Pieter Piscaer, Oleg Soloviev, and Michel Verhaegen, "Phase retrieval of large-scale time-varying aberrations using a non-linear Kalman filtering framework," J. Opt. Soc. Am. A 38, 25-35 (2021)
This paper presents a computationally efficient framework in which a single focal-plane image is used to obtain a high-resolution reconstruction of dynamic aberrations. Assuming small-phase aberrations, a non-linear Kalman filter implementation is developed whose computational complexity scales close to linearly with the number of pixels of the focal-plane camera. The performance of the method is tested in a simulation of an adaptive optics system, where the small-phase assumption is enforced by considering a closed-loop system that uses a low-resolution wavefront sensor to control a deformable mirror. The results confirm the computational efficiency of the algorithm and show a large robustness against noise and model uncertainties.
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${p_c}$ represents the rank of the approximated term in Eq. (37), $ L $ is the number of the IKF iterations, and ${L_{{\rm CG}}}$ is the average number of CG iterations. The other symbols are included in Table 1.
If not mentioned otherwise, the standard values are used. Turbulence layer 2 is located at an altitude of 5000 m and is moving at an angle of 90° w.r.t. layer 1 located at 0 m. The conversion of magnitude ${\beta _m}$ to photon flux is given by Eq. (17). The source is a single natural guide star.
Tables (4)
Table 1.
List of Frequently Used Notations and Symbols
Average number of non-zero elements per row/column of any sparse banded matrix
Number of actuators inside the aperture
Size of grid in pupil plane () and number of pixels inside aperture, respectively
${p_c}$ represents the rank of the approximated term in Eq. (37), $ L $ is the number of the IKF iterations, and ${L_{{\rm CG}}}$ is the average number of CG iterations. The other symbols are included in Table 1.
If not mentioned otherwise, the standard values are used. Turbulence layer 2 is located at an altitude of 5000 m and is moving at an angle of 90° w.r.t. layer 1 located at 0 m. The conversion of magnitude ${\beta _m}$ to photon flux is given by Eq. (17). The source is a single natural guide star.