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.

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.

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.

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.

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. The validity of the toroidal and other mirror surfaces approximating the diaboloid, and the effect of the mirror magnification, are discussed.

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.

Final 5-Year Outcomes of the Multicenter Randomized Sham-Controlled Trial of a Water Vapor Thermal Therapy for Treatment of Moderate to Severe Lower Urinary Tract Symptoms Secondary to Benign Prostatic Hyperplasia.

PURPOSE: We present final 5-year outcomes of the multicenter randomized sham-controlled trial of a water vapor therapy (Rezum™) for treatment of moderate to severe lower urinary tract symptoms due to benign prostatic hyperplasia. MATERIALS AND METHODS: A total of 197 subjects >50 years of age with International Prostate Symptom Score ≥13, maximum flow rate ≤15 ml/second and prostate volume 30 to 80 cc were randomized and followed for 5 years. From the control arm of 61 subjects, a subset of 53 subjects requalified and after 3 months received treatment as part of the crossover group and were also followed for 5 years. The total number of vapor treatments to each lobe of the prostate was determined by length of prostatic urethra and included middle lobe treatment per physician discretion. RESULTS: Significant improvement of lower urinary tract symptoms was observed at <3 months post-thermal therapy, remaining durable through 5 years in the treatment group (International Prostate Symptom Score reduced 48%, quality of life increased 45%, maximum flow rate improved 44%, Benign Prostatic Hyperplasia Impact Index decreased 48%). Surgical re-treatment rate was 4.4% with no reports of device or procedure related sexual dysfunction or sustained de novo erectile dysfunction. Results within the crossover group were similar through 5 years. CONCLUSIONS: Minimally invasive treatment with water vapor thermal therapy provides significant and durable symptom relief as well as flow rate improvements through 5 years, with low surgical re-treatment rates and without impacting sexual function. It is a versatile therapy, providing successful treatment to obstructive lateral and middle lobes.

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.

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.

Convective Thermal Therapy: Durable 2-Year Results of Randomized Controlled and Prospective Crossover Studies for Treatment of Lower Urinary Tract Symptoms Due to Benign Prostatic Hyperplasia.

PURPOSE: We report 2-year outcomes of a multicenter randomized controlled trial plus 1-year results of a crossover trial after treatment with convective radiofrequency water vapor thermal energy for lower urinary tract symptoms due to benign prostatic hyperplasia. MATERIALS AND METHODS: A total of 197 men at least 50 years old with I-PSS (International Prostate Symptom Score) 13 or greater, maximum flow rate 15 ml per second or less and prostate size 30 to 80 cc were randomized 2:1 to thermal therapy with the Rezum® System or a control group. Rigid cystoscopy with simulated active treatment sounds served as the control procedure. After unblinding at 3 months control subjects could requalify for crossover study. Convectively delivered radiofrequency thermal energy was delivered into obstructive prostate tissue, including the median lobe as needed. The primary efficacy end point was a change in severity of symptom scores. RESULTS: Convective radiofrequency thermal therapy improved urinary symptoms significantly over controls at 3 months and provided a sustained 51% reduction from baseline at 24 months (p <0.0001). This produced a 5 and 8-point or greater score decrease in 84% and 74% of subjects, respectively, at 24 months. Crossover subject symptoms, flow rate and quality of life measures were markedly improved after thermal therapy compared to after the control procedure (p = 0.024 to <0.0001). No de novo erectile dysfunction was reported. CONCLUSIONS: Convective radiofrequency water vapor thermal therapy is a minimally invasive office or outpatient procedure that provides early effective symptom relief that remains durable for 2 years and is applicable to the median lobe.

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.

Minimally Invasive Prostate Convective Water Vapor Energy Ablation: A Multicenter, Randomized, Controlled Study for the Treatment of Lower Urinary Tract Symptoms Secondary to Benign Prostatic Hyperplasia.

PURPOSE: This report reveals the results of a multicenter, randomized, controlled study using transurethral prostate convective water vapor thermal energy to treat lower urinary tract symptoms associated with benign prostatic hyperplasia. MATERIALS AND METHODS: Men 50 years old or older with an International Prostate Symptom Score of 13 or greater, maximum flow rate of 15 ml per second or less and prostate size 30 to 80 cc were randomized 2:1 between thermal therapy with the Rezum® System and control. Thermal water vapor was injected into the transition zone and median lobe as needed. The control procedure was rigid cystoscopy with simulated active treatment sounds. The primary end point compared International Prostate Symptom Score reduction at 3 months. Treatment subjects were followed for 12 months. RESULTS: There were 197 men randomized (active 136, control 61). Thermal therapy and control International Prostate Symptom Score was reduced by 11.2 ± 7.6 and 4.3 ± 6.9 respectively (p <0.0001). Treatment subject baseline International Prostate Symptom Score of 22 decreased at 2 weeks (18.6, p=0.0006) and by 50% or greater at 3, 6 and 12 months, p <0.0001. The peak flow rate increased by 6.2 ml per second at 3 months and was sustained throughout 12 months (p <0.0001). No de novo erectile dysfunction was reported. Adverse events were mild to moderate and resolved quickly. CONCLUSIONS: Convective water vapor thermal therapy provides rapid and durable improvements in benign prostatic hyperplasia symptoms and preserves erectile and ejaculatory function. Treatment can be delivered in an office or hospital setting using oral pain medication and is applicable to all prostate zones including the median lobe.

Erectile and Ejaculatory Function Preserved With Convective Water Vapor Energy Treatment of Lower Urinary Tract Symptoms Secondary to Benign Prostatic Hyperplasia: Randomized Controlled Study.

INTRODUCTION: Most surgical treatments for male lower urinary tract symptoms and benign prostatic hyperplasia affect erectile and ejaculatory functions negatively, leading to patient dissatisfaction. AIM: To determine whether water vapor thermal therapy, when conducted in a randomized controlled trial, would significantly improve lower urinary tract symptoms secondary to benign prostatic hyperplasia and urinary flow rate while preserving erectile and ejaculatory functions. METHODS: Men at least 50 years old with International Prostate Symptom Scores of at least 13, a peak flow rate of at least 5 to no higher than 15 mL/s, and prostate volume of 30 to 80 cm(3) were randomized 2:1 between Rezum System thermal therapy and control. Thermal water vapor (103°C) was injected into lateral and median lobes as required for treatment of benign prostatic hyperplasia. The control procedure entailed rigid cystoscopy with simulated active treatment sounds. MAIN OUTCOME MEASURES: Blinded group (active = 136, control = 61) comparison occurred at 3 months and the active arm was followed to 12 months for International Prostate Symptom Score, peak flow rate, and sexual function using the International Index of Erectile Function and the Male Sexual Health Questionnaire for Ejaculatory Function. The minimal clinically important difference in erectile function perceived by subjects as beneficial was determined for each erectile function severity category. Subjects not sexually active were censored from sexual function analysis. RESULTS: No treatment- or device-related de novo erectile dysfunction occurred after thermal therapy. International Index of Erectile Function and Male Sexual Health Questionnaire for Ejaculatory Function scores were not different from the control group at 3 months or from baseline at 1 year. Ejaculatory bother score improved 31% over baseline (P = .0011). Also, 32% of subjects achieved minimal clinically important differences in erectile function scores at 3 months, and 27% at 1 year, including those with moderate to severe erectile dysfunction. International Prostate Symptom Score and peak flow rate were significantly superior to controls at 3 months and throughout 1 year (P < .0001). CONCLUSION: Convective water vapor thermal therapy provides sustainable improvements for 12 months to lower urinary tract symptoms and urinary flow while preserving erectile and ejaculatory functions.

Electro-optical system for scanning microscopy of extreme ultraviolet masks with a high harmonic generation source.

A self-contained electro-optical module for scanning extreme ultraviolet (EUV) reflection microscopy at 13.5 nm wavelength has been developed. The system has been designed to work with stand-alone commercially available EUV high harmonic generation (HHG) sources through the implementation of narrowband harmonic selecting multilayers and off-axis elliptical short focal length zoneplates. The module has been successfully integrated into an EUV mask scanning microscope achieving diffraction limited imaging performance (84 nm point spread function).

Gradient descent algorithm applied to wavefront retrieval from through-focus images by an extreme ultraviolet microscope with partially coherent source.

The wavefront retrieval by gradient descent algorithm that is typically applied to coherent or incoherent imaging is extended to retrieve a wavefront from a series of through-focus images by partially coherent illumination. For accurate retrieval, we modeled partial coherence as well as object transmittance into the gradient descent algorithm. However, this modeling increases the computation time due to the complexity of partially coherent imaging simulation that is repeatedly used in the optimization loop. To accelerate the computation, we incorporate not only the Fourier transform but also an eigenfunction decomposition of the image. As a demonstration, the extended algorithm is applied to retrieve a field-dependent wavefront of a microscope operated at extreme ultraviolet wavelength (13.4 nm). The retrieved wavefront qualitatively matches the expected characteristics of the lens design.