## 1 Introduction  
The emergence and development of optical telescope systems have provided effective tools for helping people to understand the universe. In addition, optical telescopes also play an increasingly important role in target ranging, astronomical observation, earth science, laser communication, and national production. With the development of science and technology, higher requirements have been placed on the spatial resolution of these telescopes and their ability to gather light. According to the Rayleigh criterion, the most effective way to improve the spatial resolution of a telescope system is to increase its aperture. Moreover, increasing the aperture is also an important means of increasing the light collection capacity of a telescope system [1; 2]. Due to limitations on the fabrication and processing of optical crystal windows, however, it is difficult to obtain suitable optical windows for large-aperture optical systems [3]. Instead, an active intake approach can be used to prevent dust, water vapour, and other impurities in the external environment from entering a windowless beam expanding system and damaging the primary mirror. In this approach, a stable, undisturbed airflow is continuously introduced into the beam expanding system to replace its current internal gas, thus forming a stable flow field inside the system [4; 5; 6]. However, with any change in the density of the flow field, the original path of a light beam propagating through the system is also changed, which will result in deflection or a phase change of the light, and thus cause image offset, blur, jitter, energy loss, and other imaging errors on the imaging plane; these phenomena are called aero-optical effects. A large number of studiespoint out that the aero-optical effect of the flow field is essentially caused by the instability of the refractive index field. Reducing the instability of the refractive index field of the flow field is the most fundamental way to reduce the aero-optical effect [7; 8; 9].  
Many scholars have reported significant research conclusions related to aero-optical effects. For example, [PERSON] et al. and [PERSON] et al. studied the impact of external environmental loads on the imaging capabilities of telescope systems [10; 11]. [PERSON] et al. conducted relevant research on aero-optics [12; 13]. [PERSON] et al. studied the influence of the flow field in the internal channel on optical system performance [14]. However, most scholars focus on external fluidity, the internal channel and the flow field control. The effect of intake layout on the wavefront in beam expanding systems is still unclear.  
In this paper, we focus on the effect of intake layout on the wavefront in a beam expanding system. A gas intake system is proposed for the beam expanding system of the 850 mm optical telescope. In this system, the matrix of the intake is used to inflate the beam expanding system to obtain a relatively stable internal flow. To be specific, we design a model of the intake, in which the number of rows and the number of air inlet vents per row are assumed for two variables which we called variable I and variable II. We hope to find the relative optimal value of the two variables through simulation under certain conditions, so as to minimize the influence of the flow field on the beam in the expanding system and minimize the wavefront error of the beam passing through the beam expanding system. At the same time, it is necessary to find an analysis method suitable for this kind of work. In short, we hope to reduce the influence of the flow field on the light beam through the system by changing the inlet layout.