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UTILIZATION OF THE WAVEFRONT SENSOR AND SHORT-EXPOSURE IMAGES FOR SIMULTANEOUS ESTIMATION OF QUASI-STATIC ABERRATION AND EXOPLANET INTENSITY

Heretofore, the literature on exoplanet detection with coronagraphic telescope systems has paid little attention to the information content of short exposures and methods of utilizing the measurements of adaptive optics wavefront sensors. This paper provides a framework for the incorporation of the wavefront sensor measurements in the context of observing modes in which the science camera takes millisecond exposures. In this formulation, the wavefront sensor measurements provide a means to jointly estimate the static speckle and the planetary signal. The ability to estimate planetary intensities in as little as a few seconds has the potential to greatly improve the efficiency of exoplanet search surveys. For simplicity, the mathematical development assumes a simple optical system with an idealized Lyot coronagraph. Unlike currently used methods, in which increasing the observation time beyond a certain threshold is useless, this method produces estimates whose error covariances decrease more quickly than inversely proportional to the observation time. This is due to the fact that the estimates of the quasi-static aberrations are informed by a new random (but approximately known) wavefront every millisecond. The method can be extended to include angular (due to diurnal field rotation) and spectral diversity. Numerical experiments are performed with wavefront data from the AEOS Adaptive Optics System sensing at 850 nm. These experiments assume a science camera wavelength {lambda} of 1.1 {mu}, that the measured wavefronts are exact, and a Gaussian approximation of shot-noise. The effects of detector read-out noise and other issues are left to future investigations. A number of static aberrations are introduced, including one with a spatial frequency exactly corresponding the planet location, which was at a distance of Almost-Equal-To 3{lambda}/D from the star. Using only 4 s of simulated observation time, a planetary intensity, of Almost-Equal-To 1 photon ms{sup -1}, and a stellar intensity of Almost-Equal-To 10{sup 5} photons ms{sup -1} (contrast ratio 10{sup 5}), the short-exposure estimation method recovers the amplitudes' static aberrations with 1% accuracy, and the planet brightness with 20% accuracy.

79 ASTRONOMY AND ASTROPHYSICS↗

The FastrSHWFS Project Development Motivation, Analysis, & Test Results

The recent 2020 Decadal Survey of Astronomy and Astrophysics listed habitable exoplanet imaging with future extreme adaptive optics (AO) on 30m-class telescopes as a key priority in the coming decade. However, there is a current 100x contrast gap between the best systems today and what is needed to enable this goal. Astronomical AO is a required approach to enable ground-based diffraction-limited imaging of exoplanets on future extremely large telescopes. Time lag between the end of an exposure and the application of deformable mirror commands is a major contributor to the error budget in many AO systems, and detector read time is often a large component of this lag. We present two designs for a modified Shack Hartmann wavefront sensor (SHWFS), named Focal plane Actualized Shifted Technique Realized for a SHWFS (fastrSHWFS), to reduce the time lag component. This design steers the spot pattern at the focal plane into a rectangular or linear array with a custom aspect ratio, reducing readout time. The mask with focus yields aberrated results while the mask with tip/tilt only yields some defined spots. This essay outlines the current SHWFS concept, our fastrSHWFS theoretical solution to addressing time lag, reflection and quality analysis of printed mask designs, and results from testing both masks on the High Contrast Testbed at Lawrence Livermore National Lab. This work follows the test of a previous fastrSHWFS design.

79 ASTRONOMY AND ASTROPHYSICS↗

Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry

There are wide applications for zonal reconstruction methods in slope-based metrology due to its good capability of reconstructing the local details on surface profile. It was noticed in the literature that large reconstruction errors occur when using zonal reconstruction methods designed for rectangular geometry to process slopes in a quadrilateral geometry, which is a more general geometry with phase measuring deflectometry. In this paper, we present a new idea for the zonal methods for quadrilateral geometry. Instead of employing the intermediate slopes to set up height-slope equations, we consider the height increment as a more general connector to establish the height-slope relations for least-squares regression. The classical zonal methods and interpolation-assisted zonal methods are compared with our proposal. Results of both simulation and experiment demonstrate the effectiveness of the proposed idea. In implementation, the modification on the classical zonal methods is addressed. Finally, the new methods preserve many good aspects of the classical ones, such as the ability to handle a large incomplete slope dataset in an arbitrary aperture, and the low computational complexity comparable with the classical zonal method. Of course, the accuracy of the new methods is much higher when integrating the slopes in quadrilateral geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Direct binary search for improved coherent beam shaping and optical differentiation wavefront sensing

Spatially dithered distributions of binary amplitude pixels are optimized using a full direct binary search taking into account the experimental configuration for amplitude modulation of coherent waves. This design process is shown to yield a significant reduction of the noise induced by binarization and pixelation over the region of interest. In this study, we demonstrate this approach for beam shaping and optical differentiation wavefront sensing, where the region of interest is in an image plane of the pixel distribution and in the far field of the pixel distribution, respectively. Lastly, the observed reduction in error compared to a standard error diffusion algorithm is significant for both applications because it improves performance without the tighter fabrication tolerance and cost associated with smaller pixels.

47 OTHER INSTRUMENTATION↗

Hybrid method simulations of a soft x-ray beamline

A wavefront propagation analysis of a soft X-ray beamline using the HYBRID method is reported. All elements of the beamline: the energy dependence of the insertion device emission, the beamline mirrors and their measured figure errors, the variable-line-spacing grating and its measured figure error, and several exit slit settings, are included in the simulations. The analysis of the propagated undulator radiation through the beamline at two slightly different deflection parameter values demonstrates that, within the beamline angular acceptance and when the monochromator is tuned to the same energy, the flux is higher when the undulator is tuned to slightly higher energy than that of the monochromator. The energy resolution determined from the FWHM of the energy bandwidth transmitted through the exit slit is narrower when the undulator is tuned to higher energy than the monochromator. This is not the case when the resolution is based on the standard deviation of the transmitted energy band. The diffraction effects due to the exit slit size and their consequence on the spot size at the sample position are investigated for a few photon energies.

beamline↗

Beyond optimization—supervised learning applications in relativistic laser-plasma experiments

We explore the applications of machine learning techniques in relativistic laser-plasma experiments beyond optimization purposes. We predict the beam charge of electrons produced in a laser wakefield accelerator given the laser wavefront change caused by a deformable mirror. Machine learning enables feature analysis beyond merely searching for an optimal beam charge, showing that specific aberrations in the laser wavefront are favored in generating higher beam charges. Supervised learning models allow characterizing the measured data quality as well as recognizing irreproducible data and potential outliers. Furthermore, we also include virtual measurement errors in the experimental data to examine the model robustness under these conditions. This work demonstrates how machine learning methods can benefit data analysis and physics interpretation in a highly nonlinear problem of relativistic laser-plasma interaction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Adaptive shape control of wavefront-preserving X-ray mirrors with active cooling and heating

This article describes the development and testing of a novel, water cooled, active optic mirror system (called “REAL: Resistive Element Adjustable Length”) that combines cooling with applied auxiliary heating, tailored to the spatial distribution of the thermal load generated by the incident beam. This technique is theoretically capable of sub-nanometer surface figure error control even at high power density. Tests conducted in an optical metrology laboratory and at synchrotron X-ray beamlines showed the ability to maintain the mirror profile to the level needed for the next generation storage rings and FEL mirrors.

42 ENGINEERING↗

RISE: robust iterative surface extension for sub-nanometer X-ray mirror fabrication

Precision optics have been widely required in many advanced technological applications. X-ray mirrors, as an example, serve as the key optical components at synchrotron radiation and free electron laser facilities. They are rectangular silicon or glass substrates where a rectangular Clear Aperture (CA) needs to be polished to sub-nanometer Root Mean Squared (RMS) to keep the imaging capability of the incoming X-ray wavefront at the diffraction limit. The convolutional polishing model requires a CA to be extended with extra data, from which the dwell time is calculated via deconvolution. However, since deconvolution is very sensitive to boundary errors and noise, the existing surface extension methods can hardly fulfill the sub-nanometer requirement. On one hand, the figure errors in a CA were improperly modeled during the extension, leading to continuity issues along the boundary. On the other hand, uncorrectable high-frequency errors and noise were also extended. In this study, we propose a novel Robust Iterative Surface Extension (RISE) method that resolves these problems with a data fitting strategy. RISE models the figure errors in a CA with orthogonal polynomials and ensures that only correctable errors are fit and extended. Combined with boundary conditions, an iterative refinement of dwell time is then proposed to compensate the errors brought by the extension and deconvolution, which drastically reduces the estimated figure error residuals in a CA while the increase of total dwell time is negligible. To our best knowledge, RISE is the first data fitting-based surface extension method and is the first to optimize dwell time based on iterative extension. An experimental verification of RISE is given by fabricating two elliptic cylinders (10 mm × 80 mm CAs) starting from a sphere with a radius of curvature around 173 m using ion beam figuring. The figure errors in the two CAs greatly improved from 204.96 nm RMS and 190.28 nm RMS to 0.62 nm RMS and 0.71 nm RMS, respectively, which proves that RISE is an effective method for sub-nanometer level X-ray mirror fabrication.

36 MATERIALS SCIENCE↗

RGB wavefront sensor for turbulence mitigation

A compact adaptive optics system for long-range horizontal paths imaging that improves degraded images. The system uses a filter that corresponds to the three colors in a typical color detector element, one or more optic elements, a deformable mirror, and a detector. Focus errors, due to turbulence, in the image recorded by the detector element show up as image shifts in the three distinct color images. The shifts and statistics of these shifts between these simultaneous images are used to create control signals for the deformable mirror resulting in a compact adaptive optic system for horizontal paths without need for a point source located at the distance scene being imaged. Analysis of the relative pixel shifts in various regions of the image provides third order statistics revealing tip/tilt and additional Zernikes modes that are used to control a deformable mirror without the need for a guide star/point-source.

O'Neill, Mary Dominique↗

Adaptive two-regime method: Application to front propagation

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in terms of the Fisher equation [R. Fisher, Ann. Eugen. 7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An engineered design of a diffractive mask for high precision astrometry [Modeling a diffractive mask that calibrates optical distortions]

AutoCAD, Zemax Optic Studio 15, and Interactive Data Language (IDL) with the Proper Library are used to computationally model and test a diffractive mask (DiM) suitable for use in the Gemini Multi-Conjugate Adaptive Optics System (GeMS) on the Gemini South Telescope. Systematic errors in telescope imagery are produced when the light travels through the adaptive optics system of the telescope. DiM is a transparent, flat optic with a pattern of miniscule dots lithographically applied to it. It is added ahead of the adaptive optics system in the telescope in order to produce diffraction spots that will encode systematic errors in the optics after it. Once these errors are encoded, they can be corrected for. DiM will allow for more accurate measurements in astrometry and thus improve exoplanet detection. Furthermore, the mechanics and physical attributes of the DiM are modeled in AutoCAD. Zemax models the ray propagation of point sources of light through the telescope. IDL and Proper simulate the wavefront and image results of the telescope. Aberrations are added to the Zemax and IDL models to test how the diffraction spots from the DiM change in the final images. Based on the Zemax and IDL results, the diffraction spots are able to encode the systematic aberrations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SKS Polarization Anomalies Due to the Coriolis Force

The Earth’s Coriolis force has been well–known to impact surface waves and normal modes, which is essential to accurately interpret these waves. However, the Coriolis force on body waves has been assumed to be negligible and mostly ignored. It has been previously shown that the Coriolis force impacts polarizations of shear waves, whereas the wavefronts remain unaffected. We expand on the potential influences of Earth’s Coriolis force on shear–wave polarization measurements by conducting 3D numerical simulations for elastic waves generated by earthquake and explosive sources in a radially symmetric, and 3D mantle and crustal models. The Coriolis force can produce polarization anomalies of mantle shear waves up to 7° and core phases, such as SKS and SKKS, up to 4°. Uncorrected shear–wave polarizations due to the Coriolis force can cause an additional source of error (5°–10° in fast direction, and 0.2–0.3 s delay time depending on the method and seismic phase), inaccurate interpretation of station misalignments, and imprecise estimates of the core–mantle boundary topography. We show how to correct for the Coriolis force on teleseismic shear waves using 1D ray tracing for well–isolated phases. Here, we recommend the use of full waveform simulations to accurately account for earthquake sources parameters, poorly isolated phases that could include interfering phase arrivals within the measurement time window, and the effect of the Coriolis force on the polarizations of shear waves.

58 GEOSCIENCES↗

waveSZ: A Hardware-Algorithm Co-Design of Efficient Lossy Compression for Scientific Data

Error-bounded lossy compression is critical to the success of extreme-scale scientific research because of ever-increasing volumes of data produced by today's high-performance computing (HPC) applications. Not only can error-controlled lossy compressors significantly reduce the I/O and storage burden but they can retain high data fidelity for post analysis. Existing state-of-the-art lossy compressors, however, generally suffer from relatively low compression and decompression throughput (up to hundreds of megabytes per second on a single CPU core), which considerably restrict the adoption of lossy compression by many HPC applications especially those with a fairly high data production rate. In this paper, we propose a highly efficient lossy compression approach based on field programmable gate arrays (FPGAs) under the state-of-the-art lossy compression model SZ. Our contributions are fourfold. (1) We adopt a wavefront memory layout to alleviate the data dependency during the prediction for higher-dimensional predictors, such as the Lorenzo predictor. (2) We propose a co-design framework named WAVESZ based on the wavefront memory layout and the characteristics of SZ algorithm and carefully implement it by using high-level synthesis. (3) We propose a hardware-algorithm co-optimization method to improve the performance. (4) We evaluate our proposed WAVESZ on three real-world HPC simulation datasets from the Scientific Data Reduction Benchmarks and compare it with other state-of-the-art methods on both CPUs and FPGAs. Experiments show that our WAVESZ can improve SZ's compression throughput by 6.9x similar to 8.7x over the production version running on a state-of-the-art CPU and improve the compression ratio and throughput by 2.1x and 5.8x on average, respectively, respectively, compared with the state-of-the-art FPGA design.

Compression Ratio↗

X-ray mirror surface figure correction with nanometre precision controlled by layer stresses simulated by FEA

Hard X-rays with energies higher than several kiloelectronvolts can be focused to spot sizes below 10 nm with the present synchrotron beamlines, offering unique advantages for the chemical, elemental and structure analysis of matter. Nevertheless, a surface precision on the nanometre scale for the focusing optics is required and remains the main hurdle limiting X-ray analytical techniques with single-nanometre spatial resolution. On the other hand, to preserve the wavefront properties of coherent X-ray beams, precise control of the reflective mirror surface quality at the nanometre scale is demanded for X-ray free-electron laser applications. In this work, the surface shape of a multilayer-coated X-ray mirror is controlled by layer stresses. The desired surface profile of the mirror is differentiated to its second order to obtain its corresponding curvature profile. With a step size of 1 mm along the mirror length, different coating thicknesses are applied to create different layer thermal stresses from uniform temperature change. The mirror surface profile can be obtained by integrating the curvature profile to its second order and further corrected by moving constant values for the slope and height. The technical process is simulated by finite element analysis (FEA). A case study showed that the residual slope error and the residual height error between the desired shape and the FEA result are 0.22 µrad (r.m.s.) and 1.42 nm (r.m.s.), respectively.

47 OTHER INSTRUMENTATION↗

Performance of a hard X-ray split-and-delay optical system with a wavefront division

The performance of a hard X-ray split-and-delay optical (SDO) system with a wavefront division scheme was investigated at the hard X-ray free-electron laser facility SACLA. For the wavefront division, beam splitters made of edge-polished perfect Si(220) crystals were employed. We characterized the beam properties of the SDO system, and investigated its capabilities for beam manipulation and diagnostics. First, it was confirmed that shot-to-shot non-invasive diagnostics of pulse energies for both branches in the SDO system was feasible. Second, nearly ideal and identical focal profiles for both branches were obtained with a spot size of ~1.5 µm in full width at half-maximum. Third, a spatial overlap of the two focused beams with a sub-µm accuracy was achieved by fine tuning of the SDO system. Finally, a reliable tunability of the delay time between two pulses was confirmed. The time interval was measured with an X-ray streak camera by changing the path length of the variable-delay branch. As a result, errors from the fitted line were evaluated to be as small as ±0.4 ps over a time range of 60 ps.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

miniGMG

miniGMG is a compact geometric multigrid (MG benchmark designed to proxy the performance characteristics of the solves found in adaptive mesh refinement multigrid (AMR MG) applications. It solves the equation a*alpha*u - b div beta grad u = f on a large cubical domain using cell-centered values and periodic boundaries. a and b are scalar constants, alpha and beta are space varying constants, f is the right hand side, and u is the solution. The cubical domain is divided into cubical subdomains which are distributed across the supercomputer. The righthand side f is generated from a continuous function for u. Thus, one can solve this linear system of equations and verify the error properties of the discrete solution u by comparing to a sampling of the continuous u. miniGMG implements both v- and f- cycles, as well as two constant coeffficient discretications of the equation above (one 27pt 2nd order, and one 13pt 4th order). In both cases, the (embedded) v-cycles are truncated when a subdomain reaces 4^3, 2^3, or 1^3 cells (a u-cycle). The multigrd solver then swtiches to one of seven coarse grid (bottom) solves. relaxation, BiCGStab, CABiCGStab, TelescopingCABiCGStab, CG, or CACG. The code exploits two forms of communication-avoiding. The first is exemplified by the referenced SC'12 paper in which DRAM data movment is avoided when smoothing. The second, described in the IPDPS'14 paper avoids collectives in a bottom solve (the CA bottom solves). There are a number of implementations of the operators for both CPUs and NVIDIA GPUs. The CPUs have been optimized to exploit a wavefront approach to communication-avoiding. The GPU versions include a number of optimized and tunable implementations. The code has been demonstrated to scale to 46K nodes on the BGQ Mira (750K cores), 9K nodes on Edison (111K cores), and 14K GPUs on Titan (37M cuda cores). It thus acts as a scalable testbed for a wide range of computer science and applied math research. Nominally, one invokes the benchmark as ./run b x y z alpha beta gamma Each subdomain is (2^b)^3 cells Each MPI process receives a x-by-y-by-z collection of subdomains. There are alpha*beta*gamma total MPI processes For correctness (a cubical domain), *alpha==y*beta==z*gamma.

Williams, Sameul↗

Development of an ultraprecise glue-free bimorph deformable mirror with a length of 460 mm

Lead zirconate titanate (PZT) bimorph mirrors are essential for performing multiple functions, such as beam shaping, wavefront correction, and dynamic focusing with adjustable beam sizes. They typically consist of a mirror substrate with PZT electrodes bonded to the substrate using a thin epoxy film. However, glue-bonded PZT mirrors exhibit low reproducibility in measurement results. One source of this variability is water absorption by the substrate’s epoxy adhesive during wet fabrication processes, such as elastic emission machining (EEM), which leads to swelling and deformation. Additionally, longer deformable bimorph mirrors require larger PZT electrodes, further complicating their design and fabrication, particularly during bonding and ultraprecise metrology. To address these challenges, silver nanoparticles were employed to bond PZT elements to the silicon (Si) mirror, eliminating the need for epoxy glue. Here, in this study, we developed an inorganic-glue-free PZT bimorph mirror with a length of 460 mm and 28 channels. The glue-free bonding method successfully ensured the high reproducibility of measurements after water immersion. This approach resulted in a shape error of only 0.41 nm root mean square after the figure correction process using an ultraprecise EEM process. Scanning acoustic tomography and basic response function tests confirmed the success of the bonding process, showing no critical voids. Furthermore, the shape changes induced by applying voltages to the PZT electrodes closely matched predictions obtained from simulations. These results demonstrate the reliability and precision of the proposed glue-free bonding technique, paving the way for improved performance of new PZT bimorph mirrors.

Ichii, Yoshio [SLAC National Accelerator Laborator↗

Data-driven modeling and control of an X-ray bimorph adaptive mirror

Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗