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The point spread function (PSF) reflects states of a telescope and plays animportant role in development of data processing methods, such as PSF basedastrometry, photometry and image restoration. However, for wide field smallaperture telescopes (WFSATs), estimating PSF in any position of the whole fieldof view is hard, because aberrations induced by the optical system are quitecomplex and the signal to noise ratio of star images is often too low for PSFestimation. In this paper, we further develop our deep neural network (DNN)based PSF modelling method and show its applications in PSF estimation. Duringthe telescope alignment and testing stage, our method collects systemcalibration data through modification of optical elements within engineeringtolerances (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 viewfrom several discretely sampled star images. We use both simulated andexperimental data to test performance of our method. The results show that theTel--Net can successfully reconstruct PSFs of WFSATs of any states and in anypositions of the FoV. Its results are significantly more precise than resultsobtained by the compared classic method - Inverse Distance Weight (IDW)interpolation. Our method provides foundations for developing of deep neuralnetwork based data processing methods for WFSATs, which require strong priorinformation of PSFs.

Point Spread Function Estimation for Wide Field Small Aperture Telescopes with Deep Neural Networks and Calibration Data