E-PVT: enhanced position-velocity-time scheduler for computer-controlled optical finishing with comprehensive considerations of dynamics constraints, continuity and efficiency.

Deterministic computer-controlled optical finishing is an essential approach for achieving high-quality optical surfaces. Its determinism and convergence rely heavily on precise and smooth motion control to guide the machine tool over an optical surface to correct residual errors. One widely supported and smooth motion control model is position-velocity-time (PVT), which employs piecewise cubic polynomials to describe positions. Our prior research introduced a PVT-based velocity scheduling method, demonstrating sub-nanometer level convergence in ion beam figuring (IBF) processes. However, three challenges remained. Firstly, this method relies on quadratic programming, resulting in computational intensiveness for dense tool paths. Secondly, the dynamics constraints and velocity and acceleration continuities are not comprehensively considered, limiting the full potential of PVT-based control. Thirdly, no compensation mechanism existed when dynamics constraints are exceeded. In this study, in response to these challenges, we proposed the Enhanced PVT (E-PVT) method, reducing the time complexity from O(n3) to O(n) while fully addressing dynamics constraints and continuities. A novel compensation method utilizing particle swarm optimization was proposed to address situations where dynamics constraints might be exceeded while maintaining the overall processing efficiency. Validation through simulation and experimentation confirmed the improved performance of E-PVT.

Universal dwell time optimization for deterministic optics fabrication.

Computer-Controlled Optical Surfacing (CCOS) has been greatly developed and widely used for precision optical fabrication in the past three decades. It relies on robust dwell time solutions to determine how long the polishing tools must dwell at certain points over the surfaces to achieve the expected forms. However, as dwell time calculations are modeled as ill-posed deconvolution, it is always non-trivial to reach a reliable solution that 1) is non-negative, since CCOS systems are not capable of adding materials, 2) minimizes the residual in the clear aperture 3) minimizes the total dwell time to guarantee the stability and efficiency of CCOS processes, 4) can be flexibly adapted to different tool paths, 5) the parameter tuning of the algorithm is simple, and 6) the computational cost is reasonable. In this study, we propose a novel Universal Dwell time Optimization (UDO) model that universally satisfies these criteria. First, the matrix-based discretization of the convolutional polishing model is employed so that dwell time can be flexibly calculated for arbitrary dwell points. Second, UDO simplifies the inverse deconvolution as a forward scalar optimization for the first time, which drastically increases the solution stability and the computational efficiency. Finally, the dwell time solution is improved by a robust iterative refinement and a total dwell time reduction scheme. The superiority and general applicability of the proposed algorithm are verified on the simulations of different CCOS processes. A real application of UDO in improving a synchrotron X-ray mirror using Ion Beam Figuring (IBF) is then demonstrated. The simulation indicates that the estimated residual in the 92.3 mm × 15.7 mm CA can be reduced from 6.32 nm Root Mean Square (RMS) to 0.20 nm RMS in 3.37 min. After one IBF process, the measured residual in the CA converges to 0.19 nm RMS, which coincides with the simulation.

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.

Micromachined Silicon Platform for Precise Assembly of 2D Multilayer Laue Lenses for High-Resolution X-ray Microscopy.

We report on a developed micromachined silicon platform for the precise assembly of 2D multilayer Laue lenses (MLLs) for high-resolution X-ray microscopy. The platform is 10 × 10 mm2 and is fabricated on ~500 µm thick silicon wafers through multiple steps of photolithography and deep reactive-ion etching. The platform accommodates two linear MLLs in a pre-defined configuration with precise angular and lateral position control. In this work, we discuss the design and microfabrication of the platform, and characterization regarding MLLs assembly, position control, repeatability, and stability. The results demonstrate that a micromachined platform can be used for the assembly of a variety of MLLs with different dimensions and optical parameters. The angular misalignment of 2D MLLs is well controlled in the range of the designed accuracy, down to a few millidegrees. The separation distance between MLLs is adjustable from hundreds to more than one thousand micrometers. The use of the developed platform greatly simplifies the alignment procedure of the MLL optics and reduces the complexity of the X-ray microscope. It is a significant step forward for the development of monolithic 2D MLL nanofocusing optics for high-resolution X-ray microscopy.

2D MEMS-based multilayer Laue lens nanofocusing optics for high-resolution hard x-ray microscopy.

We report on the development of 2D integrated multilayer Laue lens (MLL) nanofocusing optics used for high-resolution x-ray microscopy. A Micro-Electro-Mechanical-Systems (MEMS) - based template has been designed and fabricated to accommodate two linear MLL optics in pre-aligned configuration. The orthogonality requirement between two MLLs has been satisfied to a better than 6 millidegrees level, and the separation along the x-ray beam direction was controlled on a micrometer scale. Developed planar 2D MLL structure has demonstrated astigmatism free point focus of ∼14 nm by ∼13 nm in horizontal and vertical directions, respectively, at 13.6 keV photon energy. Approaching 10 nm resolution with integrated 2D MLL optic is a significant step forward in applications of multilayer Laue lenses for high-resolution hard x-ray microscopy and their adoption by the general x-ray microscopy community.

Development of a position-velocity-time-modulated two-dimensional ion beam figuring system for synchrotron x-ray mirror fabrication.

With the rapid evolution of synchrotron x-ray sources, the demand for high-quality precision x-ray mirrors has greatly increased. Single nanometer shape accuracy is required to keep imaging capabilities at the diffraction limit. Ion beam figuring (IBF) has been used frequently for ultra-precision finishing of mirrors, but achieving the ultimate accuracy depends on three important points: careful alignment, accurate dwell time calculation and implementation, and accurate optical metrology. The Optical Metrology Group at National Synchrotron Light Source II has designed and built a position-velocity-time-modulated two-dimensional IBF system (PVT-IBF) with three novel characteristics: (1) a beam footprint on the mirror was used as a reference to align the coordinate systems between the metrology and the IBF hardware; (2) the robust iterative Fourier transform-based dwell time algorithm proposed by our group was applied to obtain an accurate dwell time map; and (3) the dwell time was then transformed to velocities and implemented with the PVT motion scheme. In this study, the technical aspects of the PVT-IBF systems are described in detail, followed by an experimental demonstration of the figuring results. In our first experiment, the 2D RMS in a $ 50\;{\rm mm} \times 5\;{\rm mm} $50mm×5mm clear aperture was reduced from 3.4 to 1.1 nm after one IBF run. In our second experiment, due to a 5 mm pinhole installed in front of the source, the 2D RMS in a $ 50\;{\rm mm} \times 5\;{\rm mm} $50mm×5mm clear aperture was reduced from 39.1 to 1.9 nm after three IBF runs, demonstrating that our PVT-IBF solution is an effective and deterministic figuring process.

Study on an effective one-dimensional ion-beam figuring method.

Ion-beam figuring (IBF) is a precise surface finishing technique used for the production of ultra-precision optical surfaces. In this study, we propose an effective one-dimensional IBF (1D-IBF) method approaching sub-nanometer root mean square (RMS) convergence for flat and spherical mirrors. Our process contains three key aspects. First, to minimize the misalignment of the coordinate systems between the metrology and the IBF hardware, a mirror holder is used to integrate both the sample mirror and the beam removal function (BRF) mirror. In this way, the coordinate relationship can be calculated using the measured BRF center. Second, we propose a novel constrained linear least-squares (CLLS) dwell time calculation algorithm combined with a coarse-to-fine scheme to ensure that the resultant nonnegative dwell time closely and smoothly duplicates the required removal amount. Third, considering the possible errors induced by the translation stage, we propose a dwell time slicing strategy to divide the dwell time into smaller time slices. Experiments using our approaches are performed on flat and spherical mirrors as demonstrations. Measurement results from the nano-accuracy surface profiler (NSP) show that the residual profile errors are reduced to sub-nanometer RMS for both types of mirrors while the surface roughness is not affected by the figuring process, demonstrating the effectiveness of the proposed 1D-IBF method for 1D high-precision optics fabrication.

Large Aperture and Wedged Multilayer Laue Lens for X-ray Nanofocusing.

Diffraction optics fabricated from multilayers offer an intriguing alternative to lithography-based zone plates due to their advantages of virtually limitless aspect ratio and extremely small feature size. However, other issues, intrinsic to thin-film deposition, such as film stress and deposition rate instability, for example, limit the total achievable aperture. Over the last decade, Multilayer Laue Lens (MLLs) have progressed from a mere curiosity with initial aperture sizes in the 3-10 µm range, to real beamline-deployed optics with apertures in the 40-50 µm range (X. Huang, et al., Scientific Reports 3, 3562 (2013); E. Nazaretski, et al., Rev. Sci. Instrum. 85, 033707 (2014); E. Nazaretski, et al., Journal of Synchrotron Radiation 24, 1113 (2017)). By optimizing deposition conditions and incorporating new materials, MLLs have now broken the 100 µm thickness milestone. A flat WSi2/Al-Si MLL with a deposition thickness of 102 µm, the largest MLL to date, is reviewed. New large aperture wedged MLLs (wMLL), which were first fabricated by APS in 2006 using the WSi2/Si material system, are presented which demonstrate high focusing efficiency across a broad energy range. These results confirm findings by other groups who have also independently fabricated wMLL (A. J. Morgan, et al., Scientific Reports 5, 9892 (2015); S. Bajt, et al., Nature Light: Science and Applications 7, 17162 (2017)) based on a similar material system.

Achieving diffraction-limited nanometer-scale X-ray point focus with two crossed multilayer Laue lenses: alignment challenges.

We discuss misalignment-induced aberrations in a pair of crossed multilayer Laue lenses used for achieving a nanometer-scale x-ray point focus. We thoroughly investigate the impacts of two most important contributions, the orthogonality and the separation distance between two lenses. We find that misalignment in the orthogonality results in astigmatism at 45° and other inclination angles when coupled with a separation distance error. Theoretical explanation and experimental verification are provided. We show that to achieve a diffraction-limited point focus, accurate alignment of the azimuthal angle is required to ensure orthogonality between two lenses, and the required accuracy is scaled with the ratio of the focus size to the aperture size.

Hard x-ray scanning imaging achieved with bonded multilayer Laue lenses.

We report scanning hard x-ray imaging with a monolithic focusing optic consisting of two multilayer Laue lenses (MLLs) bonded together. With optics pre-characterization and accurate control of the bonding process, we show that a common focal plane for both MLLs can be realized at 9.317 keV. Using bonded MLLs, we obtained a scanning transmission image of a star test pattern with a resolution of 50 × 50 nm2. By applying a ptychography algorithm, we obtained a probe size of 17 × 38 nm2 and an object image with a resolution of 13 × 13 nm2. The significant reduction in alignment complexity for bonded MLLs will greatly extend the application range in both scanning and full-field x-ray microscopies.

Fabrication and testing of a newly designed slit system for depth-resolved X-ray diffraction measurements.

A new system of slits called `spiderweb slits' have been developed for depth-resolved powder or polycrystalline X-ray diffraction measurements. The slits act on diffracted X-rays to select a particular gauge volume of sample, while absorbing diffracted X-rays from outside of this volume. Although the slit geometry is to some extent similar to that of previously developed conical slits or spiral slits, this new design has advantages over the previous ones in use for complex heterogeneous materials and in situ and operando diffraction measurements. For example, the slits can measure a majority of any diffraction cone for any polycrystalline material, over a continuous range of diffraction angles, and work for X-ray energies of tens to hundreds of kiloelectronvolts. The design is generated and optimized using ray-tracing simulations, and fabricated through laser micromachining. The first prototype was successfully tested at the X17A beamline at the National Synchrotron Light Source, and shows similar performance to simulations, demonstrating gauge volume selection for standard powders, for all diffraction peaks over angles of 2-10°. A similar, but improved, design will be implemented at the X-ray Powder Diffraction beamline at the National Synchrotron Light Source II.

New figuring model based on surface slope profile for grazing-incidence reflective optics.

Surface slope profile is widely used in the metrology of grazing-incidence reflective optics instead of surface height profile. Nevertheless, the theoretical and experimental model currently used in deterministic optical figuring processes is based on surface height, not on surface slope. This means that the raw slope profile data from metrology need to be converted to height profile to perform the current height-based figuring processes. The inevitable measurement noise in the raw slope data will introduce significant cumulative error in the resultant height profiles. As a consequence, this conversion will degrade the determinism of the figuring processes, and will have an impact on the ultimate surface figuring results. To overcome this problem, an innovative figuring model is proposed, which directly uses the raw slope profile data instead of the usual height data as input for the deterministic process. In this paper, first the influence of the measurement noise on the resultant height profile is analyzed, and then a new model is presented; finally a demonstration experiment is carried out using a one-dimensional ion beam figuring process to demonstrate the validity of our approach.

Multimodality hard-x-ray imaging of a chromosome with nanoscale spatial resolution.

We developed a scanning hard x-ray microscope using a new class of x-ray nano-focusing optic called a multilayer Laue lens and imaged a chromosome with nanoscale spatial resolution. The combination of the hard x-ray's superior penetration power, high sensitivity to elemental composition, high spatial-resolution and quantitative analysis creates a unique tool with capabilities that other microscopy techniques cannot provide. Using this microscope, we simultaneously obtained absorption-, phase-, and fluorescence-contrast images of Pt-stained human chromosome samples. The high spatial-resolution of the microscope and its multi-modality imaging capabilities enabled us to observe the internal ultra-structures of a thick chromosome without sectioning it.

One-dimensional ion-beam figuring for grazing-incidence reflective optics.

One-dimensional ion-beam figuring (1D-IBF) can improve grazing-incidence reflective optics, such as Kirkpatrick-Baez mirrors. 1D-IBF requires only one motion degree of freedom, which reduces equipment complexity, resulting in compact and low-cost IBF instrumentation. Furthermore, 1D-IBF is easy to integrate into a single vacuum system with other fabrication processes, such as a thin-film deposition. The NSLS-II Optical Metrology and Fabrication Group has recently integrated the 1D-IBF function into an existing thin-film deposition system by adding an RF ion source to the system. Using a rectangular grid, a 1D removal function needed to perform 1D-IBF has been produced. In this paper, demonstration experiments of the 1D-IBF process are presented on one spherical and two plane samples. The final residual errors on both plane samples are less than 1 nm r.m.s. The surface error on the spherical sample has been successfully reduced by a factor of 12. The results show that the 1D-IBF method is an effective method to process high-precision 1D synchrotron optics.

A one-dimensional ion beam figuring system for x-ray mirror fabrication.

We report on the development of a one-dimensional Ion Beam Figuring (IBF) system for x-ray mirror polishing. Ion beam figuring provides a highly deterministic method for the final precision figuring of optical components with advantages over conventional methods. The system is based on a state of the art sputtering deposition system outfitted with a gridded radio frequency inductive coupled plasma ion beam source equipped with ion optics and dedicated slit developed specifically for this application. The production of an IBF system able to produce an elongated removal function rather than circular is presented in this paper, where we describe in detail the technical aspect and present the first obtained results.

Diffraction properties of multilayer Laue lenses with an aperture of 102 µm and WSi2/Al bilayers.

We report on the characterization of a multilayer Laue lens (MLL) with large acceptance, made of a novel WSi2/Al bilayer system. Fabrication of multilayers with large deposition thickness is required to obtain MLL structures with sufficient apertures capable of accepting the full lateral coherence length of x-rays at typical nanofocusing beamlines. To date, the total deposition thickness has been limited by stress-buildup in the multilayer. We were able to grow WSi2/Al with low grown-in stress, and asses the degree of stress reduction. X-ray diffraction experiments were conducted at beamline 1-BM at the Advanced Photon Source. We used monochromatic x-rays with a photon energy of 12 keV and a bandwidth of ΔE/E=5.4·10(-4). The MLL was grown with parallel layer interfaces, and was designed to have a large focal length of 9.6 mm. The mounted lens was 2.7 mm in width. We found and quantified kinks and bending of sections of the MLL. Sections with bending were found to partly have a systematic progression in the interface angles. We observed kinking in some, but not all, areas. The measurements are compared with dynamic diffraction calculations made with Coupled Wave Theory. Data are plotted showing the diffraction efficiency as a function of the external tilting angle of the entire mounted lens. This way of plotting the data was found to provide an overview into the diffraction properties of the whole lens, and enabled the following layer tilt analyses.

Achieving hard X-ray nanofocusing using a wedged multilayer Laue lens.

We report on the fabrication and the characterization of a wedged multilayer Laue lens for x-ray nanofocusing. The lens was fabricated using a sputtering deposition technique, in which a specially designed mask was employed to introduce a thickness gradient in the lateral direction of the multilayer. X-ray characterization shows an efficiency of 27% and a focus size of 26 nm at 14.6 keV, in a good agreement with theoretical calculations. These results indicate that the desired wedging is achieved in the fabricated structure. We anticipate that continuous development on wedged MLLs will advance x-ray nanofocusing optics to new frontiers and enrich capabilities and opportunities for hard X-ray microscopy.

11 nm hard X-ray focus from a large-aperture multilayer Laue lens.

The focusing performance of a multilayer Laue lens (MLL) with 43.4 µm aperture, 4 nm finest zone width and 4.2 mm focal length at 12 keV was characterized with X-rays using ptychography method. The reconstructed probe shows a full-width-at-half-maximum (FWHM) peak size of 11.2 nm. The obtained X-ray wavefront shows excellent agreement with the dynamical calculations, exhibiting aberrations less than 0.3 wave period, which ensures the MLL capable of producing a diffraction-limited focus while offering a sufficient working distance. This achievement opens up opportunities of incorporating a variety of in-situ experiments into ultra high-resolution X-ray microscopy studies.