Fast Image Definition Evaluation Based on Energy Concentration for Auto-Focusing on Wide-Angle Telescope

Ground Wide Angle Cameras (GWAC) consists of 36 wide-angle telescopes to observe optical transients. It has super-large field of view, short cadence exposures and real-time data processing. Auto-focusing is crucial to the system for realizing automatic observation and increasing scientific output. Enhancing the star's energy concentration is the main purpose of auto-focusing. The current evaluation methods such as 50% energy's radius and the full width of half maximum of point spread function take too much amount of calculation. Based on the rule that the central part of stars change sharply during focusing while the entire range of stars stay roughly the same, this paper presents a fast image definition evaluation method that calculates the ratio between the flux within a certain central part of the star to its total flux, and studies on the choice of the two radiuses for aperture photometry. This paper also simplifies the photometry method, and selects the relative parameters such as background, star selection standard and star amount. A fast and accurate algorithm is archived for GWAC real-time auto-focusing system. The computation time is 0.1s per frame, which meets the requirement of GWAC auto-focusing system.