Objective  The primary mirrors of large solar telescopes are continuously affected by solar radiation, causing the mirror surface temperature to be higher than the air temperature. Under the action of the temperature difference between the mirror surfaces, the air near the mirror surface is heated, causing the air density to be unevenly divided, resulting in abnormal atmospheric refraction, resulting in mirror seeing, which degrades the image quality of the solar telescope. Solar telescopes mostly use Gregorian optical systems, and their primary mirrors are aspherical mirrors. Foreign experimental research mainly uses plane mirrors or spherical mirrors for experiments. However, due to factors such as mirror surface shape, effective aperture and experimental optical path, the theoretical relevance of the experimental results is low. Mirror seeing is the coupling effect between the mirror and the surrounding air. Only numerical simulations have been carried out in China, and no relevant experimental research has been conducted on mirror seeing. Direct experimental detection is a more reliable solution. In order to control the near-mirror seeing caused by the temperature increase of the primary mirror, the mirror temperature control target needs to be given quantitatively. The main mirrors of large-aperture solar telescopes mostly use aspherical mirrors. The experimental platform of this article uses a 1 550 mm diameter hyperbolic mirror for research to improve the universality of the experimental results.

  Methods  First, based on the solid-flow field coupling caused by temperature gradient and gas flow, this paper proposes the formation mechanism of the specular seeing effect and establishes the theory of the specular seeing effect caused by atmospheric optical turbulence. Then, based on the physical process of atmospheric turbulence producing mirror seeing, under two conditions of natural convection and forced convection (Fig.1), an experiment for a 1 550 mm large-diameter hyperbolic mirror was built (Fig.3), and the experimental data (Tab.2-4), analyze the effect of the temperature difference between the mirror surface and the surrounding air on the mirror seeing under different wind speed conditions (Fig.8-9). Finally, the experimental models under different convection conditions are summarized (Fig.10-11), and the solar telescope temperature control target is determined.

  Results and Discussions   Experimental results show that mirror seeing is related to the mirror temperature difference. The interaction between natural convection and external forced airflow near the mirror has a transition from expected stability to instability. Forced blowing causes tiny air molecules to move near the mirror. Even small-scale turbulent movements can cause very sensitive changes in mirror seeing. Mirror temperature difference and wind speed have a strong correlation with mirror seeing (Fig.8-9). Increasing active ventilation can reduce mirror seeing. When the temperature difference is 4 ℃, the mirror seeing under natural convection is 1.43″; when the temperature difference is 3 ℃, the mirror seeing under 0.2 m/s forced convection is 0.44″, and when the temperature difference is 1 m/s forced convection, the mirror seeing is 0.27″. According to the mirror seeing effect tolerance standard, combined with Tab.2-4 and Fig.9, under weak mixed convection conditions (U=0.2 m/s), the mirror-air temperature difference should be controlled below 0.2 K; in Under strong mixed convection conditions (U=1.0 m/s), the mirror-air temperature difference should be controlled below 1 K.

  Conclusions  Due to the influence of solar radiation, the temperature of the main mirror of the solar telescope is higher than that of the surrounding air, causing mixed convection above the mirror. Random fluctuations in atmospheric density or temperature trigger turbulence in the refractive field, with the temperature fluctuation being the largest and random, resulting in a mirror seeing effect in the thin area above the specular viscous conductive layer. This article starts from the theory of atmospheric optical turbulence and combines the experimental data of the 1 550 mm hyperboloid primary mirror under different convection conditions to study the quantitative relationship between mirror temperature rise and telescope observation image quality, providing a research basis for setting the temperature control target of the solar telescope's primary mirror. This study focuses on the common problem of large solar telescopes - the influence of the mirror seeing on the degradation of the telescope image quality. It analyzes the atmospheric turbulence process of the mirror from the perspective of atmospheric optical turbulence, summarizes and simplifies the experimental data, and further analyzes its impact on the telescope image. The influence caused by quality is derived from the empirical formula. In order to lay the foundation for improving the working resolution of the telescope, this work will also provide the necessary preliminary research foundation for the construction and observation of the 8-meter China Giant Solar Telescope (CGST).