Advanced Adaptive Optics Algorithms for Astronomical and X-ray Applications

Lisa Poyneer (17-ERD-063)

Executive Summary

We are exploring advanced computational processes for predictive nanometer-level control of a deformable mirror for astronomical adaptive optics and x-ray applications. This work addresses broad DOE and Lawrence Livermore National Laboratory needs to improve beam quality at existing DOE x-ray light-source user facilities.

Project Description

Adaptive optics technology provides real-time correction of image distortions in an optical system. Most commonly used in the field of astronomy, adaptive optics has enabled the direct imaging and spectral characterization of planets orbiting other stars. In a typical system, a wave-front sensor measures optical aberrations and that data is then used to adjust the surface height of a deformable mirror to correct the optical field. While innovation in adaptive optics hardware is essential for advancing optical systems performance, an alternate pathway is to develop better algorithms that translate wave-front sensor measurements into mirror commands.

Predictive control of adaptive optics provides a way to compensate for the inherent delay between when the wave-front sensor “sees” atmospheric turbulence (such as wind), and when the geometry of the telescope’s mirror is updated based on that measurement. Building on extensive prior work, we intend to improve adaptive-optics algorithms in two specific areas: predictive control for astronomical adaptive optics and mirror control for x-ray applications. The new algorithms will have the ability to improve system performance at relatively low cost (i.e., using software upgrades as opposed to new hardware designs).

For astronomical applications, we will synthesize recent research on true wind characteristics (such as speeds and direction) and implementation of predictive control to develop a scheme for computationally efficient wind prediction. For adaptive x-ray optics applications, we will focus on improved algorithms that convert wave-front sensor measurements into mirror commands. These algorithms will be experimentally tested, with the goal of developing nanometer-scale control of the deformable mirror.

This project focuses on creating new algorithms for astronomical adaptive optics and adaptive x-ray optics. Although there is some commonality, for this project the goals are distinct from each other. For astronomical adaptive optics, we will develop the specifications and implementation plan for a predictive-control algorithm that corrects wind-blown turbulence. We intend to (1) develop a comprehensive strategy of the predictive control algorithm, (2) analyze performance of the Gemini Planet Imager telescope system, (3) assess the fit of the frozen-flow model for typical atmospheres (and hence how well the algorithm will perform), and (4) examine lessons learned from both the implementation and performance of the algorithm in the Shane adaptive optics telescope system at the Lick Observatory in San Jose, California.

For adaptive x-ray optics, we will develop new control algorithms for at least one type of wave-front sensor: a grating interferometer or knife-edge probe (i.e., a sample with a very sharp edge) near focus. The knife-edge probe task is inherently more complicated due to the large number of measurements that are needed and the fact that aligning the probe at focus takes much longer than aligning the phase grating. Our algorithms will be experimentally validated at the Advanced Light Source at Lawrence Berkeley National Laboratory, with the goal of controlling the x-ray deformable mirror to within 1 nm root-mean-square height of a desired shape. We expect to develop predictive-control specifications that encompass both the algorithm and its implementation, and identify a plan for implementation. The adaptive x-ray optics algorithms we develop will demonstrate the effectiveness of nanometer-level control of a deformable optical element, and we will use this information to work with light-source partners to identify how to use adaptive x-ray optics technology to enable future equipment upgrades.

Mission Relevance

This work is relevant to Lawrence Livermore National Laboratory's strategic focus area in cyber security, space, and intelligence to enhance situational awareness for space systems, as well as the core competency in computational science and engineering. Skills gained in the development of accurate wave-front sensing benefit other researchers’ efforts to solve a wide range of problems that require imaging contrast from ground or space. Specifically, further development of advanced adaptive-optics algorithms is relevant to the Laboratory's core competency in high-performance computing, simulation, and data science. The adaptive x-ray optics work addresses broad DOE and Laboratory requirements for optics that may significantly improve beam quality at existing DOE x-ray light-source user facilities.

FY17 Accomplishments and Results

In FY17 we (1) developed a comprehensive predictive control strategy, including computational costs; (2) performed experiments to measure atmospheric strength with the Gemini Planet Imager; (3) implemented predictive control in the Shane advanced optics system with a demonstration of delay-only linear quadratic Gaussian control, showing that a hybrid Fourier prediction-matrix reconstruction approach is possible; (4) demonstrated customized beam shaping and fielded a new silicon knife-edge probe at the Advanced Light Source; and (5) began experiments at the Advanced Light Source for phase-grating closed-loop measurements.

A major goal of this project is to improve the control algorithms and sensing techniques used for closed-loop adaptive x-ray optics. In experiments at the Advanced Light Source, we demonstrated the ability to measure a 0.9 nm root-mean-square (RMS) height shape on the surface of an x-ray deformable mirror (XDM) at a signal-to-noise ratio of 2:1. This measurement is shown in the figure, with the red curve representing the measurement and the dashed blue curve representing our estimate of what it would be in the absence of photon noise. With this precise wave-front sensor and a special modal-control matrix, we were able to repeatably drive the surface of the 45-cm long mirror to within 1.2 nm RMS height of its flat figure.

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