Adaptive optics technology provides core assurance for high-resolution optical systems by real-time detecting and correcting dynamic wavefront distortions. Since the concept of adaptive optics was first proposed by Babcock in 1953, this technology has been successfully extended to fields such as astronomical observation, laser beam purification, and assisted medical treatment, achieving a significant improvement—approximately 2-fold—in indicators like the concentration of far-field spot energy (β factor). However, constrained by high-order residual aberrations, existing systems still struggle to achieve near-diffraction-limited performance. Research indicates that such residual aberrations mainly stem from high-frequency, high-order aberrations induced by vibrations of the optical platform—vibrations caused by components such as coolers, fans, etc. For instance, Rousset et al. found that high-frequency narrowband aberrations induced by vibrations of electronic components in the very large telescope (VLT) lead to a decrease in the Strehl ratio of imaging spots; Kulcsár et al. further revealed that 55 Hz narrowband disturbances excited by the cooling system of the Gemini South Telescope (GST) exhibit significant coupling effects in Zernike high-order modes (e.g., defocus and coma), severely impairing the system’s imaging quality. Effectively suppressing such high-frequency, high-order aberrations has become a key challenge in enhancing the performance of adaptive optical systems.

To achieve effective correction of high-frequency, high-order aberrations, this paper proposes a linear quadratic Gaussian (LQG) control architecture based on full-mode prediction. This method innovatively introduces a full-mode wavefront aberration coefficient prediction model. Firstly, dynamic equations for Zernike modes are established through online spectral analysis and parameter identification. Secondly, the Kalman filter is employed to perform multi-step-ahead prediction of full-mode coefficients; when combined with optimal voltage calculation, this forms a closed-loop correction mechanism, which can enhance the adaptive optical system’s capability to correct high-frequency, high-order aberrations. It is expected to achieve near-diffraction-limited correction for such aberrations.

To verify the superiority of the proposed method over proportional-integral (PI) control in correcting high-frequency, high-order aberrations, comparative experiments between the LQG and PI control methods were conducted on 25 Hz defocus aberrations (Fig. 3). When the PI control method was used to correct 25 Hz defocus aberrations, the correction effect was not significant: the root mean square (RMS) value of the input aberration only decreased from 0.371 μm (before correction) to 0.189 μm, and the peak-to-valley (PV) value decreased from 1.949 μm to 0.850 μm. In contrast, the LQG control method exhibited excellent correction performance for 25 Hz defocus aberrations: the RMS value of the input aberration significantly decreased from 0.554 μm (before correction) to 0.056 μm, and the PV value decreased from 2.271 μm to 0.295 μm (Table 1).To further validate the method’s effectiveness in correcting higher-frequency and higher-order aberrations, correction experiments were conducted on 180 Hz defocus and coma (Fig. 4). Under a sampling frequency of 500 Hz, using the proposed method to control deformable mirror (DM2) reduced the input aberration to nearly 1/10 of its initial value (Tables 2 and 3).To confirm the LQG method's correction effect on mixed high-frequency, high-order aberrations, experiments were performed on mixed high-order aberrations (180 Hz defocus, 180 Hz astigmatism, and 180 Hz coma) (Fig. 5). The LQG method achieved a spectral suppression amplitude of more than 23 dB for all mixed high-frequency, high-order aberrations (defocus, astigmatism, and coma) (Table 4).

Experimental results demonstrate that the LQG modal coefficient prediction correction method exhibits excellent suppression effects on both single-order and mixed-mode aberrations. It can extend the control bandwidth of adaptive optical systems to more than 1/3 the sampling frequency, overcoming the traditional limitation of 1/20 the sampling frequency. This holds promise for achieving near-diffraction-limited correction of high-frequency, high-order aberrations in adaptive optical systems.