Fast iterative tomographic wavefront estimation with recursive Toeplitz reconstructor structure for large-scale systems.

Tomographic wavefront reconstruction is the main computational bottleneck to realize real-time correction for turbulence-induced wavefront aberrations in future laser-assisted tomographic adaptive-optics (AO) systems for ground-based giant segmented mirror telescopes because of its unprecedented number of degrees of freedom, N, i.e., the number of measurements from wavefront sensors. In this paper, we provide an efficient implementation of the minimum-mean-square error (MMSE) tomographic wavefront reconstruction, which is mainly useful for some classes of AO systems not requiring multi-conjugation, such as laser-tomographic AO, multi-object AO, and ground-layer AO systems, but is also applicable to multi-conjugate AO systems. This work expands that by Conan [Proc. SPIE9148, 91480R (2014)PSISDG0277-786X10.1117/12.2054472] to the multi-wavefront tomographic case using natural and laser guide stars. The new implementation exploits the Toeplitz structure of covariance matrices used in an MMSE reconstructor, which leads to an overall O(N log N) real-time complexity compared with O(N2) of the original implementation using straight vector-matrix multiplication. We show that the Toeplitz-based algorithm leads to 60 nm rms wavefront error improvement for the European Extremely Large Telescope laser-tomography AO system over a well-known sparse-based tomographic reconstruction; however, the number of iterations required for suitable performance is still beyond what a real-time system can accommodate to keep up with the time-varying turbulence.

Multi time-step wavefront reconstruction for tomographic adaptive-optics systems.

In tomographic adaptive-optics (AO) systems, errors due to tomographic wavefront reconstruction limit the performance and angular size of the scientific field of view (FoV), where AO correction is effective. We propose a multi time-step tomographic wavefront reconstruction method to reduce the tomographic error by using measurements from both the current and previous time steps simultaneously. We further outline the method to feed the reconstructor with both wind speed and direction of each turbulence layer. An end-to-end numerical simulation, assuming a multi-object AO (MOAO) system on a 30 m aperture telescope, shows that the multi time-step reconstruction increases the Strehl ratio (SR) over a scientific FoV of 10 arc min in diameter by a factor of 1.5-1.8 when compared to the classical tomographic reconstructor, depending on the guide star asterism and with perfect knowledge of wind speeds and directions. We also evaluate the multi time-step reconstruction method and the wind estimation method on the RAVEN demonstrator under laboratory setting conditions. The wind speeds and directions at multiple atmospheric layers are measured successfully in the laboratory experiment by our wind estimation method with errors below 2 ms-1. With these wind estimates, the multi time-step reconstructor increases the SR value by a factor of 1.2-1.5, which is consistent with a prediction from the end-to-end numerical simulation.