As a precise optical instrument, a telescope is subject to changes in its focus position due to atmospheric disturbances, temperature changes, and installation errors. If real-time focusing is not performed, the image may be distorted, which would seriously affect the tracking and measurement effects of the telescope. With the improvement of the intelligence level, automatic focusing technology is applied to the focusing of the telescope system. The algorithm to evaluate the image sharpness is the key to the decision of the focus position of the telescope's automatic focusing technology, whose performance directly determines the accuracy of automatic focusing. The traditional algorithm for evaluating the focusing of a telescope is implemented on the basis of statistical analysis, which can hardly ensure the real-time performance and noise immunity of astronomical images. Most of the existing algorithms have relatively poor performance, and it is difficult for them to extract target features from the captured images of high-speed moving targets. Moreover, it is often impossible to evaluate the engineering level of algorithms and hardware due to insufficient hardware experiments on the system. To solve the above problems, this study proposes a half-flux diameter real-time auto-focusing sharpness evaluation algorithm with improved centering accuracy (HFD-ICA). The algorithm has a low cost, high real-time performance, and good stability and is suitable for the focusing of most telescope systems. It is expected that this method can improve the autofocusing performance of telescopes and provide references for research in related fields.

First, the acquired raw image sequence (defocus-focus-defocus) is denoised by the anisotropic diffusion method. Then, the denoised image is binarized by the Qtsu threshold method, and the target star is extracted from the background. Upon binarization, the pixels adjacent to the target are clustered, and the boundary of the target is calculated to obtain the target region of interest (ROI). According to the determined ROI domain, the improved intensity-weighted centroid (improved IWC) method is used to iteratively calculate the centroid of the star image until the centroid reaches the accuracy level of sub-pixels. After the centroid is determined, the half-flux diameter (HFD) value of the star image is measured by the HFD-ICA method, and the hyperbolic fitting method is used to further process these values. The V-shaped curve that guides the focusing of the telescope can be drawn, and the focus position of the telescope can be determined.

The HFD value measured by the proposed algorithm is V-shaped with the focus position, and the V-shaped curve represents the characteristics of the optical system consisting of the focus, telescope, and camera (Fig. 13). The focusing accuracy of the HFD-ICA algorithm is high, and its fixed focus rate is equivalent to that of the high-precision astronomical image processing software IRAF, both reaching 98% (Table 1). The anti-noise performance test of the algorithm shows that after the addition of a small amount of noise, the gray value around the star point changes, which interferes with the processing performance of the algorithm, and the precise fixed focusing rate of the algorithm is affected to a certain extent. In comparison, the anti-noise performance of HFD-ICA is the best (Table 2). Furthermore, compared with other algorithms in terms of operation time, the HFD-ICA algorithm has a faster calculation time and the best real-time performance. Compared with the results of the HFD method, the real-time performance is improved by about four times. The full width at half maximum (FWHM) method takes a lot of time because it requires curve fitting during measurement. The average processing time reaches 32.4 s, which is about 6.89 times that of HFD-ICA. The software IRAF with relatively high processing accuracy has an average processing time as high as 45.7 s, which is nearly 10 times longer than that of the HFD-ICA method (Table 3).

This paper mainly studies the algorithm for evaluating the image sharpness under the automatic focusing of telescopes. The experiments verify that the HFD-ICA method is stable, efficient, and robust and can handle the image frames seriously out of focus when it is used to guide the automatic focusing of the 1.2 m telescope system. Compared with the HFD method without improved centering accuracy, the algorithm has improved performance, and its precise fixed focusing rate is comparable to that of the high-precision astronomical image processing software IRAF, both reaching 98%. The average processing time of the algorithm in the process of guiding focusing is only 4.7 s, 1/10 of that of IRAF, which meets the real-time requirements of the focusing system. Compared with the case of the system's original manual focusing, this study improves the system's average focusing efficiency by roughly 37%. To a certain extent, the research lays the foundation for the fully automated observation of future stations and also provides a reference for the automatic focusing of other telescope systems.