Engineering topics

Goldberg, Kenneth A.

Publications and source records attributed to Goldberg, Kenneth A..

11 records

DOE OSTI2024

Controlling cantilevered adaptive X-ray mirrors

Modeling the behavior of a prototype cantilevered X-ray adaptive mirror (held from one end) demonstrates its potential for use on high-performance X-ray beamlines. Similar adaptive mirrors are used on X-ray beamlines to compensate optical aberrations, control wavefronts and tune mirror focal distances at will. Controlled by 1D arrays of piezoceramic actuators, these glancing-incidence mirrors can provide nanometre-scale surface shape adjustment capabilities. However, significant engineering challenges remain for mounting them with low distortion and low environmental sensitivity. Finite-element analysis is used to predict the micron-scale full actuation surface shape from each channel and then linear modeling is applied to investigate the mirrors' ability to reach target profiles. Using either uniform or arbitrary spatial weighting, actuator voltages are optimized using a Moore–Penrose matrix inverse, or pseudoinverse, revealing a spatial dependence on the shape fitting with increasing fidelity farther from the mount.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Thickness dependence of piezo-bimorph adaptive mirror bending

A new generation of adaptive x-ray optics (AXO) is being installed on high-coherent-flux x-ray beamlines worldwide to correct and control the optical wavefront with sub-nm precision. These ultra-smooth mirrors achieve high reflectivities at glancing angles of incidence and can be hundreds of mm long. One type of adaptive x-ray mirror relies on piezoelectric ceramic strips which are segmented into channels and actuated to induce local, longitudinal bending, generating one-dimensional shape changes in the mirror substrate. A recently described mirror model uses a three-layer geometry with parallel actuators on the front and back surfaces of a thicker mirror substrate. By analogy to a solved problem in the thermal actuation of a tri-metal strip, we show that the achievable bending radius varies approximately as the square of the substrate thickness. We provide an analytic solution and simulate bending using a finite-element model.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Real-time machine-learning-driven control system of a deformable mirror for achieving aberration-free X-ray wavefronts

A neural-network machine learning model is developed to control a bimorph adaptive mirror to achieve and preserve aberration-free coherent X-ray wavefronts at synchrotron radiation and free electron laser beamlines. The controller is trained on a mirror actuator response directly measured at a beamline with a real-time single-shot wavefront sensor, which uses a coded mask and wavelet-transform analysis. The system has been successfully tested on a bimorph deformable mirror at the 28-ID IDEA beamline of the Advanced Photon Source at Argonne National Laboratory. It achieved a response time of a few seconds and maintained desired wavefront shapes (e.g., a spherical wavefront) with sub-wavelength accuracy at 20 keV of X-ray energy. This result is significantly better than what can be obtained using a linear model of the mirror’s response. The developed system has not been tailored to a specific mirror and can be applied, in principle, to different kinds of bending mechanisms and actuators.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle

Ellipsoidal and plane-elliptical surfaces are widely used as reflective, point-to-point focusing elements in many optical systems, including X-ray optics. Here the classical optical path function approach of Fermat is applied to derive a closed-form expression for these surfaces that are uniquely described by the object and image distances and the angle of incidence at a point on a mirror surface. A compact description facilitates design, modeling, fabrication, and testing to arbitrary accuracy. Congruent surfaces in two useful coordinate systems — a system centered on the ellipsoid's axes of symmetry and a mirror-centered or `vertex' system with the surface tangent to the xy plane at the mirror's center — are presented. Expressions for the local slope and radii of curvature are derived from the result, and the first several terms of the Maclauren series expansion are provided about the mirror center.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Analytic descriptions of parabolic X-ray mirrors

On X-ray beamlines and telescopes, glancing-incidence mirrors with parabolic profiles are used to collimate, focus, and collect light. Here, analytic descriptions for paraboloidal, plane-parabolic, and parabolic cylindrical mirrors in several congruent geometries that are commonly used in fabrication, metrology, and modeling are provided. The exact expressions are derived directly from Fermat's principle, without coordinate transformations, in several mirror-centered coordinate systems, including one with the surface tangent to the central point of intersection. Coefficients for a sixth-order polynomial series approximation are calculated for that coordinate system.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Wavefront Preservation in Soft X-Ray Beamlines for the Advanced Light Source Upgrade

In the 4th generation of X-ray light sources, including Free-Electron Lasers (FEL) and Diffraction-Limited Storage Rings (DLSR), the emittance of the electron beam is small or negligible compared to the emittance of the photon beam produced by insertion devices, thus generating coherent beams of light. Over the next few years, several lightsource facilities will be built or upgraded to produce X-ray beams of unprecedented coherent flux. Delivering these exceptional beams to the sample chambers requires beamline optical systems that are designed to preserve the wavefront properties. Our goal in the Advanced Light Source upgrade project (ALS-U) is to create a new class of beamlines that reach diffraction-limited X-ray optical quality through tightly integrated, efficient optical systems, diagnostics, and adaptive mirrors, thus providing users with new scientific capabilities offered by coherent X-ray light interactions with matter. Herein we describe aspects of the beamlines’ design as they enter the project’s final design phase.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Simulations of applications using diaboloid mirrors

The diaboloid is a reflecting surface that converts a spherical wave to a cylindrical wave. This complex surface may find application in new Advanced Light Source bending-magnet beamlines or in other beamlines that now use toroidal optics for astigmatic focusing. Here, the numerical implementation of diaboloid mirrors is described, and the benefit of this mirror in beamlines exploiting diffraction-limited storage rings is studied by ray tracing. The use of diaboloids becomes especially interesting for the new low-emittance storage rings because the reduction of aberration becomes essential for such small sources. Here, the validity of the toroidal and other mirror surfaces approximating the diaboloid, and the effect of the mirror magnification, are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Diaboloidal mirrors: algebraic solution and surface shape approximations

A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X-ray optics is the collimated two-crystal monochromator, with toroidal mirror refocusing. The element here replaces the toroid, and in such a system provides completely aberration free, point-to-point imaging of rays from the on-axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Pseudo-gray-scale halftone gratings for shearing and Hartmann wavefront sensors

Now in use on x-ray beamlines worldwide, shearing interferometry and Hartmann wavefront sensing provide effective feedback for measuring and optimizing high-quality beams. Conventionally, both approaches spatially modulate the beam properties (amplitude or phase) using two-tone, binary patterns, leading to deleterious diffraction effects that must be mitigated. In shearing, the presence of multiple diffraction orders affects measurement near boundaries. In Hartmann, diffraction limits the measurement point density. We demonstrate that the use of pseudo-gray-scale halftone patterns in the diffracting elements can improve the performance of both techniques.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Binary Amplitude Reflection Gratings for X-ray Shearing and Hartmann Wavefront Sensors

New, high-coherent-flux X-ray beamlines at synchrotron and free-electron laser light sources rely on wavefront sensors to achieve and maintain optimal alignment under dynamic operating conditions. This includes feedback to adaptive X-ray optics. We describe the design and modeling of a new class of binary-amplitude reflective gratings for shearing interferometry and Hartmann wavefront sensing. Compact arrays of deeply etched gratings illuminated at glancing incidence can withstand higher power densities than transmission membranes and can be designed to operate across a broad range of photon energies with a fixed grating-to-detector distance. Coherent wave-propagation is used to study the energy bandwidth of individual elements in an array and to set the design parameters. We observe that shearing operates well over a ±10% bandwidth, while Hartmann can be extended to ±30% or more, in our configuration. We apply this methodology to the design of a wavefront sensor for a soft X-ray beamline operating from 230 eV to 1400 eV and model shearing and Hartmann tests in the presence of varying wavefront aberration types and magnitudes.

47 OTHER INSTRUMENTATION↗