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.
Multilayer Laue lenses (MLLs) are promising optics for high efficiency nano focusing in the hard x-ray regime. However, since MLLs are one-dimensional focusing elements, a pair of MLLs need to be orthogonally aligned with respect to each other to achieve point focusing. This involves eight independent motions with nanoscale resolutions. This requirement poses significant technical challenges for a microscopy system and requires a highly specialized and stable instrument. The development of monolithic 2D MLL nano focusing optics could greatly reduce the instrument complexity, increase focusing stability, and minimize the degrees of a nanoscale motion needed for operating the MLL optics. A critical step in building 2D MLL optics is to ensure the orthogonality between two MLLs during the alignment. In this work, we report our approach for precise angular alignment of 2D MLL optics. This process, by utilizing a machine learning algorithm on the interferometer data, can automatically and precisely detect the small orthogonality error of 2D MLL optics. It is easy to use, accurate, and robust, and remarkably simplifies the procedure of 2D MLL alignment.
In this paper we report on the modeling and characterization of transmission windows for in-situ interferometric measurements of cryogenically cooled mirrors. Specifically, we present a model of the temperature distribution and strain in the transmission window, and the corresponding spatial dependence of the window’s index of refraction. We also present experimental results which characterize the effect of the windows on interferometric measurement.
X-ray microscopy is an invaluable and powerful characterization tool applied in many scientific fields, such as materials science, biology, environmental science, and energy research. In recent years it has been driven by rapid developments of novel technologies and systems resulting in imaging experiments elucidating structural inhomogeneities and chemical reactions at the nanometer scale. To obtain high spatial resolution comprehensive chemical and structural information, an X-ray microscope must be equipped with adequate capabilities and allow for simultaneous acquisition of multiple datasets. In recent years, a number of X-ray microscopes have been designed, constructed, and commissioned at NSLS-II. Here we provide an overview of the microscopy instrumentation development program at NSLS-II and specifically focus on the multilayer Laue lens–based hard X-ray nanoprobe optimized for ~10 nm spatial resolution imaging, its current status, and future upgrades along with recently constructed Kirkpatrick-Baez based scanning microscope designed for ~100 nm spatial resolution experiments.
Testing of an X-ray mirror by a point diffraction interferometer (PDI) D7 with two beams is described. Thanks to the two independent test and reference beams, mirrors metrology using the D7 coupled with accessory optics becomes straightforward and reliable. Therefore procedure of systematic error removal and sub-aperture measurements with stitching are simplified. In this paper, we describe the main technique to achieve high accuracy of stitching sub-aperture wavefronts, followed by further perspectives of the described instrument.
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.
An ongoing collaboration among four US Department of Energy (DOE) National Laboratories has demonstrated key technology prototypes and software modeling tools required for new high-coherent flux beamline optical systems. New free electron laser (FEL) and diffraction-limited storage ring (DLSR) light sources demand wavefront preservation from source to sample to achieve and maintain optimal performance. Fine wavefront control was achieved using a novel, roomtemperature cooled mirror system called REAL (resistive element adjustable length) that combines cooling with applied, spatially variable auxiliary heating. Single-grating shearing interferometry (also called Talbot interferometry) and Hartmann wavefront sensors were developed and used for optical characterization and alignment on several beamlines, across a range of photon energies. Demonstrations of non-invasive hard x-ray wavefront sensing were performed using a thin diamond single-crystal as a beamsplitter.
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.
X-ray microscopy is a mature characterization tool routinely used to answer various questions of science, technology and engineering. The high penetration power of X-rays allows to utilize different characterization methods and reveal elemental composition, crystalline phases, strain distribution, oxidation states etc. in macroscopic and microscopic samples. To obtain comprehensive chemical and structural information at the nanometer scale an X-ray microscope must be equipped with adequate capabilities and allow acquisition of multiple datasets simultaneously. Full-field or scanning X-ray microscopes usually serve this purpose and complement each other. In the recent years, a number of X-ray microscopes have been designed, constructed and commissioned at NSLS-II. In this work we provide an overview of the microscopy instrumentation developments at NSLS-II. It includes the multilayer Laue Lens based nanoprobe optimized for 10 nm spatial resolution imaging, it’s current status and future upgrades; the zone plate based full-field imaging system capable of nano-tomography measurements in less than 1 minute; a laser scanning system optimized for ptychography measurements along with algorithms development, and a new Kirkpatrick-Baez based scanning microscope designed for sub-100 nm spatial resolution experiments.
The need for smaller focal spot sizes to meet the demands for higher resolution imaging is driving the adoption of adaptive optics in x-ray beamlines. Closed-loop control of the mirror shape, position, and orientation can greatly enhance the performance of these optics by allowing for rejection of perturbations. We demonstrate the performance of an array of interferometric absolute position sensors as a means of providing real-time feedback on shape changes of the reflecting surface of a bimorph mirror by comparison to a Fizeau interferometer.
Synchrotron Radiation Workshop (SRW) is a powerful synchrotron radiation simulation tool and has been widely used at synchrotron facilities all over the world. During the last decade, many types of X-ray wavefront sensors have been developed and used. In this work, we present our recent effort on the development of at-wavelength metrology simulation based on SRW mainly focused on the Hartmann Wavefront Sensor (HWS). Various conditions have been studied to verify that the simulated HWS is performing as expected in terms of accuracy. This at-wavelength metrology simulation tool is then used to align KB mirrors by minimizing the wavefront aberrations. We will present our optimization process to perform an ‘in situ’ alignment using conditions as close as possible to the real experiments (KB mirrors with different levels of figure errors or different misalignment geometry).
KEYWORDS: Deflectometry, 3D metrology, Phase measurement, Mathematical modeling, Optical metrology, Ray tracing, 3D modeling, Nonlinear optics, Cameras, 3D acquisition
Phase Measuring Deflectometry (PMD) is a powerful tool to measure the three-dimensional shape for freeform specular surfaces. In this work, a model based method is applied to PMD, called as Modal Phase Measuring Deflectometry (MPMD). The surface height and slopes are represented in mathematical models and updated by optimizing the model coefficients, in order to minimize the discrepancy between the reprojection in ray tracing and the actual measurement. The pose of the screen relative to the camera is pre-calibrated and then optimized together with the surface shape coefficients. Moreover, the correspondence residuals because of the discrepancies between the modal estimation and practical acquisition are analyzed. Slope residuals are calculated from these discrepancies. Zonal integration methods which are good at dealing with local variations are used to reconstruct the height residual for compensation. Simulations and experiments are conducted to demonstrate the feasibility of the proposed approach.
Over the past decade, the concept of x-ray Deformable Mirror (DM) has matured from early experimental stages to a standard tool now available at many synchrotron/free-electron laser facilities. Indeed, x-ray active optics has become an integral part of all present and future large x-ray and EUV projects and will be essential in exploiting the full potential of the new sources currently under construction. These DMs mainly are employed to correct wavefront errors or provide variable x-ray beam sizes. Due to the coupling between the N actuators of a DM, it is usually necessary to perform a calibration or training step to be able to control the DM to the right target. To determine the optimum actuators settings in order to minimize slope/height errors, an initial measurement need to be collected, with all actuators set to 0 and then either N or 2N measurements are necessary. In this work, we present a fast and accurate method to drive an x-ray active bimorph mirror to a target shape with only 3 or 4 measurements. Instead of sequentially measuring and calculating the influence functions of all actuators and then predicting the needed voltages for any desired shape, we make use of the metrology data to directly guide the mirror from current status towards the particular target slope/shape via iterative compensations. The feedback for the iteration process is the discrepancy in curvature determined by height/slope measurement data. Experiments demonstrate the feasibility of this simple approach.
The push for high quality x-ray optics is closely linked to improvements in metrology technology. During the last decade, we have seen an ultra-fast progress in x-ray optics performances. This enhancement is directly linked to the development of the necessary tools to control these optical components. These metrology tools are necessary for the fabrication (to guide some polishing deterministic process) and also for the ultimate characterization used to validate surface parameters (often inside their own mechanical support) prior to installation in a beam line. It is now necessary to characterize optical surface figure, slope errors and roughness on meter-long optics over spatial frequencies as short as 0.1 mm and with slope errors reaching less than 100 nrad rms or surface figure errors close to 1 nm in order to not spoiled and preserve the high brightness made available by third and fourth generation synchrotron/FEL sources like NSLSII or LCLS. For this purpose, the new NSLS-II Optical Metrology Laboratory (NSLSII-OML) includes commercial instruments for measuring long spatial frequency figure errors, mid spatial frequencies and high frequency roughness and had started some research and development activities. This paper provides a brief description of the instruments currently available in the laboratory and gives an overview of the very active research and development efforts within the NSLSII-OML.
After years of development from a concept to early experimental stage, X-ray Deformable Mirrors (XDMs) are used in many synchrotron/free-electron laser facilities as a standard x-ray optics tool. XDM is becoming an integral part of the present and future large x-ray and EUV projects and will be essential in exploiting the full potential of the new sources currently under construction. The main objective of using XDMs is to correct wavefront errors or to enable variable focus beam sizes at the sample. Due to the coupling among the N actuators of a DM, it is usually necessary to perform a calibration or training process to drive the DM into the target shape. Commonly, in order to optimize the actuators settings to minimize slope/height errors, an initial measurement need to be collected, with all actuators set to 0, and then either N or 2N measurements are necessary learn each actuator behavior sequentially. In total, it means that N+1 or 2N+1 scans are required to perform this learning process. When the actuators number N is important and the actuator response or the necessary metrology is slow then this learning process can be time consuming. In this work, we present a fast and accurate method to drive an x-ray active bimorph mirror to a target shape with only 3 or 4 measurements. Instead of sequentially measuring and calculating the influence functions of all actuators and then predicting the voltages needed for any desired shape, the metrology data are directly used to “guide” the mirror from its current status towards the particular target slope/height via iterative compensations. The feedback for the iteration process is the discrepancy in curvature calculated by using B-spline fitting of the measured height/slope data. In this paper, the feasibility of this simple and effective approach is demonstrated with experiments.
The Software Configurable Optical Test System (SCOTS) uses deflectometry to measure surface slopes of general optical shapes without the need for additional null optics. Careful alignment of test geometry and calibration of inherent system error improve the accuracy of SCOTS to a level where it competes with interferometry. We report a SCOTS surface measurement of an off-axis superpolished elliptical x-ray mirror that achieves <1 nm root-mean-square accuracy for the surface measurement with low-order term included.
Wafer-level-optics now is widely used in smart phone camera, mobile video conferencing or in medical equipment that require tiny cameras. Extracting quantitative phase information has received increased interest in order to quantify the quality of manufactured wafer-level-optics, detect defective devices before packaging, and provide feedback for manufacturing process control, all at the wafer-level for high-throughput microfabrication. We demonstrate two phase imaging methods, digital holographic microscopy (DHM) and Transport-of-Intensity Equation (TIE) to measure the phase of the wafer-level lenses. DHM is a laser-based interferometric method based on interference of two wavefronts. It can perform a phase measurement in a single shot. While a minimum of two measurements of the spatial intensity of the optical wave in closely spaced planes perpendicular to the direction of propagation are needed to do the direct phase retrieval by solving a second-order differential equation, i.e., with a non-iterative deterministic algorithm from intensity measurements using the Transport-of-Intensity Equation (TIE). But TIE is a non-interferometric method, thus can be applied to partial-coherence light. We demonstrated the capability and disability for the two phase measurement methods for wafer-level optics inspection.
Phase is not easy to detect directly as intensity, but sometimes it contains the really desired
information. The transport-of-intensity equation (TIE) is a powerful tool to retrieve the phase from the
intensity. However, by considering the boundary energy exchange and the whole energy conversation in
the field of view, the current popular Fast Fourier transform (FFT) based TIE solver can only retrieve the
phase under homogeneous Neumann boundary condition. For many applications, the boundary condition
could be more complex and general. A novel TIE phase retrieval method is proposed to deal with an optical
field under a general boundary condition. In this method, an arbitrarily-shape hard aperture is added in the
optical field. In our method, the TIE is solved by using iterative discrete cosine transforms (DCT) method,
which contains a phase compensation mechanism to improve the retrieval results. The proposed method is
verified in simulation with an arbitrary phase, an arbitrarily-shaped aperture, and non-uniform intensity
distribution. Experiment is also carried out to check its feasibility and the method proposed in this work is
very easy and straightforward to use in a practical measurement as a flexible phase retrieval tool.
The Chinese magic mirror is an ancient convex bronze mirror, it reflects parallel light rays to form a unique image within
the reflected patch of light by altering the reflected ray paths. Using Phase Measuring Reflectometry (PMR), surface
irregularities of a micron range were found to be present on the mirror; these irregularities concentrate and disperse
reflected light rays, giving rise to brighter and darker patches on the reflected image, forming a contrast, allowing the
unique pattern to be observed. To ascertain location and nature of the surface defects that come in forms of indentations
and raised platforms, other measurement techniques were employed. Reverse engineering then facilitated the exploration
of reproduction of a very own original Chinese Magic Mirror with the use of optical principles behind the mirror.
The three-dimensional (3D) metrology for specular reflecting surfaces attracted much attention due to their
various applications in optics, electronics, or semiconductor industry. Fringe reflection technique is an effective tool to
measure the specular surface slopes (gradient information), and then reconstruct the surface shape from gradient.
However, most of the fringe reflection systems are built up for middle size (~10,000 mm2) or larger size (~100,000 mm2) objects by using the off-the-shelf desktop displays. In order to measure samples with smaller size (~200 mm2) with higher measuring resolution, a compact fringe reflection system is proposed. The performance of the compact specular 3D shape measurement system is demonstrated with experiments.
Inspired by dominant flight of the natural flyers and driven by civilian and military purposes, micro air vehicle (MAV) has been developed so far by passive wing control but still pales in aerodynamic performance. Better understanding of flapping wing flight mechanism is eager to improve MAV’s flight performance. In this paper, a simple and effective 4D metrology technique to measure full-field deformation of flapping membrane wing is presented. Based on fringe projection and 3D Fourier analysis, the fast and complex dynamic deformation, including wing rotation and wing stroke, of a flapping wing during its flight can be accurately reconstructed from the deformed fringe patterns recorded by a highspeed camera. An experiment was carried on a flapping-wing MAV with 5-cm span membrane wing beating at 30 Hz, and the results show that this method is effective and will be useful to the aerodynamicist or micro aircraft designer for visualizing high-speed complex wing deformation and consequently aid the design of flapping wing mechanism to enhanced aerodynamic performance.
Phase Shift Reflectometry has recently been seen as a novel alternative to interferometry since it can provide warpage
measurement over large areas with no need for large optical components. To confirm its capability and to explore the use
of this method for sub-surface defect detection, a Chinese magic mirror is used. This bronze mirror which dates back to
the Chinese Han Dynasty appears at first sight to be an ordinary convex mirror. However, unlike a normal mirror, when
illuminated by a beam of light, an image is formed onto a screen. It has been hypothesized that there are indentations
inside the mirror which alter the path of reflected light rays and hence the reflected image. This paper explores various
methods to measure these indentations. Of the methods test Phase Shift Reflectometry (PSR) was found suitable to be
the most suitable both in terms of the sensitivity and the field of view.
An improvement is made to the traditional 2D integration with least squares method by introducing an
iterative compensation procedure. The issue of inaccurate reconstruction due to imperfection of Southwell grid model is
solved through the introduced iterative compensations. The feasibility and superiority of the proposed method are
investigated with simulations. Moreover, the proposed method is compared with the integration method with radial basis
functions.
Three-dimensional shape metrology using fringe projection technique and fringe reflection technique are
effective ways to reconstruct three-dimensional shape for surfaces with different reflectance properties. Fringe projection
technique is used for measuring objects with diffuse surfaces and relies on the principle of triangulation, while fringe
reflectometry is used for specular reflective specimens based on principle of reflection. While fringe projection directly
provides the profile, fringe reflectometry measures the slope of the surface from which the profile is integrated. In this
study, the performance of these two fringe based techniques are investigated in relation to sensitivity and accuracy.
Accurate phase retrieval from single fringe pattern is significant for dynamic phase
measurement. Although it brings issues of speckle noise and severe non-sinusoidal waveform,
the interference fringe pattern by coherent light is still often used for profile measurement,
especially for measuring target with low reflective surface. Both simulation and experiment
are carried out to study performance of two-dimensional Fourier transform, windowed
Fourier transform(including windowed Fourier filtering and windowed Fourier ridges), and
wavelet transform methods. The influence of the speckle noise and non-sinusoidal waveform
to those phase retrieval methods is compared and discussed.
A compact fringe projection profilometer is recently developed for profiling small objects. A handphone-size microprojector
with LED illumination is assembled into our system to minimize the size optical 3D sensor. In our compact 3D
shape measurement system, the approaches of phase shifting, temporal phase unwrapping and modified least-squares
calibration are utilized to achieve high precision and an easy procedure. The portable system allows for easy and
convenient 3D profile measurement to meet the requirements under diverse application conditions, such as profiling
small turbine blades in aerospace workshop. Experimental results testify to the robust and reliable performance of this
LED micro-projector based FPP system.
The least-squares method can be utilized in the calibration procedure for fringe projection profilometry to make it easier
and more flexible, since the geometric parameters of the system are not to be measured and the precise control of plane
moving is not required as well. Furthermore, the system components can be arbitrarily arranged which brings much
convenience to practical measurement. With a consideration of camera lens distortion, a modified least-squares phaseheight
mapping description is proposed. In this method, camera lens distortion effect is involved into the mathematical
description of the system for least-squares estimation to reduce the influence of lens distortion. Both simulation and
experiment are demonstrated to show the feasibility and convenience of this modified least-squares phase-height
mapping method.
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