High-accuracy metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate x-ray light with nanometer-scale wavelengths. The current capabilities and possibility for improvements in x-ray mirror manufacturing are limited by inherent imperfections of the integrated metrology tools. In the case of Fizeau interferometry, metrology tools are currently calibrated with super-polished flat test-standard/reference mirrors. This is acceptable for measuring slightly curved x-ray optics. However, for even moderately curved aspherical x-ray mirrors the flat-reference calibration is not sufficiently accurate and stitching Fizeau interferometer-based surface metrology is used to mitigate the problem. But still, the retrace and aberration errors, as well as the limited spatial resolution, described with the instrument transfer function (ITF), can be transferred into the optical surface topography of x-ray mirrors obtained in stitching metrology. For ITF calibration, we have developed an original technique, based on test standards structured as two-dimensional (2D) highly-randomized (HR) binary pseudo-random arrays (BPRAs). The technique employs the unique properties of the HR BPRA patterns in the spatial frequency domain., i.e. the inherent 2D power spectral density of the HR BPRA pattern has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. Here, we explore technological, metrological, and analytical aspects essential for calibration of the retrace and aberration errors of Fizeau interferometers using different types of tilted test samples, including a super-polished reference mirror for the re-trace calibration and the uniformly redundant array (URA) BPRA standards for the geometrical distortion (aberration) calibration. While the first method was previously demonstrated by researchers at DIAMOND Light Source, a method based on the URA BPRA is described and demonstrated here for the first time. We outline the design and fabrication process used in fabrication of URA BPRA test standards, and present the results of application of the URA BPRA standards demonstrating the high efficacy of our approach to geometrical distortion calibration of Fizeau interferometers. We also discuss the possible sources of unexpected peculiarities of the systematic errors, including an astigmatic character of the retrace error, observed with Fizeau interferometers at the Advanced Light Source X-Ray Optics Laboratory.
Binary pseudo-random array (BPRA) test samples are useful devices for calibrating the instrument transfer function (ITF) of Fizeau interferometers, interferometric microscopes, and other optical and non-optical surface and wavefront metrology instruments. The intrinsic white noise character of the power spectral density (PSD) function of the BPRA pattern simplifies the extraction of the ITF from the measured PSD. The ITF determined in a dedicated calibration experiment can be used to reconstruct the surface height profile from the measured data, effectively enhancing the instrument’s spatial resolution. For a high confidence reconstruction procedure, a reliable analytical model of the IFT is desirable. Usually, the model accounts for the contributions to the ITF related the imperfections of the instrument’s optical and detector systems. Here, we experimentally demonstrate that in the case of surface height metrology with Fizeau interferometers, the PSD measurements and, therefore, the efficacy of the ITF calibration of the tool, are strongly affected by the instrument data acquisition and processing procedures, as well as by the shape of the optic under test and its alignment with respect to the interferometer.
Binary pseudo-random array (BPRA) “white noise” artifacts are highly effective for characterizing the instrument transfer function (ITF) of surface topography metrology tools and wavefront measurement instruments. These BPRA artifacts feature all spatial frequencies within the instrument bandpass equally, resulting in a power spectral density with a white-noise-like character. This characteristic allows for direct ITF determination with uniform sensitivity across the entire spatial frequency range. We have developed a novel BPRA calibration standard that combines the diffractive pattern of a reflection computer-generated hologram (CGH) with the white noise generating BPRA pattern. By integrating these technologies using the same lithographic techniques, the resulting calibration sample enables ITF characterization of a Fizeau interferometer with a transmission sphere, or any nulling optic.
We present a two-carriage, air-bearing system on a common ceramic support beam designed to utilize multiple modes of long-trace-profiler (LTP) operation, with movable and stationary optical sensors for both coherent and incoherent light probes, dubbed the LTP-2020. Measurements with different movable and stationary sensors integrated in the LTP-2020 system allow on-bench round-robin comparisons for ensuring high-accuracy metrology of x-ray optics. In the case of variable-line-spacing (VLS) gratings, one sensor can characterize the zero-order surface, and the second, in Littrow configuration, can record diffraction angle changes without introducing uncertainty of the mutual alignment between tools. We also aspire to preserve the major advantage of the current ALS LTP-II with the capability of raising and lowering the ceramic beam with the carriages and sensors. This design allows characterization of unmounted optical substrates, as well as multi-element optical systems and large mirror assemblies, such as bendable x-ray mirrors. The modular design of the LTP-2020 gantry system together with reconfigurable optical sensors mounted to separate carriages allows operation for scanning optical surfaces at three native orientations: face-up, side-facing, face-down. We also discuss the gantry system motion control algorithms and software that enable us to perform sophisticated data acquisition based on advanced optimal scanning strategies for anti-correlation of temporal drift and systematic errors. Experimental data illustrating the high performance of the developed gantry system is also presented. This work was supported in part by the U. S. Department of Energy under contract number DE-AC02-05CH11231.
High-accuracy metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate X-ray light with nanometer-scale wavelengths. However, surface topography measurements are instrument dependent, and without the knowledge of how the instrument performs under the practical usage conditions, the measured data contain some degree of uncertainty. Binary Pseudo Random Array (BPRA) “white noise” artifact are effective and useful for characterizing the Instrument Transfer Function (ITF) of surface topography metrology tools and wavefront measurement instrument. BPRA artifact contains features with all spatial frequencies in the instrument bandpass with equal weight. As a result, power spectral density of the patterns has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range. The application examples include electron microscopes, x-ray microscopes, interferometric microscopes, and large field-of-view Fizeau Interferometers. Furthermore, we will introduce the application of BPRA method to characterizing the ITF of Cylindrical Wavefront Interferometry (CWI), by developing the BPRA artifact which matches the radius of curvature of the cylindrical wavefront. The data acquisition and analysis procedures for different applications of the ITF calibration technique developed are also discussed.
Binary pseudo-random array (BPRA) artifacts are useful devices for calibrating the instrument transfer function (ITF) of interferometric microscopes and other optical and non-optical surface and wavefront measurement instruments. The intrinsic white noise character of the power spectral density function of the artifact simplifies the deconvolution of the ITF from the measured power spectral density (PSD). However, resampling of the BPRA intrinsic artifact features with the measurement tool’s specific sampling pattern modifies the white noise character of the intrinsic spectrum and needs to be accounted for in the ITF-based data deconvolution process. We have developed an analytic solution to the spectrum of a resampled one- and two- dimensional BPRA. The resultant nominal PSD function is a simple two-parameter cosine function with a period equal to the resampled pixel width. A transfer function model for interferometric microscopes that incorporates this function, along with an ITF that includes aliasing effects and variable numerical aperture (NA), wavelength, and obscuration factor, is used to fit to the BPRA PSDs measured by an interference microscope for a range of objective and zoom lens magnification combinations.
The thorough realization of the advantages of the new generation x-ray light sources, such as the Upgraded Advanced Light Source (ALS˗U) under construction, requires near-perfect x-ray optics, capable of delivering light without significant degradation of brightness and coherence. The stringent requirements of beamline optics drive the state of the art in ex situ optical metrology. Here, we present the results of the ongoing efforts at the ALS X-Ray Optics Laboratory to develop a new generation long trace profiler, LTP-2020. We discuss the system design that incorporates different types of surface slope sensors. In addition to the classical pencil beam interferometry (PBI) sensor with an improved optical design, we develop a deflectometry sensor based on a customized electronic autocollimator (AC). By applying a new data processing algorithm to the AC raw image data available from the customized AC, we significantly reduce the quasi-periodic systematic error of the AC equipped with a small size aperture. We also treat the possibility to use the AC as a PBI sensor with external light beam sources based on super-luminescent emitting diode (SLED) and single-mode laser diode (SMLD). Operation modes with stationary and/or translated sensors are possible due to the two-carriage gantry system with adjustable vertical position. The variety of the available operation modes allows optimization of the LTP-2020 experimental arrangement for providing the best possible performance in measurements with state-of-the-art aspherical x-ray optics, variable-line-spacing diffraction gratings, and multi-element optical systems.
Improvements in the quality of synchrotron beamline x-ray optics required for next-generation light sources (e.g. the ALS Upgrade project) drive the need to improve the performance of the metrology instrumentation used to measure these components. The Long Trace Profiler (LTP) that is in use at many synchrotron metrology laboratories around the world has some known issues that affect the accuracy of its measurements. The main error source is optical path difference (OPD) phase error introduced into the probe beam by inhomogeneities in the glass components used in the optical head. We have developed a new optical head design, LTP-2020, that replaces the cube polarizing beamsplitter (PBS) with a thin wedge plate polarizing beamsplitter (WPBS) and replaces the cemented doublet lens with an aspheric singlet. Both of these components significantly reduce the glass volume traversed by the laser probe beam. Careful attention to ghost ray interference produced by back reflection from optical surfaces is necessary to minimize distortion in the primary image that translates into systematic error in the slope angle measurement. We make extensive use of a commercial raytracing program to model the back reflections and adjust component parameters as necessary to minimize distortion. Deliberate misalignment of components is necessary to make the system perform correctly. Stringent requirements are placed on the 45° incidence coatings on the WPBS and on the normal incidence coatings on the lens and camera window elements. We encourage our colleagues who wish to upgrade their current LTP systems to join us in the procurement of these custom optical components.
We describe details of a recent deep upgrade of the MicroMap-570 interferometric microscope available at the Advanced Light Source X-Ray Optics Laboratory. The upgrade has included an improvement of the microscope optical sensor and data acquisition software, design and implementation of automated optic alignment and microscope translation systems, and development of a specialized software for data processing in the spatial frequency domain. With the upgraded microscope, we are now capable for automated (remoted) measurements with large x-ray optics and optical systems. The results of experimental evaluation of the upgraded microscope performance and calibration of its instrument transfer function are also discussed. Because the same already obsolete MicroMap-570 microscopes have been used for years at other metrology laboratories at the x-ray facilities around the globe, we believe that our experience on upgrade of the microscope describe in detail in the present paper is broadly interesting and useful.
The reliability of the instrument transfer function (ITF) calibration technique based on binary pseudo-random array (BPRA) standards is investigated and demonstrated in application to interferometric microscopes. We demonstrate the linearity of the calibration (that is, independence of the ITF calibration on the standards root-mean-square roughness) via comparison of the ITF measurements with a number of artifacts with the etched depth varying from 30 nm to 120 nm. We also show that the calibration does not depend on the surface reflectivity, at least in the range between ~36% and ~80%. The criteria for selection of the geometrical parameters of the BPRA standard design appropriate for a particular interferometric microscope arrangement (including optical magnification), as well as the data acquisition and analysis procedures for different applications are also discussed.
We report on recent work towards improving interference microscopy metrology of variable-line-spacing (VLS) x-ray diffraction gratings through a combination of techniques: image reconstruction to correct for distortion and blurring, multi-image super-resolution data acquisition to increase resolution beyond the single-image limit, and image stitching to increase the measurement area. Here, we concentrate on precision characterization and correction for lens distortion (aka geometrical distortion) and provide precise measurements of the effective image pixel distribution. We present and analyze the results of geometrical distortion measurements performed with test samples, including traditional checkerboard test artifacts and binary pseudo-random array (BPRA) standards patterned with two-dimensional uniformly redundant arrays (URA). The URA BPRA standards are also useful for measurement of the instrument transfer function (ITF), a measure of the optical aberrations and limited lateral resolution of the instrument. We also outline other essential elements and the next steps of the project on development of so-called super-resolution interference microscopy, enabling more precise measurements of VLS groove density than previously possible. The global aim of this project is to integrate our metrology technique into the manufacture of high-resolution x-ray gratings.
Interferometric microscopes are used to measure surface roughness, from which the computed power spectral density function can be used to extract bandwidth-limited values of the various surface properties, such as root-mean-square (rms) height and slope errors. Measurements with a microscope equipped with different objectives that have an overlapping spatial frequency range usually give different rms results over the common frequency bandwidth. This is a result of different instrument transfer functions (ITFs) that attenuate spatial frequencies by different amounts over the overlapping range. We report on the use of binary pseudo-random array (BPRA) standards to characterize the ITF of an interferometric microscope with the various objectives. We use a simple model of a 1D binary Results show that the spectrum for an undersampled array is a cosine function, rather than a straight line, constant white noise spectrum. We have an analytical model of the ITF that includes the effects of an obscured aperture and defocus, in addition to the usual parameters of numerical aperture, wavelength, and sampling period. In addition, the model includes the effect of aliasing of spatial frequency components beyond the Nyquist back into the sub-Nyquist region. We compare the model PSD predictions to the measurements performed with different objectives. Departures of the measured PSDs from the model predictions indicate that there are higher-order ITF corrections yet to be identified and included in the model.
High-accuracy surface metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate x-ray light with nanometer-scale wavelengths. The current capabilities and possibility for improvements in x˗ray mirror manufacturing are limited by inherent imperfections of the integrated metrology tools. Metrology tools are currently calibrated with super-polished flat test-standard/reference mirrors. This is acceptable for fabrication of slightly curved x-ray optics. However, for even moderately curved aspherical x-ray mirrors the flat-reference calibration is not sufficiently accurate. In the case of micro-stitching interferometry developed for surface measurements with curved xray mirrors, the tool aberration errors are known to be transferred into the optical surface topography of x-ray mirrors. Our approach to improvement of the metrology is to thoroughly calibrate the measuring tool and apply the results of the calibration to gain the reliability of the metrology via calibration-based deconvolution of the measured data. Thus, we explore the application of a recently developed technique for calibrating the instrument’s transfer function (ITF) of 3D optical surface profilers to the metrology with significantly curved x-ray optics. The technique, based on test standards structured as two-dimensional (2D) binary pseudo-random arrays (BPRAs), employs the unique properties of the BPRA patterns in the spatial frequency domain. The inherent 2D power spectral density of the pattern has a deterministic whitenoise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. The high efficacy of the technique has been previously demonstrated in application to metrology with flat and slightly curved optics. Here, we concentrate on development of an efficient fabrication process for production of highly randomized (HR) BPRA test standards on flat and 500-mm spherical optical substrates. We also compare and discuss the results of the ITF calibration of an interferometric microscope when using the HR BPRA standards on flat and curved substrates.
Accurate topography measurements of engineered surfaces over a wide range of spatial frequencies are required in many applications. The instrument transfer function (ITF) of the microscope used to characterize the surface topography must be taken into consideration to ensure that the height, or depth, of features with higher spatial frequency content is not underestimated. This applies especially when comparing surface topography measurements made by different types of microscopes. We discuss ITF measurements of a confocal microscope and an interferometric microscope using a binary pseudo-random array (BPRA) standard. BPRA standards are surfaces designed to have constant inherent power spectral density (PSD) over the spatial frequency passband of a microscope. The ITF of a microscope can thus be derived from a PSD measurement of a BPRA standard in a straight-forward manner. We further show how BPRA standards can be used as efficient diagnostic tools to characterize aspects of the imaging performance of topography-measuring microscopes.
We describe a technique for measuring the instrument transfer function (ITF) of an interferometric microscope, allowing both characterization and data processing to increase the fidelity and effective resolution of the tool. The technique, based on test samples structured as two-dimensional (2D) binary pseudo-random arrays (BPRAs), employs the unique properties of the BPRA patterns in the spatial frequency domain. The inherent 2D power spectral density of the pattern has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. As such, the BPRA samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error. We discuss the results of the development and application of highly randomized (HR) BPRA test samples with elementary feature sizes in the range from 80 nm and up to 2.5 μm, optimized for the ITF characterization of interferometric microscopes broadly used for 2D optical surface profiling. The data acquisition and analysis procedures for different applications of the ITF calibration technique developed are also discussed.
Recently, a technique for calibrating the modulation transfer function (MTF) of a broad variety of metrology instrumentation has been demonstrated. This technique is based on test samples structured as one-dimensional binary pseudo-random (BPR) sequences and two-dimensional BPR arrays (BPRAs). The inherent power spectral density of BPR gratings (sequences) and arrays has a deterministic white-noise-like character that allows direct determination of the MTF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. As such, the BPR samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error. Here we discuss our recent developments directed to the optimization of the sample design, fabrication, application, and data processing procedures, suitable for thorough characterization of large aperture optical interferometers. Compared with the previous coded-aperture based design, the improved, ‘highly randomized’ BPRA pattern of the new test standard provides better accuracy and reliability of instrument MTF and aberration characterization, and enables operation optimization of large aperture optical interferometers. We describe the pattern generation algorithm and tests to verify the compliance to desired BPRA topography. The data acquisition and analysis procedures for different applications of the technique are also discussed.
Modern deterministic polishing processes allow fabrication of x-ray optics with almost any arbitrary aspherical surface shape. Among these optics, the so called “diaboloid” mirror is of special interest. The diaboloid mirror that converts a cylindrical wave to a spherical wave would improve focusing in x-ray beamlines implementing a diffraction element between a parabolic cylinder and a toroidal mirror. The replacement of the toroidal mirror in existing beamlines by the diaboloid mirror would mitigate aberrations. The shape of the diaboloid mirror is usually calculated numerically based on a truncated polynomial solution of the optical path problem. Here, we present an exact analytical solution for the shape of a diaboloid mirror as a function of the conjugate parameters of the mirror placed in a beamline. The derived analytical expressions for the diaboloid mirror in both the canonical and mirror-based coordinate systems are implemented in ray-tracing simulations to verify the beamline performances.
To fully exploit the advantages of fourth-generation synchrotron light sources, diffraction-limited-storage-rings (DLSR) and fully coherent free electron lasers (FELs), beamline mirrors and diffraction grating must be of exceptional quality. To achieve the required mirror and grating quality, the metrology instrumentation and methods used to characterize these challenging optics and, even more so, optical assemblies must also offer exceptional functionality and performance. One of the most widely used slope measuring instruments for characterizing x-ray optics is the long trace profiler (LTP). The easily reconfigurable mechanical design of the LTP allows optimization of the profiler arrangement to the specifics of a particular metrology task. Here, we discuss the optical schematic, design, and performance of an original multifunctional light beam source that provides functional flexibility of the LTP optical sensor. With this source, the LTP can be easily reconfigured for measurements of x-ray mirrors or diffraction gratings that have widely different source coherence requirements. Usage of a source with a low degree of coherence for mirror metrology helps to suppress the LTP systematic errors due to spurious interference effects in the LTP optical elements. A high-coherence narrow-band source is used for groove-density-distribution characterization of x-ray diffraction gratings. The systematic error and spatial resolution of the LTP with the different sources is also measured and analyzed.
The long trace profiler, LTP-II, available at the Advanced Light Source (ALS) X-ray Optics Laboratory (XROL), was recently upgraded by replacing a multimode diode laser light source with a single-mode, wavelength-stabilized, fibercoupled diode laser system. The upgrade enables us to reliably characterize the lateral variation of groove density of variable-line-spacing (VLS) x-ray diffraction gratings. Here, we discuss the LTP-II performance with an example of measurements with a VLS grating with the groove density at the grating center of 300 lines/mm. For the measurements, we use the LTP-II in two different operation arrangements, the single Gaussian beam and the pencil beam interferometer arrangements. For each operation arrangement, we apply two data processing algorithms: with calculating the centroid position and with determining the position of a characteristic features of the detected beam intensity distributions. We discuss the observed strong correlation between the LTP-II modes of operation and the resulted (extracted) groove density variations. We also speculate on possible origin of the correlation.
The optical design of the Long Trace Profiler optical system is explored with a commercial raytrace program, Zemax OpticStudio™ (ZOS)1, with the intent of finding and correcting sources of systematic error. ZOS provides both geometric raytracing tools and physical optics Gaussian beam propagation and diffraction image calculation tools, and two design modes, sequential component (SC) and non-sequential component (NSC) that are optimized for different aspects of the design process. The original LTP-II system employs a singlet lens with a 1250 mm focal length. It is optimized to provide minimum distortion over a surface slope angle range of ±5 mrad. Using the ZOS tools, we are able to simulate ghost rays that produce distortion in the beam spot image and can minimize the distortion by deliberate misalignment of the beamsplitter (BS) components. Unfortunately, the reference beam is compromised because of the component tilts. The most recent LTP500 system design simplifies the optical system and makes the reference beam usable again, even with misalignment of the polarizing beamsplitter (PBS). Two lenses are designed for the LTP500 – a cemented doublet that has been fabricated, and a singlet with one aspheric surface. Both have focal distances of 500 mm with an expanded angular measurement range of ±10 mrad. The aspheric singlet provides superior performance. ZOS allows the import of wavefront measurement data produced by commercial interferometer software. We apply the wavefront error measurement from the cemented doublet to the model to show that the 19nm RMS wavefront error needs to be improved by at least a factor of ten in order to reduce the systematic error to a level that will allow the LTP to approach its design limit of a few tens of nanoradians.
X-ray optics, desired for beamlines at free-electron-laser and diffraction-limited-storage-ring x-ray light sources, must have almost perfect surfaces, capable of delivering light to experiments without significant degradation of brightness and coherence. To accurately characterize such optics at an optical metrology lab, two basic types of surface slope profilometers are used: the long trace profilers (LTPs) and nanometer optical measuring (NOM) like angular deflectometers, based on electronic autocollimator (AC) ELCOMAT-3000. The inherent systematic errors of the instrument’s optical sensors set the principle limit to their measuring performance. Where autocollimator of a NOM-like profiler may be calibrated at a unique dedicated facility, this is for a particular configuration of distance, aperture size, and angular range that does not always match the exact use in a scanning measurement with the profiler. Here we discuss the developed methodology, experimental set-up, and numerical methods of transferring the calibration of one reference AC to the scanning AC of the Optical Surface Measuring System (OSMS), recently brought to operation at the ALS Xray Optics Laboratory. We show that precision calibration of the OSMS performed in three steps, allows us to provide high confidence and accuracy low-spatial-frequency metrology and not ‘print into’ measurements the inherent systematic error of tool in use. With the examples of the OSMS measurements with a state-of-the-art x-ray aspherical mirror, available from one of the most advanced vendors of X-ray optics, we demonstrate the high efficacy of the developed calibration procedure. The results of our work are important for obtaining high reliability data, needed for sophisticated numerical simulations of beamline performance and optimization of beamline usage of the optics. This work was supported by the U. S. Department of Energy under contract number DE-AC02-05CH11231.
We investigate and compare the spatial (lateral) resolution, or more generally, the optical/instrumental transfer function (OTF/ITF) of surface slope measuring profilometers of two different types that are commonly used for high accuracy characterization of x-ray optics at the long-spatial-wavelength range. These are an autocollimator based profiler, Optical Surface Measuring System (OSMS), and a long trace profiler, LTP-II, both available at the Advanced Light Source (ALS) X˗Ray Optics Lab (XROL). In the OSMS, an ELCOMAT-3000 electronic auto-collimator, vertically mounted to the translation carriage and equipped with an aperture of 2.5 mm diameter, is scanned along the surface under test. The LTP˗II OTF has been measured for two different configurations, a classical two-beam pencil-beam-interferometry and a single-Gaussian-beam deflectometry. For the ITF calibration, we apply a recently developed method based on test surfaces with one-dimensional (1D) linear chirped height profiles of constant slope amplitude. Analytical expressions for the OTFs, empirically deduced based on the experimental results, are presented. We also discuss the application of the results of the ITF measurements and modeling to improve the surface slope metrology with state-of-the-art x-ray mirrors. This work was supported by the U. S. Department of Energy under contract number DE-AC02-05CH11231.
We discuss experimental, analytical, and numerical methods recently developed at the Advanced Light Source (ALS) X˗Ray Optics Laboratory (XROL) for calibration and precision shaping of bendable x-ray mirrors. The methods are based on ex situ measurements with the mirrors using surface slope profilers available at the ALS XROL. The first realization of methods and dedicated software has allowed the optimization of the beamline performance of bendable mirrors by adjustment of the mirror shape to minimize the root-mean-square variation of residual (after subtraction of the ideal desired shape) slope deviations from ideal (specified) surface figure. Here, we further develop the methods that in application to elliptically bent mirrors adapt as a figure of merit the minimum of the rms size of the focused beam. The efficacy of the developed methods is demonstrated with examples of optimal tuning of an elliptically bendable cylindrical mirror designed for the ALS beamline 10.3.2.
To preserve the brightness and coherence of x-rays produced by diffraction-limited-storage-ring (DLSR) and free-electron-
laser (FEL) light sources, beamline optics must have unprecedented quality. For example, in the case of the
most advanced beamlines for the DLSR source under development at the Advanced Light Source (ALS), the ALS-U, we
need highly curved x-ray mirrors with surface slope tolerances better than 50–100 nrad (root-mean-square, rms). At the
ALS X-Ray Optics Lab (XROL), we are working on the development of a new Optical Surface Measuring System
(OSMS) with the required measurement accuracy. The OSMS is capable for the two-dimensional (2D) surface slope
metrology over the spatial range from the sub-mm scale to the clear aperture. Usage of different arrangements of the
OSMS sensors allows measuring the mirrors in the face-up or side-facing orientation, corresponding to the beamline
application. The OSMS translation system and data acquisition software are designed to support multi scan measurement
runs optimized for automatic suppression and compensation of instrumental drifts and major angular and spatial
systematic errors. Here, we discuss the recent results of the OSMS research and development project. We provide details
of the OSMS design and describe results of experimental performance tests of the gantry system. In particular, we show
that the system is capable for measurement repeatability with strongly curved mirrors on the level of 20 nrad (rms). The
high angular resolution of the OSMS rotational tip-tilt stage is adequate for implementation of instrumental calibration
with using the mirror under test as a reference. The achieved measuring accuracy is demonstrated via comparison to
metrology with the carefully calibrated Developmental Long Trace Profiler, also available at the XROL.
Recently, a technique for calibration of the Modulation Transfer Function (MTF) of a broad variety of metrology instrumentation has been established. The technique is based on test samples structured according to binary pseudorandom (BPR) one-dimensional sequences and two-dimensional arrays. The inherent power spectral density of BPR gratings and arrays, has a deterministic white-noise-like character that allows a direct determination of the MTF with a uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. As such, the BPR samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error. Here we discuss our recent developments working with support of the U.S. Department of Energy on industrialization of the technique. The goal is to develop affordable BPR test samples, application procedures, and data processing software, suitable for thorough characterization of optical interferometers and microscopes, as well as x-ray, electron (scanning and transmission), and atomic force microscopes. We report on the development of BPR array test samples optimized for advanced characterization (including the instrumental MTF and aberrations) and operation optimization of large aperture optical interferometers. We describe the sample fabrication process and tests to verify the compliance to desired surface topography. The data acquisition and analysis procedures for application of the technique for precise focusing of Fizeau interferometer are discussed in detail.
The development of fully coherent free electron lasers and diffraction limited storage ring x-ray sources has brought to focus the need for higher performing x-ray optics with unprecedented tolerances for surface slope and height errors and roughness. For example, the proposed beamlines for the future upgraded Advance Light Source, ALS-U, require optical elements characterized by a residual slope error of <100 nrad (root-mean-square) and height error of <1-2 nm (peak-tovalley). These are for optics with a length of up to one meter. However, the current performance of x-ray optical fabrication and metrology generally falls short of these requirements. The major limitation comes from the lack of reliable and efficient surface metrology with required accuracy and with reasonably high measurement rate, suitable for integration into the modern deterministic surface figuring processes. The major problems of current surface metrology relate to the inherent instrumental temporal drifts, systematic errors, and/or an unacceptably high cost, as in the case of interferometry with computer-generated holograms as a reference. In this paper, we discuss the experimental methods and approaches based on correlation analysis to the acquisition and processing of metrology data developed at the ALS X-Ray Optical Laboratory (XROL). Using an example of surface topography measurements of a state-of-the-art x-ray mirror performed at the XROL, we demonstrate the efficiency of combining the developed experimental correlation methods to the advanced optimal scanning strategy (AOSS) technique. This allows a significant improvement in the accuracy and capacity of the measurements via suppression of the instrumental low frequency noise, temporal drift, and systematic error in a single measurement run. Practically speaking, implementation of the AOSS technique leads to an increase of the measurement accuracy, as well as the capacity of ex situ metrology by a factor of about four. The developed method is general and applicable to a broad spectrum of high accuracy measurements.
The R&D work on the ALS upgrade to a diffraction limited electron ring, ALS-U, has brought to focus the need for near-perfect x-ray optics, capable of delivering light to experiments without significant degradation of brightness and coherence. The desired quality of the optics is illustrated by the residual surface slope and height errors of <50−100 nrad (rms) and <1−2 nm (rms), respectively. This catalyzes the development at the ALS new ultra-high accuracy metrology methods. Fundamental to the optimization of beamline performance of such x-ray optics, metrology must be capable of characterizing the optics with accuracy even better than the specification. The major limiting factors of the current absolute accuracy are systematic errors inherent to the metrology instruments. Here, we discuss details of work at the Advanced Light Source (ALS) X-Ray Optics Laboratory (XROL) on the development of advanced experimental methods and techniques to suppress, measure, and eliminate the instrumental systematic errors. With examples, we show how the implementation of these methods allows us to significantly improve the capabilities and performance of the existing lab equipment used for characterization and optimal tuning of high quality x-ray optics. We will also review the ALS XROL plans for instrumentation upgrades and development of sophisticated methods for metrology data processing and usage. The discussion will be illustrated with the results of a broad spectrum of measurements of x-ray optics and optical systems performed at the lab. Supported by the U.S. Department of Energy under contract number DE- AC02-05CH11231.
The development of deterministic polishing techniques has given rise to vendors that manufacture high quality threedimensional x-ray optics. The surface metrology on these optics remains a difficult task. For the fabrication, vendors usually use unique surface metrology tools, generally developed on site, that are not available in the optical metrology labs at x-ray facilities. At the Advanced Light Source X-Ray Optics Laboratory, we have developed a rather straightforward interferometric-microscopy-based procedure capable of sub microradian characterization of sagittal slope variation of x-ray optics for two-dimensionally focusing and collimating (such as ellipsoids, paraboloids, etc.). In the paper, we provide the mathematical foundation of the procedure and describe the related instrument calibration. We also present analytical expression describing the ideal surface shape in the sagittal direction of a spheroid specified by the conjugate parameters of the optic’s beamline application. The expression is useful when analyzing data obtained with such optics. The high efficiency of the developed measurement and data analysis procedures is demonstrated in results of measurements with a number of x-ray optics with sagittal radius of curvature between 56 mm and 480 mm. We also discuss potential areas of further improvement.
The advents of fully coherent free electron lasers and diffraction limited synchrotron storage ring sources of x-rays are catalyzing the development of new, ultra-high accuracy metrology methods. To fully exploit the potential of these sources, metrology needs to be capable of determining the figure of an optical element with sub-nanometer height accuracy. Currently, the two most prevalent slope measuring instruments used for characterization of x-ray optics are the auto-collimator based nanometer optical measuring device (NOM) and the long trace profiler (LTP) using pencil beam interferometry (PBI). These devices have been consistently improved upon by the x-ray optics metrology community, but appear to be approaching their metrological limits. Here, we revise the traditional optical schematic of the LTP. We experimentally show that, for the level of accuracy desired for metrology with state-of-the-art x-ray optics, the Dove prism in the LTP reference channel appears to be one of the major sources of instrumental error. Therefore, we suggest returning back to the original PBI LTP schematics with no Dove prism in the reference channel. In this case, the optimal scanning strategies [Yashchuk, Rev. Sci. Instrum. 80, 115101 (2009)] used to suppress the instrumental drift error have to be used to suppress a possible drift error associated with laser beam pointing instability. We experimentally and by numerical simulation demonstrate the usefulness of the suggested approach for measurements with x-ray optics with both face up and face down orientations.
The research and development work on the Advanced Light Source (ALS) upgrade to a diffraction limited storage ring light source, ALS-U, has brought to focus the need for near-perfect x-ray optics, capable of delivering light to experiments without significant degradation of brightness and coherence. The desired surface quality is characterized with residual (after subtraction of an ideal shape) surface slope and height errors of <50-100 nrad (rms) and <1-2 nm (rms), respectively. The ex-situ metrology that supports the optimal usage of the optics at the beamlines has to offer even higher measurement accuracy. At the ALS X-Ray Optics Laboratory, we are developing a new surface slope profiler, the Optical Surface Measuring System (OSMS), capable of two-dimensional (2D) surface-slope metrology at an absolute accuracy below the above optical specification. In this article we provide the results of comprehensive characterization of the key elements of the OSMS, a NOM-like high-precision granite gantry system with air-bearing translation and a custom-made precision air-bearing stage for tilting and flipping the surface under test. We show that the high performance of the gantry system allows implementing an original scanning mode for 2D mapping. We demonstrate the efficiency of the developed 2D mapping via comparison with 1D slope measurements performed with the same hyperbolic test mirror using the ALS developmental long trace profiler. The details of the OSMS design and the developed measuring techniques are also provided.
The advent of fully coherent free-electron laser and diffraction-limited synchrotron radiation storage ring sources of x-rays is catalyzing the development of new ultrahigh accuracy metrology methods. To fully exploit these sources, metrology needs to be capable of determining the figure of an optical element with subnanometer height accuracy. The major limiting factors of the current absolute accuracy of ex situ metrology are drift errors due to temporal instabilities of the lab’s environmental conditions and systematic errors inherent to the metrology instruments. Here, we discuss in detail work at the Advanced Light Source X-Ray Optics Laboratory on building of advanced environmental control that is a key component in the development of ultrahigh accuracy ex situ metrology for x-ray optics. By a few examples, we show how the improvement of the environmental conditions in the lab allows us to significantly gain efficiency in performing ex situ metrology with high-quality x-ray mirrors. The developed concepts and approaches, included in the design of the new X-Ray Optics Laboratory, are described in detail. These data are essential for construction and successful operation of a modern metrology facility for x-ray optics, as well as high-precision measurements in many fields of experimental physics.
This work reports on the development of a binary pseudo-random test sample optimized to calibrate the MTF of optical microscopes. The sample consists of a number of 1-D and 2-D patterns, with different minimum sizes of spatial artifacts from 300 nm to 2 microns. We describe the mathematical background, fabrication process, data acquisition and analysis procedure to return spatial frequency based instrument calibration. We show that the developed samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error.
Performance of state-of-the-art surface slope measuring profilers, such as the Advanced Light Source’s (ALS) long trace
profiler (LTP-II) and developmental LTP (DLTP) is limited by the instrument’s systematic error. The systematic error is
specific for a particular measurement arrangement and, in general, depends on both the measured surface slope value and
the position along a surface under test. Here we present an original method to characterize or measure the instrument’s
systematic error using a bendable X-ray mirror as a test surface. The idea of the method consists of extracting the
systematic error from multiple measurements performed at different mirror bendings. An optimal measurement strategy
for the optic, under different settings of the benders, and the method of accurate fitting of the measured slope variations
with characteristic functions are discussed. We describe the procedure of separation of the systematic error of an actual
profiler from surface slope variation inherent to the optic. The obtained systematic error, expressed as a function of the
angle of measurement, is useful as a calibration of the instrument arranged to measure an optic with a close curvature
and length. We show that accounting for the systematic error enables the optimal setting of bendable optics to the desired
ideal shape with accuracy limited only by the experimental noise. Application of the method in the everyday metrology
practice increases the accuracy of the measurements and allows measurements of highly curved optics with accuracy
similar to those achieved with flat optics. This work was supported by the U.S. Department of Energy under Contract
No. DE-AC02-05CH11231.
The autocollimator and moveable pentaprism based DLTP [NIM A 616 (2010) 212-223], a low-budget, NOM-like
profiler at the Advanced Light Source (ALS), has been upgraded to provide fast, highly accurate surface slope metrology
for long, side-facing, x-ray optics. This instrument arrangement decreases sensitivity to environmental conditions and
removes the gravity effect on mirror shape. We provide design details of an affordable base tool, including clean-room
environmental arrangements in the new ALS X-ray Optics Laboratory with advanced temperature stabilization and
turbulence reduction, that yield measurements in under 8 hours with accuracy better than 30 nanoradians (rms) for super
polished,190 mm flat optics, limited mainly by residual temporal instability of the experimental set-up. The upgraded
DLTP has been calibrated for highly curved x-ray optics, allowing same day measurements of a 15 m ROC sphere with
accuracy of better than 100 nanoradians (rms). The developed calibration procedure is discussed in detail. We propose
this specific 15 m ROC sphere for use as a round-robin calibration test optic.
The X-Ray Optics Laboratory (XROL) at the Advanced Light Source (ALS), a unique optical metrology lab, has been
recently moved to a new, dedicated clean-room facility that provides improved environmental and instrumental
conditions vitally required for high accuracy metrology with state-of-the-art X-ray optics. Besides the ALS, the XROL
serves several DOE labs that lack dedicated on-site optical metrology capabilities, including the Linac Coherent Light
Source (LCLS) at SLAC and LBNL’s Center for X-Ray Optics (CXRO). The major role of XROL is to proactively
support the development and optimal beamline use of x-ray optics. The application of different instruments available in
the lab enables separate, often complementary, investigations and addresses of different potential sources of error
affecting beamline performance. At the beamline, all the perturbations combine to produce a cumulative effect on the
performance of the optic that makes it difficult to optimize the optic's operational performance. Ex situ metrology allows
us to address the majority of the problems before the installation of the optic at a beamline, and to provide feedback on
design and guidelines for the best usage of optics. We will review the ALS XROL mission, lab design and arrangement,
ex situ metrology capabilities and performance, as well as the future plans for instrumentation upgrades. The discussion
will be illustrated with the results of a broad spectrum of measurements of x-ray optics and optical systems performed at
the XROL.
We discuss an application of correlation analysis to surface metrology of high quality x-ray optics with the aim of
elicitation and, when possible, suppression of the instrumental systematic errors in the final metrology results. We
describe and present the mathematical foundation for a novel method consisting of the randomization of the systematic
error by the averaging of multiple measurements, specially arranged to mutually anti-correlate. We also discuss the
possibility to apply correlation analysis to the entire residual surface slope distribution in order to find anti-correlation
parameters of the distribution. In this case, repeated measurements with the corresponding change of the experimental
arrangement (position of the surface and/or its overall tilt) can be used to identify the origin of the observed anticorrelation
features by analyzing the difference between the measurements. If the corresponding minimum of the autocorrelation
function is due to a systematic error, averaging over the repeated measurements will provide an efficient
suppression of the systematic error. If the observed anti-correlation properties are due to the polishing process, and
therefore belong to the surface itself, we suggest that the possibility of re-polishing the surface based on the correlation
analysis be considered. Throughout the present work we have discussed correlation analysis of surface slope metrology
data. However, a similar consideration can be applied to surface topography in the height domain measured with other
metrology instrumentation, for example: interferometers and interferometric microscopes.
We describe a systematic procedure developed for surface characterization of super polished x-ray optical components with an interferometric microscope. In this case, obtaining trustworthy metrology data requires thorough accounting of the instrument’s optical aberrations, its spatial resolution, and random noise. We analyze and cross compare two general experimental approaches to eliminate the aberration contribution. The reference surface approach relies on aberration evaluation with successive measurements of a high quality reference mirror. The so called super smooth measurement mode consists of subtracting two surface profiles measured over two statistically uncorrelated areas of the optics under test. The precisely measured instrument’s modulation transfer function (MTF) and random noise spectrum allows us to correct the aberration-amended surface topography in the spatial frequency domain. While the developed measurement procedure is general and can be applied to various metrology instruments, the specific results presented are from a Zygo NewView™ 7300 microscope.
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