## 2 Auto-Focus Experiment Set  
Generally speaking, if a CCD camera sensor is off the focal plane of an optical system, one can only obtain defocused images with blurred edges. In the frequency domain, this means that the high-frequency components of an image with distinct edges are filtered out due to the low-frequency pass characteristics of the system [18]. To capture a clear image, the basic idea of the AFT is to adjust the lens of the optical system to a proper position so that the CCD camera sensor is well positioned at the focal plane, and abundant high-frequency (HF) components are then obtained to provide a distinct boundary contour of the image. In digital image processing techniques, an HF filter is used to obtain the HF components of the fast Fourier transform (FFT) results of the CCD image [19]. If the amplitudes of corresponding HF components are larger than some present value, then we can say that the CCD image is clear enough, i.e., auto-focus has been achieved [20].  
Applying the auto-focus principle above, the AFT of a Cassegrain telescope EOTS system was investigated, as shown in Figure 1. The EOTS system mainly consists of five parts [21]: Cassegrain telescope, CCD camera, PC control module, stepper motor, and mechanical conversion module. In the experiment, a Cassegrain telescope composed of a fold back mirror structure with two primary and secondary parabolic reflectors was used to collect the information of detected objects. To enhance the imaging quality, a Schmidt corrector was mounted in front of the telescope; there was also a CCD [22] camera with a narrow band filter to detect the image and to send the filtered results to the PC control module. In the control module, based on the image estimation, a stepper motor was used to adjust the position of the primary mirror of the telescope in the control device.  
In Figure 1, the auto-focus process is given as follows [23; 24]: firstly, the CCD camera captures information of tracked objects through the telescope and sends the image to the PC control program. Next, the PC control program performs an estimation of the CCD image and sends commands to rotate the stepper motor in a clockwise or counter-clockwise direction. Then, a mechanical conversion module turns the rotation force into a driver that adjusts the position of the primary mirror in the telescope forward or backward, and subsequently changes the imaging position. The above processes are repeated until the CCD camera is on the image plane of the telescope so that a clear image is obtained, making this auto-focus process a closed-loop system.  
The focus search algorithm determines the concrete focus process of the system. In the experiment, the hill-climbing search method was used to achieve a better focusing effect. The specific steps are shown in Figure 2. First, we initialize the starting position of the motor knob and set a large initial rotation step length, recording the initial IEF value as the maximum value. The stepper motor rotates the knob at the current step length to adjust the focal length of the system and constantly calculates the IEF value. When the IEF value starts to decrease, it means that the best focusing position has been missed, and the knob is then rotated one step backward. Then, the current step length size is halved and the above search process is repeated until the search is completed with the minimum step size (accuracy) of the stepper motor. Then, the auto-focus process can be considered as finished.