Peter J. Hampton

Distributed modal command for a two-deformable-mirror adaptive optics system.

The design of future single-altitude conjugated adaptive optics (AO) systems may include at least two deformable mirrors (DMs) instead of one as in the current AO system. Each DM will have to correct for a specific spatial frequency range. A method is presented to derive a DM modal basis based on the influence functions of the DM. The modal bases are derived such that they are orthogonal to a given set of modes that restrict the DM correction to a spatial frequency domain. The modal bases have been tested on the woofer-tweeter test bench at the University of Victoria. It has been shown that the rms amplitude of the woofer DM and tweeter DM stroke can be reduced by factors of 3 and 9, respectively, when making the transition from a zonal-driven closed loop to a modal-driven closed loop with the same performance in both cases.

Evaluation of a MEMS deformable mirror for an adaptive optics test bench

An adaptive optics (AO) test bed has been designed and implemented to evaluate the effectiveness of the next generation of AO components and their associated control system. The optical design presented herein incorporates a turbulence generator, tip-tilt mirror, 140-actuator micro-electro-mechanical-system (MEMS) deformable mirror, Shack-Hartmann wave front sensor, and a science camera. This system has been operated in a closed AO loop at a 261 Hz sample rate. This paper focuses on the performance of the MEMS DM. It was examined using an interferometer to determine the influence functions, response time, and the quadratic relationship of displacement of the actuators to an applied voltage.

Control of a woofer tweeter system of deformable mirrors

This paper describes the control of two deformable mirrors (DM) and a tip tilt mirror for adaptive optics. The purpose of this experimental adaptive optics system at the University of Victoria is to prove the Woofer Tweeter concept for use in instruments for the Thirty Meter Telescope (TMT) which is currently under development. The first deformable mirror is a large stroke DM (Woofer) capable of lower frequency correction in both the temporal and spatial domains. The other DM (Tweeter) is capable of the high temporal and spatial frequency corrections of the turbulence. The response speed of the Woofer is incorporated into the Tweeter controller in order to allow for appropriate offloading from the Tweeter to the Woofer. In order to determine which Tweeter shapes must compensate for the slower Woofer and which are not coupled to the Woofer, the cross correlation of the devices is determined. The method of converting the wave front sensor (WFS) measurements to control signal error is given. The transfer functions of the controller are provided, along with rejection ratio plots, bandwidths and amplitude response to system noise.

A conceptual design for the Thirty Meter Telescope adaptive optics systems

In this paper, we provide an overview of the adaptive optics (AO) program for the Thirty Meter Telescope (TMT) project, including an update on requirements; the philosophical approach to developing an overall AO system architecture; the recently completed conceptual designs for facility and instrument AO systems; anticipated first light capabilities and upgrade options; and the hardware, software, and controls interfaces with the remainder of the observatory. Supporting work in AO component development, lab and field tests, and simulation and analysis is also discussed. Further detail on all of these subjects may be found in additional papers in this conference.

A New Wave-Front Reconstruction Method for Adaptive Optics Systems Using Wavelets

A new technique for wave-front reconstruction from gradient measurements on a square data set is presented. This technique is based on obtaining the Haar wavelet image decomposition of the original wave-front by appropriate filtering and down-sampling of the gradient measurement data. The use of the wavelet decomposition leads to an algorithm with complexity of O(N), where N is the number of data points in the reconstruction, and at the same time allows denoising of the data using the wavelet coefficients. The proposed technique is illustrated with two examples and its reconstruction accuracy, computational speed and denoising performance are discussed. Results indicate that the proposed technique is a computationally efficient and accurate technique for wave-front and/or image reconstruction from gradient measurements.

Radial thresholding to mitigate laser guide star aberrations on centre-of-gravity-based Shack–Hartmann wavefront sensors

Sodium laser guide stars (LGSs) are elongated sources due to the thickness and the finite distance of the sodium layer. The fluctuations of the sodium layer altitude and atom density profile induce errors on centroid measurements of elongated spots, and generate spurious optical aberrations in closed-loop adaptive optics (AO) systems. According to an analytical model and experimental results obtained with the University of Victoria LGS bench demonstrator, one of the main origins of these aberrations, referred to as LGS aberrations, is not the centre-of-gravity (CoG) algorithm itself, but the thresholding applied on the pixels of the image prior to computing the spot centroids. A new thresholding method, termed ‘radial thresholding’, is presented here, cancelling out most of the LGS aberrations without altering the centroid measurement accuracy.

Closed-loop control of a woofer–tweeter adaptive optics system using wavelet-based phase reconstruction

A novel closed-loop control technique for adaptive optics (AO) systems based on a wavelet-based phase reconstruction technique and a woofer-tweeter controller is presented. The wavelet-based reconstruction technique is based on obtaining a Haar decomposition of the phase screen directly from gradient measurements and has been extended here with the use of a Poisson solver to improve performance. This method is O(N) (i.e., a linear computation cost as number of actuators increases) and is the fastest of the known O(N) reconstruction techniques. The controller configuration is based on the woofer-tweeter controller to control low- and high-spatial-frequency aberrations, respectively. The separation of the woofer and tweeter signals is done using a computationally efficient method that is based on the availability of a low-spatial-resolution reconstruction during the wavelet synthesis process. The performance of the proposed technique is evaluated using a simulated AO system and phase screens generated to reflect atmospheric turbulence with various dynamic characteristics. Results indicate that the combination of the wavelet-based phase reconstruction and woofer-tweeter controller leads to very good results with respect to speed and accuracy.

A wavelet based method for image reconstruction from gradient data with applications

In this paper, an algorithm for image reconstruction from gradient data based on the Haar wavelet decomposition is proposed. The proposed algorithm has two main stages. First, the Haar decomposition of the image to be reconstructed is obtained from the given gradient data set. Then, the Haar wavelet synthesis is employed to produce the image. The proposed algorithm is based on the relationship between the Haar analysis and synthesis filters and the model for the discretized gradient. The approach presented here is based on the one by Hampton et al. (IEEE J Sel Top Signal Process 2(5):781–792, 2008) for wavefront reconstruction in adaptive optics. The main strength of the proposed algorithm lies in its multiresolution nature, which allows efficient processing in the wavelet domain with complexity

The Woofer-Tweeter Experiment

{\fancyscript{O}}(N)