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Machine learning is finding increasingly broad applications in the physical sciences. This most often involves building a model relationship between a dependent, measurable output, and an associated set of controllable, but complicated, independent inputs. We present a tutorial on current techniques in machine learning—a jumping-off point for interested researchers to advance their work. We focus on deep neural networks with an emphasis on demystifying deep learning. We begin with background ideas in machine learning and some example applications from current research in plasma physics. We discuss supervised learning techniques for modeling complicated functions, beginning with familiar regression schemes, and then advancing to more sophisticated deep learning methods. We also address unsupervised learning and techniques for reducing the dimensionality of input spaces. Along the way, we describe methods for practitioners to help ensure that their models generalize from their training data to as-yet-unseen test data. We describe classes of tasks—predicting scalars, handling images, and fitting time-series—and prepare the reader to choose an appropriate technique. We finally point out some limitations to modern machine learning and speculate on some ways that practitioners from the physical sciences may be particularly suited to help.

Adaptive optics (AO) is a technology that corrects in real time for the blurring effects of atmospheric turbulence, in principle allowing Earth‐bound telescopes to achieve their diffraction limit and to “see” as clearly as if they were in space. The power of AO using natural guide stars has been amply demonstrated in recent years on telescopes up to 3–4 m in diameter. The next breakthrough in astronomical resolution was expected to occur with the implementation of AO on the new generation of large, 8–10 m diameter telescopes. In this paper we report the initial results from the first of these AO systems, now coming on line on the 10 m diameter Keck II Telescope. The results include the highest angular resolution images ever obtained from a single telescope (0 \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsx...

High-brightness and short-pulse-width ( approximately 200 ps) x-ray lasers offer biologists the possibility of high-resolution three-dimensional imaging of specimens in an aqueous environment without the blurring effects associated with natural motions. As a first step toward developing the capabilities of this type of x-ray microscopy we have used a tantalum x-ray laser (lambda = 4.483 nm) together with an x-ray zone plate lens to image a test pattern. The observed image shows a detector-limited resolution of approximately 75 nm and paves the way to three dimensional biological imaging with high spatial resolution (20-30 nm).

x-Ray computed axial tomography (CT) provides cross-sectional views of materials, components, and assemblies for industrial non-destructive evaluation. We have applied CT imaging to quantitatively measure the 3-D distribution ogf x-ray attenuation at reasonably high resolutions. In our industrial x-ray CT-studies, we have centered on two technical approaches: a first-generation translate/rotate CT system that consist of well-collimated (∼ 0.55 mm) photon source detector, and a third-generation scanner that uses a fluoroscopy detector.

The Solid-State, Heat-Capacity Laser (SSHCL), under development at Lawrence Livermore National Laboratory is a large aperture (100 cm{sup 2}), confocal, unstable resonator requiring near-diffraction-limited beam quality. There are two primary sources of the aberrations in the system: residual, static aberrations from the fabrication of the optical components and predictable, time-dependent, thermally-induced index gradients within the gain medium. A deformable mirror placed within the cavity is used to correct the aberrations that are sensed externally with a Shack-Hartmann wavefront sensor. Although it is more challenging than external correction, intracavity correction enables control of the mode growth within the resonator, resulting in the ability to correct a more aberrated system longer. The overall system design, measurement techniques and correction algorithms are discussed. Experimental results from initial correction of the static aberrations and dynamic correction of the time-dependent aberrations are presented.

The use of a Hartmann wave-front sensor to accurately measure the line-integrated electron density gradients formed in laser-produced and z-pinch plasma experiments is examined. This wave-front sensor may be used with a soft-x-ray laser as well as with incoherent line emission at multikilovolt x-ray energies. This diagnostic is significantly easier to use than interferometery and moire deflectometry, both of which have been demonstrated with soft-x-ray lasers. This scheme is experimentally demonstrated in the visible region by use of a Shack-Hartmann wave-front sensor and a liquid-crystal spatial light modulator to simulate a phase profile that could occur when an x-ray probe passes through a plasma. The merits of using a Hartmann sensor include a wide dynamic range, broadband or low-coherence-length light capability, high x-ray efficiency, two-dimensional gradient determination, multiplexing capability, and experimental simplicity. Hartmann sensors could also be utilized for wavelength testing of extreme-ultraviolet lithography components and x-ray phase imaging of biological specimens.

We introduce a wave-optics based simulation code written to model a complete free space laser communications link, including a detailed model of an adaptive optics compensation system. We present the results obtained by this model, where the phase of a communications laser beam is corrected, after it propagates through a turbulent atmosphere. The phase of the received laser beam is measured using a Shack-Hartmann wavefront sensor, and the correction method utilizes a MEMS mirror. Strehl improvement and amount of power coupled to the receiving fiber results for both 1 km horizontal and 28 km slant paths will be presented.

Direct detection of photons emitted or reflected by an extrasolar planet is an extremely difficult but extremely exciting application of adaptive optics. Typical contrast levels for an extrasolar planet would be 109 - Jupiter is a billion times fainter than the sun. Current adaptive optics systems can only achieve contrast levels of 106, but so-called extreme adaptive optics systems with 104 -105 degrees of freedom could potentially detect extrasolar planets. We explore the scaling laws defining the performance of these systems, first set out by Angel (1994), and derive a different definition of an optimal system. Our sensitivity predictions are somewhat more pessimistic than the original paper, due largely to slow decorrelation timescales for some noise sources, though choosing to site an ExAO system at a location with exceptional r0 (e.g. Mauna Kea) can offset this. We also explore the effects of segment aberrations in a Keck-like telescope on ExAO; although the effects are significant, they can be mitigated through Lyot coronagraphy.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Horizontal path laser communications are beginning to provide attractive alternatives for high-speed optical communications. In particular, companies are beginning to sell fiberless alternatives for intranet and sporting event video. These applications are primarily aimed at short distance applications (on the order of 1 km pathlength). There exists a potential need to extend this pathlength to distances much greater than a 1km. For cases of long distance optical propagation, atmospheric turbulence will ultimately limit the maximum achievable data rate. In this paper, we propose a method of improved signal quality through the use of adaptive optics. In particular, we show work in progress toward a high-speed, small footprint Adaptive Optics system for horizontal path laser communications. Such a system relies heavily on recent progress in Micro-Electro-Mechanical Systems (MEMS) deformable mirrors as well as improved communication and computational components. In this paper we detail two Adaptive Optics approaches for improved through-put, the first is the compensated receiver (the traditional Adaptive Optics approach), the second is the compensated transmitter/receiver. The second approach allows for correction of the optical wavefront before transmission from the transmitter and prior to detection at the receiver.

We have developed a high-resolution wavefront control system based on an optically addressed nematic liquid crystal spatial light modulator with several hundred thousand phase control points, a Shack-Hartmann wavefront sensor with two thousand subapertures, and an efficient reconstruction algorithm using Fourier transform techniques. We present quantitative results of experiments to characterize the performance of this system.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The wavefront controller for the Keck Observatory AO system consists of two separate real-time control loops: a tip-tilt control loop to remove tilt from the incoming wavefront, and a deformable mirror control loop to remove higher-order aberrations. In this paper, we describe these control loops and analyze their performance using diagnostic data acquired during the integration and testing of the AO system on the telescope. Disturbance rejection curves for the controllers are calculated from the experimental data and compared to theory. The residual wavefront errors due to control loop bandwidth are also calculated from the data, and possible improvements to the controller performance are discussed.

Results of experiments with the laser guide star adaptive optics system on the 3-meter Shane telescope at Lick Observatory have demonstrated a factor of 4 performance improvement over previous results. Stellar images recorded at a wavelength of 2 micrometers were corrected to over 40 percent of the theoretical diffraction-limited peak intensity. For the previous two years, this sodium-layer laser guide star system has corrected stellar images at this wavelength to approximately 10 percent of the theoretical peak intensity limit. After a campaign to improve the beam quality of the laser system, and to improve calibration accuracy and stability of the adaptive optics system using new techniques for phase retrieval and phase-shifting diffraction interferometry, the system performance has been substantially increased. The next step will be to use the Lick system for astronomical science observations, and to demonstrate this level of performance with the new system being installed on the 10-meter Keck II telescope.

The Keck AO system is nearing completion and is nearly ready for system integration in the optics laboratory at Keck Headquarters. because of the ambitious scientific objectives of this project, the AO system is quite complex in design. The optics bench alone has 33 motion control axes, and potentially 6 image planes. Calibration will play a major role in making the AO system function as planned. We have identified approximately 35 separate calibration procedures that will be needed to be performed during the integration phase in the laboratory. Many of these procedures are quite straightforward. Other calibrations are quite involved and are mini 'research projects' in themselves. It is this last category that will be discussed in this paper.

We will review the status of the natural/laser guide star adaptive optics facility that is being constructed for the Keck II telescope.

We have developed and tested a method for minimizing static aberrations in adaptive optics systems. In order to correct the static phase aberrations, we need to measure the aberrations through the entire system. We have employed various phase retrieval algorithms to detect these aberrations. We have performed simulations of our experimental setup demonstrating that phase retrieval can improve the static aberrations to below the 20 nm rms level, with the limiting factor being local turbulence in the A0 system. Experimentally thus far, we have improved the static aberrations down to the 50 nm level, with the limiting factor being the ability to adjust the deformable mirror. This should be improved with better control algorithms now being implemented.

The laser guide star adaptive optics system currently being developed for the Keck 2 telescope consists of several major subsystems: the optical bench, wavefront control, user interface and supervisory control, and the laser system. The paper describes the design and implementation of the wavefront control subsystem that controls a 349 actuator deformable mirror for high order correction and tip-tilt mirrors for stabilizing the image and laser positions.

Atmospheric turbulence severely limits the resolution of ground-based telescopes. Adaptive optics can correct for the aberrations caused by the atmosphere, but requires a bright wavefront reference source in close angular proximity to the object being imaged. Since natural reference stars of the necessary brightness are relatively rare, methods of generating artificial reference beacons have been under active investigation for more than a decade. In this paper, we report the first significant image improvement achieved using a sodium-layer laser guide star as a wavefront reference for a high-order adaptive optics system. An artificial beacon was created by resonant scattering from atomic sodium in the mesosphere, at an altitude of 95 km. Using this laser guide star, an adaptive optics system on the 3 m Shane Telescope at Lick Observatory produced a factor of 2.4 increase in peak intensity and a factor of 2 decrease in full width at half maximum of a stellar image, compared with image motion compensation alone. The Strehl ratio when using the laser guide star as the reference was 65% of that obtained with a natural guide star, and the image full widths at half maximum were identical, 0.3 arc sec, using either the laser or the natural guide star. This sodium-layer laser guide star technique holds great promise for the world's largest telescopes.

Our objective in this report is to develop methods to determine the output pupil wavefront using intensity measurements directly from the science detector. This wavefront can then be used to determine a reference wavefront which will precorrect for the non-common-path aberrations and produce the desired wavefront at the science detector. We describe two phase retrieval algorithms that can be used and a set of simulation studies of AO system calibration. We present the initial experimental results of applying this technique in calibration of the Lick Observatory laser guidestar AO system in a later paper.

A sodium-layer laser guide star adaptive optics system has been developed at Lawrence Livermore National Laboratory (LLNL) for use on the 3-meter Shane telescope at Lick Observatory. The system is based on a 127-actuator continuous-surface deformable mirror, a Hartmann wavefront sensor equipped with a fast-framing low-noise CCD camera, and a pulsed solid-state-pumped dye laser tuned to the atomic sodium resonance line at 589 nm. The adaptive optics system has been tested on the Shane telescope using natural reference stars yielding up to a factor of 12 increase in image peak intensity and a factor of 6.5 reduction in image full width at half maximum (FWHM). The results are consistent with theoretical expectations. The laser guide star system has been installed and operated on the Shane telescope yielding a beam with 22 W average power at 589 nm. Based on experimental data, this laser should generate an 8th magnitude guide star at this site, and the integrated laser guide star adaptive optics system should produce images with Strehl ratios of 0.4 at 2.2 {mu}m in median seeing and 0.7 at 2.2 {mu}m in good seeing.

We will describe an adaptive optics system developed for the 1 meter Nickel and 3 meter Shane telescopes at Lick Observatory. Observing wavelengths will be in the visible for the 1 meter telescope and in the near IR on the 3 meter. The adaptive optics system design is based on a 69 actuator continuous surface deformable mirror and a Hartmann wavefront sensor equipped with an intensified CCD framing camera. The system has been tested at the Cassegrain focus of the 1 meter telescope where the subaperture size is 12.5 cm. The wavefront control calculations are performed on a four processor single board computer controlled by a Unix-based system. We will describe the optical system and give details of the wavefront control system design. We will present predictions of the system performance and initial test results.

We present the design and implementation of a very compact adaptive optics system that senses the return light from a sodium guide-star and controls a deformable mirror and a pointing mirror to compensate atmospheric perturbations in the wavefront. The deformable mirror has 19 electrostrictive actuators and triangular subapertures. The wavefront sensor is a Hartmann sensor with lenslets on triangular centers. The high-bandwidth steering mirror assembly incorporates an analog controller that samples the tilt with an avalanche photodiode quad cell. An f/25 imaging leg focuses the light into a science camera that can either obtain long-exposure images or speckle data. In laboratory tests overall Strehl ratios were improved by a factor of 3 when a mylar sheet was used as an aberrator. The crossover frequency at unity gain is 30 Hz.

We discuss issues in optimizing the design of adaptive optics and laser guide star systems for the Keck Telescope. The initial tip-tilt system will use Keck's chopping secondary mirror. We describe design constraints, choice of detector, and expected performance of this tip-tilt system as well as its sky coverage. The adaptive optics system is being optimized for wavelengths of 1 - 2.2 micrometers . We are studying adaptive optics concepts which use a wavefront sensor with varying numbers of subapertures, so as to respond to changing turbulence conditions. The goal is to be able to `gang together' groups of deformable mirror subapertures under software control, when conditions call for larger subapertures. We present performance predictions as a function of sky coverage and the number of deformable mirror degrees of freedom. We analyze the predicted brightness of several candidate laser guide star systems, as a function of laser power and pulse format. These predictions are used to examine the resulting Strehl as a function of observing wavelength. We discuss laser waste heat and thermal management issues, and conclude with an overview of instruments under design to take advantage of the Keck adaptive optics system.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Recent results from the Laser Guide Star Project at Lawrence Livermore National Laboratory are presented. Photometry of the return signal has shown that the photon return is approximately 10 photons/cm2/ms at the pupil of the receiving telescope in agreement with a detailed model of the sodium interaction. Wavefronts of the laser guide star have also been measured with a Shack-Hartmann technique and power spectra have been shown to agree with those of nearby natural stars. Plans for closed loop demonstrations using the laser guide star at LLNL and nearby Lick Observatory are discussed.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Tomographic x-ray holography may make possible the imaging of biological objects at high resolution in three dimensions. We performed a demonstration experiment with soft x-rays to explore the feasibility of this technique. Coherent 3.2 nm undulator radiation was used to record Fourier transform holograms of a microfabricated test object from various illumination angles. The holograms were numerically reconstructed according to the principles of diffraction tomography, yielding images of the object that are well resolved in three dimensions.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

This paper gives a basic overview of holography as applied to x-ray microscopy. Topics discussed include fourier transform holography, phase recovery from a hologram, reconstruction of scattered fields, and the use of straight ray approximations. Three dimensional spatial resolution below 100 nm is possible. (GH)

In this paper we discuss the potential for application of x-ray holographic imaging techniques to the sequencing of DNA. We formulate an approximate model for the scattering of partially coherent x-rays from an oriented DNA fiber and show the feasibility of reconstruction of heavy atom label positions from the x-ray scattering data. A series of simulations has been done to demonstrate the required reconstruction algorithms. An x-ray experiment is currently in progress to demonstrate the real feasibility of the technique. The potential of x-ray imaging techniques for the sequencing of DNA is attractive because of their inherently parallel nature. Hundreds or thousands of base pairs could be sequenced in a single set of x-ray images. The fundamental idea is to attach heavy atom labels to a selected base type on the DNA fragment to be sequenced. A large number (> 1012) of identical fragments can be constructed as an oriented fiber and illuminated with partially coherent x-rays. The heavy label positions can then be determined from the recorded pattern of scattered x-rays. If this operation is repeated for each of the four bases, the sequence can be reconstructed. The phase determination problem is solved by attaching to each DNA fragment a reference label in a known position. The scattered field then forms a Fourier transform hologram of the averaged DNA fragment. Because of the high photoelectric absorption of DNA relative to its coherent scattering cross-section, a single molecule would be damaged before an image could be formed. We solve this problem by distributing the damage over a large number of identical copies of the DNA fragment. In this paper we model a relatively simple experiment whose objective is to form a Fourier transform hologram of a labelled DNA fiber using 1 .54 A x-rays. We will first describe the hologram formation process and then the method for reconstructing the label positions.

We describe the design and the early results of a feasibility experiment for sodium-layer laser-guide-star adaptive optics. Copper-vapor-laser-pumped dye lasers from Lawrence Livermore National Laboratory’s Atomic Vapor Laser Isotope Separation program are used to create the guide star. The laser beam is projected upward from a beam director that is located ~5 m from a 0.5-m telescope and forms an irradiance spot ~2 m in diameter at the atmospheric-sodium layer (at an altitude of 95 km). The laser guide star is approximately fifth magnitude and is visible to the naked eye at the top of the Rayleigh-scattered laser beam. To date, we have made photometric measurements and open-loop wave-front-sensor measurements of the laser guide star. We give an overview of the experiment’s design and the laser systems, describe the experimental setup, show preliminary photometric and open-loop wave-front-sensor data on the guide star, and present predictions of closed-loop adaptive-optics performance based on these experimental data. The long-term goal of this effort is to develop laser guide stars and adaptive optics for use with large astronomical telescopes.

We describe a series of experiments to characterize the sodium-layer guide star that was formed with the high-power laser developed for the Lawrence Livermore National Laboratory Atomic Vapor Laser Isotope Separation program. An emission spot size of 3.0 m was measured, with an implied laser irradiance spot diameter of 2.0 m. The rms spot motion at the higher laser powers, with active beam-pointing control, was less than 0.5 arcsec and had little effect on the observed spot size under these conditions. We measured the resonant backscatter from the sodium layer as a function of laser power to obtain a saturation curve. With a transmitted power of 1100 W and an atmospheric transmission of 0.6, the irradiance from the guide star at the ground was 10 (photons/cm2)/ms, corresponding to a visual magnitude of 5.1. The implications for the performance of wave-front sensors with a laser guide star of this magnitude and resulting closed-loop adaptive-optics performance are discussed.

The angular resolution of long-exposure images from ground-based telescopes equipped with laser guide star adaptive optics systems is fundamentally limited by the the accuracy with which the tip-tilt aberrations introduced by the atmosphere can be corrected. Assuming that a natural star is used as the tilt reference, the residual error due to tilt anisoplanatism can significantly degrade the long-exposure resolution even if the tilt reference star is separated from the object being imaged by a small angle. Given the observed distribution of stars in the sky, the need to find a tilt reference star quite close to the object restricts the fraction of the sky over which long-exposure images with diffraction limited resolution can be obtained. In this paper, the authors present a comprehensive performance analysis of tip-tilt compensation systems that use a natural star as a tilt reference, taking into account properties of the atmosphere and of the Galactic stellar populations, and optimizing over the system operating parameters to determine the fundamental limits to the long-exposure resolution. Their results show that for a ten meter telescope on Mauna Kea, if the image of the tilt reference star is uncorrected, about half the sky can be imaged in the Vmore » band with long-exposure resolution less than 60 milli-arc-seconds (mas), while if the image of the tilt reference star is fully corrected, about half the sky can be imaged in the V band with long-exposure resolution less than 16 mas. Furthermore, V band images long-exposure resolution of less than 16 mas may be obtained with a ten meter telescope on Mauna Kea for unresolved objects brighter than magnitude 22 that are fully corrected by a laser guide star adaptive optics system. This level of resolution represents about 70% of the diffraction limit of a ten meter telescope in the V band and is more than a factor of 45 better than the median seeing in the V band on Mauna Kea.« less