Ion-beam figuring (IBF) capable of providing sub-nanometer shape accuracy, is often used for fabrication of ultra-precise x-ray optics. However, in the case of gratings, the optical surface may degrade during the following ruling procedure or etching processes. This leads to the necessity for a post-ruling surface correction to recover the ultra-precise shape of the optics, while the IBF substrate finish prior the ruling could be omitted. If so, the gratings can be made using relatively inexpensive substrates produced with conventional mechanical or chemical-mechanical polishing with medium optical surface quality and then processed with a post-ruling IBF to bring the shape to the sub-nanometer accuracy. The key question is whether the grating grooves survive the IBF treatment. In this work we investigate the possibility of post-production IBF correction for lamellar x-ray gratings. A 200 lines/mm lamellar grating made using a lambda/20 Si substrate was processed with IBF to achieve a sub-nanometer flat optical surface of the final grating. We report on impact of the IBF process on groove profile, surface roughness, and diffraction efficiency of the grating.
Achieving sub-nanometer precision in ion beam figuring (IBF) processes demands a comprehensive understanding and optimization of various key aspects, including metrology, dwell time optimization, velocity scheduling, positioning, and final inspection. In this study, these aspects are analyzed and discussed. Our solutions for the challenges in each aspect are highlighted, with implications for a wide range of applications requiring ultra-precise optical components.
Stitching interferometry is a powerful metrology technique used to measure the surface topography of optical mirrors with high precision and extended field of view. At the National Synchrotron Light Source II (NSLS-II), stitching interferometry with a Fizeau interferometer or a coherence scanning interferometer has been established to measure the surface topography of synchrotron mirrors.
Stitching interferometry allows the inspection of synchrotron mirrors supplied by the optics vendors. Before the mirrors are installed into the synchrotron beamlines, they must be evaluated to ensure that they meet the stringent specifications (sub-nm RMS over the clear aperture). By employing stitching interferometry, surface deviations can be quantified to estimate the performance at a beamline.
By analyzing the surface topography data collected with the stitching interferometry, we can use the surface residual errors with respect to the target shape to feedback to our developed deterministic fabrication method, Ion Beam Figuring (IBF), to further improve the mirror surface quality.
Position-velocity-time (PVT) is a motion mode supported by many modern motion controllers. It describes the motion with piecewise cubic polynomials, which results in smoother motion profiles. However, there is no PVT-based motion scheduler available for implementing dwell time in computer controlled optical surfacing (CCOS) applications. To fill this gap, we present a novel PVT-based motion scheduler constrained by the machine dynamics for CCOS. The principle of the proposed method is explained, followed by the verification of smoothness and accuracy with different type of tool paths. Finally, a PVT-based surface generation simulator is demonstrated.
We introduce an X-ray Hartmann Wavefront Sensor (HWS) simulation tool developed under the Synchrotron Radiation Workshop (SRW) framework. This metrology package can mimic an in-situ wavefront measurement experiment with a particular beamline optical layout, predict the expected Hartmanngrams, and then give access to the wavefront results under different beamline configurations. From the HWS design point of view, this SRW HWS simulation tool can be used to optimize the wavefront sensor parameters, such as the size and pitch of the Hartmann mask and the distance between the mask and the detector, in a specific X-ray energy range and help to tolerance complicated optical setup. Besides the X-ray HWS simulation in SRW, we also address some initial tests of a hard X-ray HWS under development at NSLS-II. Initial tests can be performed to evaluate the basic functionality of the X-ray HWS, such as the measurement repeatability and sensitivity to beam imperfections. It can provide a comprehensive evaluation of the performance of an X-ray HWS and help to optimize its design and functionality as a diagnostic tool for specific research questions and experimental conditions.
Dwell time calculation is one of the most important process in a highly deterministic computer-controlled Ion Beam Figuring (IBF) process. It is modeled as a deconvolution process between the desired removal map and the beam removal function, which is an ill-posed inverse problem. A good dwell time solution should fulfill four requirements: 1) it must be non-negative; 2) it should closely duplicate the shape of the desired removal map; 3) the total dwell time is expected to be as short as possible; 4) the calculation time is reasonable. Dwell time algorithms, such as Fourier transform-based algorithm, matrix-based algorithm, and Bayesian-based algorithm, have been proposed and applied to IBF. However, their performances were never clearly examined and described accordingly. In this research, we provide a quantitative study on the performances of these dwell time algorithms based on the aforementioned four requirements.
With the progressive development in synchrotron radiation facilities and free electron lasers (FELs), the requirement of the X-ray mirror is getting higher with tighter specifications. It challenges the X-ray mirror metrology in two major application scenes. On one hand, a reliable mirror measurement technique is needed to provide trustable feedback to the deterministic polishing in mirror fabrication or re-polishing process. On the other hand, it demands a more accurate mirror metrology technique to offer better services for the X-ray mirror inspection at synchrotrons and FELs to control the quality of X-ray mirrors to be installed into beamlines.
Since the stitching interferometry can provide two-dimensional laterally extendable (stitched) results with sub-nanometer height resolution and precision, several stitching interferometric techniques are studied for synchrotron mirror metrology. It is not only to enhance the mirror inspection capability in NSLS-II optical metrology laboratory but also to act in concert with the ongoing ion beam figuring project at NSLS-II. Various stitching methods with different stitching parameters are investigated at our stitching interferometric platform. Some experimental results are revealed to demonstrate the validity and performance of the developed system and stitching methods.
We demonstrate a novel One-Dimensional Ion-Beam Figuring (1D-IBF) solution from Brookhaven National Laboratory. Three improvements are introduced to the new 1D-IBF system. First, the misalignment of the coordinate systems between the metrology and the 1D-IBF hardware is minimized by integrating both the sample mirror and the Beam Removal Function (BRF) mirror into a single mirror holder. The measured BRF center is then used as a reference to calibrate the coordinate correspondence. Second, a Constrained Linear Least-Squares (CLLS) algorithm with a coarse-to-fine scheme is proposed to keep the non-negativity of the dwell time as well as ensure it smoothly duplicate the required removal amount. Third, a dwell time slicing strategy is used to smooth the implementation of the dwell time in the real 1D-IBF fabrication process. Experimental results demonstrate that the proposed 1D-IBF solution reduces the residual profile errors to sub-nanometer Root Mean Square (RMS) for both flat and spherical mirrors.
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