH-SWCS can reconstruct the residual wavefront with a root-mean-square error of 0.0083μm to 0.0378μm for an observed target of magnitude 6 and turbulence intensity D/r₀=10～26（d/r₀=5～13）,which exceeds the accuracy of the modal method by more than 80%for an observed target of magnitude 3.In addition,the reconstruction accuracy is still stable at magnitude 8,which is not much different from that at magnitude 6.With the same small amount of retraining,SH-SWCS can quickly adapt to the adjustment of the number of microlenses and maintain the performance of reconstructing the wavefront with high accuracy.Through the research in this paper,the model or system based on the Transformer structure achieves high-precision direct wavefront reconstruction under changing observation conditions or hardware conditions,solves the contradiction between detection accuracy and detection capability of traditional SHWFS,simplifies the process of wavefront reconstruction,greatly improves the accuracy of wavefront reconstruction,and provides a new direction for SHWFS wavefront reconstruction.