Problems with twilight/supersky flat-field for wide-field robotic telescopes and the solution

Twilight/night sky images are often used for flat-fielding CCD images, but the brightness gradient in twilight/night sky causes problems of accurate flat-field correction in astronomical images for wide-field telescopes. Using data from the Antarctic Survey Telescope (AST3), we found that when the sky brightness gradient is minimum and stable, there is still a gradient of 1% across AST3's field-of-view of 4.3 square degrees. We tested various approaches to remove the varying gradients in individual flat-field images. Our final optimal method can reduce the spatially dependent errors caused by the gradient to the negligible level. We also suggest a guideline of flat-fielding using twilight/night sky images for wide-field robotic autonomous telescopes.