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.

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.

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.

Compensation of heat load deformations using adaptive optics for the ALS upgrade: a wave optics study.

A realistic wave optics simulation method has been developed to study how wavefront distortions originating from heat load deformations can be corrected using adaptive X-ray optics. Several planned soft X-ray and tender X-ray insertion-device beamlines in the Advanced Light Source upgrade rely on a common design principle. A flat, first mirror intercepts the white beam; vertical focusing is provided by a variable-line-space monochromator; and horizontal focusing comes from a single, pre-figured, adaptive mirror. A variety of scenarios to cope with thermal distortion in the first mirror are studied by finite-element analysis. The degradation of the intensity distribution at the focal plane is analyzed and the adaptive optics that correct it is modeled. The range of correctable wavefront errors across the operating range of the beamlines is reported in terms of mirror curvature and spatial frequencies. The software developed is a one-dimensional wavefront propagation package made available in the OASYS suite, an adaptable, customizable and efficient beamline modeling platform.

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.

Reflective binary amplitude grating for soft x-ray shearing and Hartmann wavefront sensing.

We demonstrate a reflective wavefront sensor grating suitable for the characterization of high-quality x-ray beamlines and optical systems with high power densities. Operating at glancing incidence angles, the optical element is deeply etched with a two-level pattern of shearing interferometry gratings and Hartmann wavefront sensor grids. Transverse features block unwanted light, enabling binary amplitude in reflection with high pattern contrast. We present surface characterization and soft x-ray reflectometry of a prototype grating array to demonstrate function prior to wavefront measurement applications. A simulation of device performance is shown.

Amplitude versus phase effects in extreme ultraviolet lithography mask scattering and imaging.

It is now well established that extreme ultraviolet (EUV) mask multilayer roughness leads to wafer-plane line-width roughness (LWR) in the lithography process. Analysis and modeling done to date has assumed, however, that the roughness leading to scatter is primarily a phase effect and that the amplitude can be ignored. Under this assumption, simple scattering measurements can be used to characterize the statistical properties of the mask roughness. Here, we explore the implications of this simplifying assumption by modeling the imaging impacts of the roughness amplitude component as a function of the balance between amplitude and phase induced scatter. In addition to model-based analysis, we also use an EUV microscope to compare experimental through focus data to modeling in order to assess the actual amount of amplitude roughness on a typical EUV multilayer mask. The results indicate that amplitude roughness accounts for less than 1% of the total scatter for typical EUV masks.

Coded aperture detector: an image sensor with sub 20-nm pixel resolution.

We describe the coded aperture detector, a novel image sensor based on uniformly redundant arrays (URAs) with customizable pixel size, resolution, and operating photon energy regime. In this sensor, a coded aperture is scanned laterally at the image plane of an optical system, and the transmitted intensity is measured by a photodiode. The image intensity is then digitally reconstructed using a simple convolution. We present results from a proof-of-principle optical prototype, demonstrating high-fidelity image sensing comparable to a CCD. A 20-nm half-pitch URA fabricated by the Center for X-ray Optics (CXRO) nano-fabrication laboratory is presented that is suitable for high-resolution image sensing at EUV and soft X-ray wavelengths.

Attenuated internal reflection terahertz imaging.

We present a terahertz (THz) imaging technique based on attenuated internal reflection, which is ideally suited for the analysis of liquid and biological samples. Inserted in a THz time-domain system, and using a high-resistivity low loss silicon prism to couple the THz wave into the sample, the detection scheme is based on the relative differential spectral phase of two orthogonal polarizations. Biological sample imaging as well as subwavelength (λ/16) longitudinal resolution are demonstrated.

Brewster's angle silicon wafer terahertz linear polarizer.

We present a new cost-effective terahertz linear polarizer made from a stack of silicon wafers at Brewster's angle, andevaluate its performances. We show that this polarizer is wide-band, has a high extinction ratio (> 6 × 10(3)) and very small insertion losses (< 1%). We provide measurements of the temporal waveforms after linearly polarizing the THz beam and show that there is no distortion of the pulse. We compare its performances with a commercial wire-grid polarizer, and show that the Brewster's angle polarizer can conveniently be used to control the power of a terahertz beam.

Beam waist measurement for terahertz time-domain spectroscopy experiments.

Classical masking aperture methods are found to be mostly inaccurate to determine the terahertz beam size in terahertz time-domain spectroscopy (TDS) experiments, owing to complex diffraction effects. Here, we present a simple and reliable method for measuring beam waists in terahertz TDS. It is based on the successive diffraction by an opaque disk followed by a small circular aperture.

Extreme ultraviolet microscope characterization using photomask surface roughness.

We demonstrate a method for characterizing the field-dependent aberrations of a full-field synchrotron-based extreme ultraviolet microscope. The statistical uniformity of the inherent, atomic-scale roughness of readily-available photomask blanks enables a self-calibrating computational procedure using images acquired under standard operation. We characterize the aberrations across a 30-um field-of-view, demonstrating a minimum aberration magnitude of smaller than [Formula: see text] averaged over the center 5-um area, with a measurement accuracy better than [Formula: see text]. The measured field variation of aberrations is consistent with system geometry and agrees with prior characterizations of the same system. In certain cases, it may be possible to additionally recover the illumination wavefront from the same images. Our method is general and is easily applied to coherent imaging systems with steerable illumination without requiring invasive hardware or custom test objects; hence, it provides substantial benefits when characterizing microscopes and high-resolution imaging systems in situ.