For gradient refractive index media with large refractive index gradients, traditional ray tracing methods based on refined elements or spatial geometric steps have problems such as low tracing accuracy and efficiency. The ray tracing method based on refractive index steps proposed in this paper can effectively solve this problem. This method uses the refractive index step to replace the spatial geometric step. The starting point and the end point of each ray tracing step are on the constant refractive-index surfaces. It avoids the problem that the traditional tracing method cannot adapt to the area of sudden change in the refractive index and the area where the refractive index changes sharply. Therefore, a suitable distance can be performed in the iterative process. It can achieve high-efficiency and precise ray tracing in areas whether the refractive index changes slowly or sharply. According to the comparison of calculation examples, this method can achieve a tracing accuracy of ${10}^{-5}$ mm. The speed and precision of ray tracing are better than traditional methods.

This paper proposes a dual-motor configuration to enhance closed-loop performance of a telescope control system. Two identical motors are mounted on each side of a U-type frame to drive the telescope elevation axis instead of a single motor drive, which is usually used in a classical design. This new configuration and mechanism can reduce the motor to half the size used in the former design, and it also provides some other advantages. A master-slave current control mode is employed to synchronize the two motors. Acceleration feedback control is utilized to further enhance the servo performance. Extensive experiments are used to validate the effectiveness of the proposed control algorithm in synchronization, disturbance attenuation and low-velocity tracking.

The main disadvantage of windowless beam expansion systems is that they cannot achieve a good sealing effect. Turbulence and impurities in the environment can easily affect the imaging and primary mirror. Thus, in this study, a matrix of small holes was introduced for inflation to form a stable and smooth flow inside the system to avoid these disadvantages. In order to study the layout of the matrix, the flow state of the model was analysed, and the Lorentz–Lorenz formula and Barron gradient operator were used for ray tracing. Simulation results show that when the matrix of small holes is arranged in 16 rows with 360 holes in each row, inflation has a lesser effect on the wavefront aberration of the system. Moreover, the root mean square (RMS) of wavefront aberration was only 0.077 μm, which was superior to the other layouts considered. Experimental results show that the RMS was 0.08 μm in this state, which is consistent with the analysis. This indicates that this analysis method can meet actual work needs. The calculation methods and calculation results have high reliability and, thus, can be also used in similar situations.

In order to reduce the influence of the backlash in the planetary gears, this paper presents a control method of the double speed loops. The motor speed loop is used as the inner loop and the load velocity loop as the outer loop. Combining with the theoretical analysis and simulation .It is concluded that the double speed loops has a good effect on the non-linear disturbance caused by the backlash. 2. Planetary gear control system structure and performance analysis 2.1 Single speed loop control system structure and performance analysis Will only single-speed loop planetary gear drive model is simplified as shown in Figure 1: