Experimental validation of single-iteration multigrid wavefront reconstruction at the Palomar Observatory

Abstract

Single-iteration multigrid (SIMG) wavefront reconstruction schemes were implemented and validated on the adaptive optics system at the Hale 5.1 m telescope at the Palomar Observatory. Results indicate that even the simplest such method produces a performance indistinguishable from that of the standard leastsquares reconstructor for both bright and dim guide stars. SIMG provides a dramatic reduction in computational cost when compared to vector-matrix multiplication and can be implemented in parallel, making it the obvious choice for reconstruction in future large-scale adaptive optics systems. [6]. In this Letter, we detail the experimental validation of this work on a real SCAO system.Two computationally efficient methods that have previously been tested on-sky are the FD method [7] and a sparse method [4]. These methods are O͑n log n͒. The SIMG is O͑n͒ and shows no performance degradation when compared to the leastsquares reconstructor.A good model for the wavefront sensor (WFS) is [6,8] where x is the wavefront phase, y are the measurements, v is white noise, and G is a sparse influence matrix. The least-squares reconstruction matrix is found by taking the pseudoinverse. In practice, we can compute it by evaluating K = ͑G T G + ⑀I͒ −1 G T for a small ⑀. This ensures that unobservable modes such as piston and waffle are zeroed out. The SIMG method [6] uses a single multigrid sweep with an initial guess of 0 to obtain an approximate solution to the equationIf the measurements are taken in open-loop, x is the wavefront phase. In this case, x 0 = 0 is a bad guess, so multiple iterations are required to achieve acceptable convergence [6]. However, when we operate in closedloop, x is the change in wavefront phase between successive time steps, and only one iteration is required. Our tests were performed on the Palomar Adaptive Optics (PALAO) system on the Hale 5.1 m telescope [9]. The PALAO system has a deformable mirror (DM) with 241 active actuators and a ShackHartmann WFS array with 256 subapertures, producing a total of 512 measurements. The DM and WFS are aligned in a Fried geometry.The AO system collects measurements y at up to 2 kHz. Tip and tilt are removed from the wavefront using a fast-steering mirror (FSM) and proportionalintegral (PI) controller. The rest of the wavefront offset x is reconstructed by VMM: x = Ky. This estimate is fed back through a second PI loop to the DM. The closed-loop corrected wavefront is split using a dichroic mirror. The near-infrared portion is sent to the Palomar High Angle Resolution Observer (PHARO) [10]. See Fig. 1.To implement the SIMG on the PALAO system, virtual actuators were added to fill the 17ϫ 17 grid containing the circular actuator arrangement, and the influence matrix G was augmented with zeros appropriately, as in [3]. The new system is y = Ḡ x, where Ḡ is 512ϫ 289 instead of 512ϫ 241. This new system is September 15, 2008 / Vol. 33, No. 18 / OPTICS LETTERS 2047 0146-9592/08/182047-3/$15.00

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

“…At cold start, where MINRES iteration starts with a zero initial guess, the system converges with 141 iterations in 71 ms to a WFE RMS of 115 nm. At warm start [27], the number of iterations is reduced to 70 in 36 ms.…”

Weighted Fried reconstructor and spatial-frequency response optimization of Shack–Hartmann wavefront sensing

“…As can be seen from Eqs. (16) and (17), the weighted Fried response functions are both real functions, which have phase spectrums that are evenly zero for all frequencies.…”

“…(16) and (17) seem too cumbersome to operate, the simplified one-dimensional (1-D) versions with α β are preferred when performing the optimization. As can be seen from Fig.…”

“…Though the optimized reconstructors seem to be a bit more complicated than the classical ones, as shown in Section 2, the increase in computation time is expected to be mild when a matrix-vector-multiple (MVM) method is used. As for other advanced computational methods, such as multigrid [15,16], the reconstruction speed of weighted Fried II can also be guaranteed, since these methods mainly require that the matrix of the sensor geometry is sparse, while the weighted Fried II one obviously has sufficient sparsity. Especially in AO systems for high-power laser wavefront control, the speed effect can usually be neglected.…”