Effects of surface scatter on the optical performance of x-ray synchrotron beam-line mirrors

Distance-based generation of a unicursal random path on a non-grid point set for optical polishing

In modern ultra-precision polishing, sub-aperture technologies are prone to mid-spatial frequency errors due to identical patterns of a path. A random tool path on a regular point set is widely used to suppress mid-spatial frequency errors. In this study, two non-grid uniform point sets, the Fibonacci and the three-directional, were introduced into optical polishing. To solve the time-consuming problem caused by a large amount of distance calculation, a distance-based weighted random (DBWR) algorithm and a linear programming and connecting (LPC) algorithm were presented. The DBWR algorithm reduces the generation time by strengthening the weight of the neighboring points in a specific direction, while the LPC algorithm adjusts the order and distance of points artificially. Then a random stitching method was proposed for the large-scale point set applying to large-sized optical surfaces, which dramatically reduced the generation time. Finally, experiments validated that the algorithms for non-grid sets can be effectively used for optical surface figuring without introducing an apparent mid-spatial frequency.

Polishing performance of a magnetic nanoparticle-based nanoabrasive for superfinish optical surfaces

Superfine optical components are necessary for advanced engineering applications such as x-ray optics, high-power lasers, lithography, synchrotron optics, laser-based sensors, etc. Fabrication of such superfine surfaces is one of the major challenges for optical and semiconductor industries. This research focuses on the development of a magnetic nanoparticle-based nanoabrasive for superfine optical polishing. The superparamagnetic iron oxide nanoparticle (SPION)-based nanoabrasive is synthesized via a hydrothermal route by employing cost-effective precursors. Detailed characterizations of the prepared nanoabrasive are presented. Transmission electron microscopy results confirm the irregular cubic and spherical shaped morphology of the SPION nanoabrasive along with particle size distribution varying from 10-60 nm, enabling the homogenous cutting effect of the aqueous slurry for polishing. Furthermore, the high surface area and pore size are determined by Brunauer-Emmet-Teller analysis and found to be 30.98m²/g and 6.13 nm, respectively, providing homogenous distribution of the nanoabrasive on the surface of a BK7 substrate for material removal. Application of the developed SPION abrasive is demonstrated for superfinish optical polishing on a BK7 optical disc. The experimental polishing results show superfine surface finishing with an average roughness value of 3.5 Å. The superparamagnetic property of the developed nanoabrasive is confirmed by alternative gradient magnetometry, and it helps in recovering the used nanoabrasive after polishing. Moreover, the polishing performance of the SPION nanoabrasives is compared with a cerium nanoabrasive, which is also synthesized in this study.

Influence and suppression of periodic contour error of tool path and velocity deviations on surface error

When using multi-axis machines with a pneumatic tool to polish large-aperture optical surfaces, the paths generated by the computer numerical control system deviate from the desired ones. This causes periodic contour errors and surface ripples. In addition, because of the different machine layouts, the tool end velocity also can change. We introduce a multi-axis machine and analyze the surface error and power spectral density (PSD) of three commonly used paths (raster, spiral, and random path) in terms of the contour error using different position interpolation methods. A cubic polynomial is introduced to smooth the axis motion, and a velocity compensation method is considered to diminish the velocity deviation from the machine layout. The results show that the circular interpolation method exhibits a balanced performance in terms of both the contour error and the PSD for various paths. In addition, the optimization can be performed before G-code generation without affecting the characteristics of the original optimization system.

Fast convolution-based performance estimation method for diffraction-limited source with imperfect X-ray optics

Although optical element error analysis is always an important part of beamline design for highly coherent synchrotron radiation or free-electron laser sources, the usual wave optics simulation can be very time-consuming, which limits its application at the early stage of the beamline design. In this work, a new theoretical approach has been proposed for quick evaluations of the optical performance degradation due to optical element error. In this way, time-consuming detailed simulations can be applied only when truly necessary. This approach treats the imperfections as perturbations that convolve with the ideal performance. For simplicity, but not by necessity, the Gaussian Schell-model has been used to show the application of this theoretical approach. The influences of the finite aperture size and height error of a focusing mirror are analysed using the proposed theory. The physical explanation of the performance degradation acquired from the presented approach helps to give a better definition of the critical range of error spatial frequencies that most affect the performance of a mirror. An example comparing two mirror surface errors with identical power spectral density functions is given. These two types of mirror surface errors result in very different intensity profiles. The approach presented in this work could help beamline designers specify the error tolerances on general optical elements more accurately.

Modelling phase imperfections in compound refractive lenses

A framework based on physical optics for simulating the effect of imperfect compound refractive lenses (CRLs) upon an X-ray beam is described, taking into account measured phase errors obtained from at-wavelength metrology. A CRL stack is modelled, with increasing complexity, as a single thin phase element, then as a more realistic compound element including absorption and thickness effects, and finally adding realistic optical imperfections to the CRL. Coherent and partially coherent simulations using Synchrotron Radiation Workshop (SRW) are used to evaluate the different models, the effects of the phase errors and to check the validity of the design equations and suitability of the figures of merit.

Two-dimensional in situ metrology of X-ray mirrors using the speckle scanning technique

In situ metrology overcomes many of the limitations of existing metrology techniques and is capable of exceeding the performance of present-day optics. A novel technique for precisely characterizing an X-ray bimorph mirror and deducing its two-dimensional (2D) slope error map is presented. This technique has also been used to perform fast optimization of a bimorph mirror using the derived 2D piezo response functions. The measured focused beam size was significantly reduced after the optimization, and the slope error map was then verified by using geometrical optics to simulate the focused beam profile. This proposed technique is expected to be valuable for in situ metrology of X-ray mirrors at synchrotron radiation facilities and in astronomical telescopes.

Modeling of light scattering in different regimes of surface roughness

The light scattering of rough metallic surfaces with roughness levels ranging from a few to several hundred nanometers is modeled and compared to experimental data. Different modeling approaches such as the classical Rayleigh-Rice vector perturbation theory and the new Generalized Harvey-Shack theory are used and critically assessed with respect to ranges of validity, accuracy, and practicability. Based on theoretical calculations and comparisons with Rigorous Coupled Wave Analysis for sinusoidal phase gratings, it is demonstrated that the approximate scatter models yield surprisingly accurate results and at the same time provide insight into light scattering phenomena. For stochastically rough metal surfaces, the predicted angles resolved scattering is compared to experimental results at 325 nm, 532 nm, and 1064 nm. In addition, the possibilities of retrieving roughness information from measured scattering data for different roughness regimes are discussed.

Angle-resolved scattering and reflectance of extreme-ultraviolet multilayer coatings: measurement and analysis

Roughness-induced light scattering critically affects the performance of optical components, in particular at short wavelengths. We present a stand-alone instrument for angle-resolved scattering and reflectance measurements at 13.5 nm in the extreme-ultraviolet (EUV) spectral range. The achieved dynamic range allows even the scattering of high-quality EUV mirrors on extremely smooth substrates to be investigated. For Mo/Si multilayers, total scatter losses of several percent have been observed, depending on the substrate qualities as well as on roughening and smoothing effects during coating. Different approximate models for estimating the impact of roughness on scatter losses are discussed and compared with experimental results.

Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors

Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a 15 keV point source, which indicate nearly diffraction-limited focusing at the 40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than 0.1 mm have a minor effect on the focal spot size and intensity.

Advanced laser-backlit Grazing-Incidence X-Ray Imaging Systems for Inertial Confinement Fusion Research. II. Tolerance Analysis

Two example ultrahigh-spatial-resolution laser-backlit grazing-incidence x-ray microscope designs for inertial confinement fusion (ICF) research have been described [Appl. Opt. 40, 4570 (2001)]. Here details of fabrication, assembly, and optical surface errors that are characteristic of present state-of-the-art superpolished multilayer-coated spherical mirrors are given. They indicate that good image qualities can be expected; in particular, <0.5-mum spatial resolution at very high x-ray energies (up to 25 keV) appears to be feasible: Existing ICF imaging diagnostics approach ~2 mum spatial at low (<2 keV) energy. The improvement in resolution compared with that of other grazing-incidence devices is attributed to a fortuitous residual on-axis aberration dependence on short wavelengths; recent advances in mirror fabrication, including a new thin-film deposition technique to correct figure errors precisely in one dimension; and novel design. For even higher resolutions, a means of creating precise aspherical mirrors of spheric-quality microroughness may be possible by use of the same deposition technique.