Point Spread Function Estimation for Wide Field Small Aperture
  Telescopes with Deep Neural Networks and Calibration Data
  The point spread function (PSF) reflects states of a telescope and plays an
important role in development of data processing methods, such as PSF based
astrometry, photometry and image restoration. However, for wide field small
aperture telescopes (WFSATs), estimating PSF in any position of the whole field
of view 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
(Tel--Net). After training, the Tel--Net 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 the
Tel--Net can 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 deep neural
network based data processing methods for WFSATs, which require strong prior
information of PSFs.
