NIAOT has made new progress in improving telescopes alignment based on machine learning for image-based point spread functions estimation----Nanjing institute of Astronomical optics & Technology National Astronomical O bservatories .CAS

Optical telescopes with large field of view and excellent image quality is the working horse for astronomical and space targets survey. However, misalignment of optical elements in the optical system will introduce aberrations in different field of views which would generate point spread functions (PSFs) with irregular and asymmetry shape and reduce the quality of observed images. The key technology to recognize the alignment states of the optical system with star images by machine learning algorithms have been developed recently.

Since PSFs can not only reflect the quality of images obtained by optical telescopes with large field of view and high image quality directly, but can also be used to measure shape, magnitude and position of celestial objects. In recent years, PSF modelling and application of PSF models have attracted wide interest from astronomical optical instruments and data processing areas.

In order to improve the performance of PSF modeling method and that of the telescope misalignment perception method with PSFs, the team lead by Dr. Li Zhengyang from Nanjing Institute of Astronomical Optics Technology, Chinese Academy of Sciences, with the team lead by Dr. Jia Peng from the School of Physics and Optoelectronic Engineering of Taiyuan University of Technology have carried out research on PSF estimation method for telescopes with large field of view and high image quality with arbitrary misalignment states based on deep learning algorithm.

Then estimated PSFs are used to calculate telescope misalignment errors. The related work was published in Monthly Notices of the Royal Astronomical Society respectively in 2020(https://doi.org/10.1093/mnras/staa319) and 2021(https://doi.org/10.1093/mnras/stab1461).

The team has established mapping between star images with low signal-to-noise ratio (SNR) in some predefined positions of the field of view and PSFs; and further established the corresponding relationship between PSFs and optical element misalignment with convolutional neural networks (DAE-NET). With simulation data, the team have found that the DAE-NET can improve the accuracy of PSF modelling method in different field of views, and can also improve the accuracy of optical system elements misalignment estimation. The DAE-NET has been highly praised by reviewers, “The topic is interesting and has the potential to revolutionize the reduction and interpretation of on-going and future small aperture wide-field telescope imaging data”.

Fig. 1. Images in the first row are original PSFs, images in the second row are images with low SNR and images in the third row are PSFs estimated from the low SNR images.

It can be seen from above figures that DAE-NET can reconstruct original PSFs from low SNR images. However, the misalignment estimation algorithm should be able to estimate misalignments from stars in random positions. Therefore, the team further established the mapping relationship (Tel-Net) between telescopes with any misalignment states and PSFs randomly distributed in different field of views. The algorithm is based on a coding and decoding network and includes Fixup method, which avoids the influence of Batch- Normalization on PSF values and thus ensures the accuracy of estimated PSF values.

To further verify the practicability and reliability of the Tel-Net, the team set up an experimental platform in Nanjing Institute of Astronomical Optics Technology, and obtained a large number of images to verify the algorithm. The results show that the accuracy of PSF reconstruction method proposed by the team is nearly one order of magnitude better than that obtained by the interpolation method (IDE), if they are evaluated with root mean square error. When there are only sparsely sampled star images, Tel-Net is still superior to traditional IDE method. The work has been highly praised by the reviewer, “Overall this work does a great job of solving a problem in modern astronomy by leveraging deep learning”.

Fig. 2. The left figure shows the MSE mean distribution of PSF estimation results in different field of views of any misaligned states obtained by interpolation IDE, the middle figure shows the MSE mean distribution of PSF estimation results in different field of views in any misaligned state of telescope obtained by Tel-Net and the right figure shows the MSE histogram distribution of PSFs obtained by different methods.

Fig. 3. The left figure shows the experimental platform to collect images from different alignment states, and the right figure shows the estimated residual distribution of PSF of measured data.

The Tel-Net and the DAE-Net reflects application prospect of introduction DNNS in PSF estimation and telescope state perception. The works have provided a foundation for further intelligent astronomical instrument design and smart astronomical data processing algorithm research. The project team will further conduct experiments and algorithm design for active alignment of telescopes, such as: the prototype of Si Tian Project, the 1.6-meter multi-channel photometric telescope and the Antarctic Survey Telescope.

This work is supported by National Natural Science Foundation of China 11503018, Astronomical Joint Funds U1631133 and U1931207, Yunnan University 1.6-meter multi-channel photometric telescope project, Chinese Academy of Sciences Youth Innovation Promotion Association 2017083, Shanxi Youth Fund General Project 201901D211081, Shanxi Science and Technology Research Project 201903D121161. Shanxi Higher Education Research Project 2019L022, Polish Educational Research Fund 02/140/RGJ21/0012, BK-225/RAu-11/2021 and French National Research Fund ANR-19-CE31-0011,etc.