Adaptive optics (AO) applied in compensation for atmospheric turbulence usually requires a sufficient guide star (GS) in the isoplanatic patch around the interesting object to provide accurate information of the wave-front distortion induced by atmospheric turbulence. However, as there are not enough bright and available natural guide stars (NGSs) in the sky, the concept of a sodium laser guide star (LGS) has been publicly proposed for overcoming the limitations due to the finite sky coverage of the observation telescope with AO, which is generated by resonance scattering from the sodium atoms in the mesospheric layer with a ground-based projected laser with a wavelength of 589 nm. Due to sufficient sampling of the atmospheric turbulence at high altitude, the concept of a sodium LGS has been receiving huge attention from the moment it was proposed and was first to be applied in the field of high-resolution astronomical observation through atmospheric turbulence with AO. However, due to the limitations of the excitation efficiency of LGS lasers and the sodium column density of the mesospheric layer, the actual brightness of the generated sodium laser guide star is limited. Therefore, so far, in the field of astronomical observation, almost all sodium LGS AO systems have to operate at night, so their operation hours have been greatly limited. Under daytime conditions, the effectiveness of sub-aperture segmentation wavefront centroid detection using a Hartmann-Shack (HS) sensor with weak photon returns from sodium LGS is challenging, due to the fact that the intensity of the skylight background can reach several thousand times that of the sodium LGS. The objective of this paper is to develop a reliable and practical atmospheric turbulence wave-front sensing technique for sodium LGS, which can provide a certain theoretical reference and engineering experience for daytime applications of sodium LGS AO systems in the future.

Based on the aforementioned purpose, by combining theoretical analysis, parameter design, component development, system integration and detection experiment, an atmospheric wave-front active sensing technique for sodium LGS during daytime has been investigated in this paper. Our guiding ideology is to use spectral filtering, spatial filtering, and temporal filtering to match and suppress strong stray light interference while making an effort to maintain the photon returns from the sodium LGS at the wavelength of 589 nm. The above mentioned strong stray light interference includes the skylight background and Rayleigh back scattering at 589 nm of the atmospheric molecules. Firstly, based on the optical spectrum distribution characteristics of the skylight background, the feasibility of spectral filtering for a high optical transmittance with a nanometer scale line-width and a 589.16 nm center wavelength is analyzed. Secondly, based on the field of view (FOV) distribution characteristics of the skylight background, the feasibility of spatial filtering for accurately matching the FOV of the sub-aperture for the HS sensor is analyzed. Finally, in combination with the universal dual telescope mode for pulsed sodium LGS laser projection/sodium LGS photon return detection, the mathematical expressions of important parameters such as the duration of the pulsed resonance sodium LGS scattered return-light Δt_Na(E), the suppression duration of the Rayleigh scattered light from low altitudes Δt_{Rayleigh-Stop}(E) and so on are derived, which constitute the theoretical foundation of our temporal filtering. Based on the above analysis and combined with the construction of an experimental system, parameter design, detection ability estimation, and component development are carried out for our synthetic filtering and applied in traditional HS sensors. A daytime atmospheric wave-front detection experiment for sodium LGS is carried out.The experimental results are in good agreement with those of the theoretical analysis.

Due to the demand for atmospheric wave-front detection for sodium LGS AO during daytime, an active wavefront sensing technique with synthetic filtering (namely, spectral filtering, spatial filtering and temporal filtering) is proposed in this paper. The detection ability after synthetic filtering is estimated, it can achieve effective atmospheric wavefront detection of an equivalent of 7-magnitude brightness sodium LGS under typical 12 W/(m²·sr) skylight background conditions (Table 1). Compared with traditional sodium atom filtering (Table 2), it has advantages regarding the equivalent photon returns maintained and the signal to noise (SNR) ratio for sodium LGS in an HS sensor. Based on this technique, a real-time detection of atmospheric wave-front distortion with sodium LGS under 10 W/(m²·sr) skylight background conditions is achieved (Fig.11), which is a beneficial attempt for daytime atmospheric wave-front detection with sodium LGS.

In response to the demand for atmospheric wavefront distortion detection with sodium LGS under strong skylight background, an active wavefront detection technique with synthetic filtering is proposed and investigated in this paper. Synthetic filtering is used to match and suppress strong stray light interference while making an effort to maintain the photon returns from sodium LGS. The theoretical analysis, parameter design and detection capability estimation for this technique are discussed. Then, using this technique, atmospheric wave-front distortion detection for AO using sodium LGS is carried out experimentally. When the brightness of the sky background is 10 W/(m²·sr), the atmospheric wave-front distortion is effectively detected based on the pulsed sodium LGS in real-time. This work is helpful in expanding the working period of the sodium LGS AO systems.