An Ultrafast Image Simulation Technique with Spatially Variable Point-spread Functions

Simulated images are essential in algorithm development and instrument testing for optical telescopes. During real observations, images obtained by optical telescopes are affected by spatially variable point-spread functions (PSFs), a crucial effect requiring accurate simulation. Traditional methods segment images into patches, convolve patches with individual PSFs, and reassemble them as a whole image. Although widely used, these approaches suffer from slow convolution processes and reduced image fidelity due to abrupt PSF transitions between different patches. This paper introduces a novel method for generating simulated images with spatial continuously varying PSFs. Our approach first decomposes original images into PSF basis derived with the principal component analysis method. The entire image is then convolved with this PSF basis to create image basis. Finally, we multiply the coefficients of image basis by the corresponding PSF basis for each pixel and add the multiplication results along each pixel to obtain the final simulated image. Our method could generate high-fidelity simulated images with spatially variable PSFs without boundary artifacts. The method proposed in this paper significantly improves the speed of astronomical image simulation, potentially advancing observational astronomy and instrumental development.