Modelling the Point Spread Function of Wide Field Small Aperture Telescopes With Deep Neural Networks -- Applications in Point Spread Function Estimation

The point spread function (PSF) reflects states of a telescope and plays an important role in development of smart data processing methods. However, for wide field small aperture telescopes (WFSATs), estimating PSF in any position of the whole field of view (FoV) is hard, because aberrations induced by the optical system are quite complex and the signal to noise ratio of star images is often too low for PSF estimation. In this paper, we further develop our deep neural network (DNN) based PSF modelling method and show its applications in PSF estimation. During the telescope alignment and testing stage, our method collects system calibration data through modification of optical elements within engineering tolerances (tilting and decentering). Then we use these data to train a DNN. After training, the DNN can estimate PSF in any field of view from several discretely sampled star images. We use both simulated and experimental data to test performance of our method. The results show that our method could successfully reconstruct PSFs of WFSATs of any states and in any positions of the FoV. Its results are significantly more precise than results obtained by the compared classic method - Inverse Distance Weight (IDW) interpolation. Our method provides foundations for developing of smart data processing methods for WFSATs in the future.

PSF--NET: A Non-parametric Point Spread Function Model for Ground Based Optical Telescopes

Ground based optical telescopes are seriously affected by atmospheric turbulence induced aberrations. Understanding properties of these aberrations is important both for instruments design and image restoration methods development. Because the point spread function can reflect performance of the whole optic system, it is appropriate to use the point spread function to describe atmospheric turbulence induced aberrations. Assuming point spread functions induced by the atmospheric turbulence with the same profile belong to the same manifold space, we propose a non-parametric point spread function -- PSF-NET. The PSF-NET has a cycle convolutional neural network structure and is a statistical representation of the manifold space of PSFs induced by the atmospheric turbulence with the same profile. Testing the PSF-NET with simulated and real observation data, we find that a well trained PSF--NET can restore any short exposure images blurred by atmospheric turbulence with the same profile. Besides, we further use the impulse response of the PSF-NET, which can be viewed as the statistical mean PSF, to analyze interpretation properties of the PSF-NET. We find that variations of statistical mean PSFs are caused by variations of the atmospheric turbulence profile: as the difference of the atmospheric turbulence profile increases, the difference between statistical mean PSFs also increases. The PSF-NET proposed in this paper provides a new way to analyze atmospheric turbulence induced aberrations, which would be benefit to develop new observation methods for ground based optical telescopes.