Active Optics Correction for the Thick Primary Mirror of the Lijiang 2.4 m Telescope Using Free-Vibration Modes

Modern large telescopes rely on active optics for optimal image quality, but this technology is challenging to apply to thick mirror systems due to their high rigidity. The 2.4-m telescope at Lijiang Observatory has experienced significant image quality degradation, with the stellar full width at half maximum (FWHM) increasing from approximately 1 to over 2 arcseconds despite similar seeing conditions. This decline is attributed to high-order aberrations, including astigmatism, trefoil, and tetrafoil, which are uncorrectable by conventional focus adjustments. This study investigates, for the first time in China to our knowledge, the application of free-vibration-mode-based active correction—previously successful on thin-mirror telescopes—to a thick-mirror system. Using an 18-point active support system, we employed finite element modeling to evaluate the correction capabilities for various aberration modes. The simulations demonstrate high correction efficiency for astigmatism (>95%), along with significant correction for trefoil (84.47%) and tetrafoil (74.50%). However, the actuator forces required to correct trefoil, tetrafoil, and spherical aberration (31.33% efficiency) exceed practical limits. Therefore, the 18-point system is primarily effective for astigmatism correction. These results validate that free-vibration mode-based active optics offer a practical and effective solution for mitigating astigmatism in existing thick-mirror telescopes, thereby improving their observational performance.