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Non-linearities in interferometric displacement measurements commonly affect both homodyne and heterodyne optical interferometers. Unwanted back reflections (ghost reflections) or polarisation leakage introduce non-linearity terms at harmonics of the illuminating wavelength that cannot be fully corrected for with standard non-linearity correction techniques. A two-wavelength interferometric approach, operating at 632.8 and 785 nm, is presented here that is capable of correcting such non-linearities. Non-linearities are separated from the difference between two displacement measurements made at differing wavelengths with a Fourier approach. Compared to a standard Heydemann ellipse fitting correction, the proposed approach reduces estimated residual non-linearities from 84 to 11 pm in the case of a linear displacement profile. In particular this approach is applicable to the correction of higher order non-linearities that are caused by multiple reflections, and that are therefore very sensitive to alignment conditions.

Long synonymous with medical imaging, X-ray computed tomography (CT) is proving its worth in industrial applications such as material characterization, defect analysis, and dimensional inspection e.g., of manufactured components. Since 2005, when the first purpose-built industrial X-ray CT instrument was made commercially available, there have been significant efforts to understand just how reliable X-ray CT dimensional measurements are. In metrology, the ultimate measure of confidence is metrological traceability—a clearly-defined but often not well-understood property of a measurement result. Metrological traceability places measurements on a comparable scale and provides a quantitativeindication of measurement quality in the form of an uncertainty statement. From a practical perspective, achieving traceability can be divided into two tasks: (1) ensuring traceability of the scale with which the measurements are made and(2) assessing uncertainty in the resulting quantity assigned to the measurand. Based on this breakdown of the traceability problem, we provide a high-level discussion about traceability of X-ray CT dimensional measurements, review relevant work in understanding X-ray CT measurement uncertainty, and propose a framework for model-based uncertainty assessment per the Monte Carlo Simulation method and instrument scale calibration as a unified approach to traceability.

This work concerns the accurate dimensional measurement of metal parts directly in a production environment. Applying an approach with the simultaneous measurement of part dimension and temperature over time (dynamically) followed by modeling of the thermo-mechanical effects, the corrected length at 20 °C and its measurement uncertainty can be predicted. This paper describes a test campaign where the local diameter of a 40 mm cylindrical steel workpiece cooling down from an initial surface temperature after turning of 27 °C to an ambient temperature of 21 °C was predicted after 10 min with a systematic error of 0.5 µm and an expanded uncertainty (k = 2) of 0.9 µm.

The dimensional metrology group at the National Institute of Standards and Technology (NIST) has developed an ultra-high accuracy laser micrometer capable of external diameter measurements with a targeted expanded uncertainty, U(k = 2), of less than 20 nm. This instrument is an advanced iteration of a design developed at NIST in the 1990s and has been continuously improved since its inception. This newest approach takes advantage of the lessons learned through two decades of operation, process control measurement data, and performance analysis. This approach advances the state of the art for diameter measurements within an artifact diameter range of 0.02 mm to 55 mm. The instrument makes use of low thermal expansion materials, a stable structural design, environmental control, and remote manipulation of the artifacts to address the most significant uncertainty sources identified in previous versions of the instrument. A review of the instrument development and components will be presented. We will outline the significant contributions to the operational measurement uncertainty budget for this instrument along with identifying the high accuracy applications that will benefit from this effort.

Image focus is an important parameter which depends on various other parameters of an imaging system. One among them is the distance of the object plane from the lens. This parameter is referred as the depth in computer vision literatures. Since depth affects the focus level of pixels in an image, focus measurement can be used to interpret the depth of points of an object. The paper presents the details of the novel indigenously developed automated measurement system which can perform high-precision movements based on feedback control. The measurement system is inspired by classical systems used in techniques such as shape from focus. This system fundamentally being a mechatronics system integrates a high-precision multi-stage translation mechanism which is actuated with a servo motor with sensors such as camera, linear encoder, optical limit switches. The hardware interface is developed for automated measurement through a USB data acquisition system. The paper presents the methodology of surface reconstruction and detailed description of the various challenges encountered in the integration. The surface reconstruction is performed for various millimetres and sub millimetres level engineered specimens. The paper presents the future direction of research and also various potential application possibilities for such measurement setup.

To improve the accuracy of dimensional x-ray computed tomography (CT), error sources have to be characterised and accounted for. A variety of error sources have been comprehensively described in the literature. However, the influence of geometrical distortion of the flat-panel detector has rarely been considered. In this paper, the deviation from nominal geometry of a flat-panel x-ray detector was characterised using a calibrated ball plate. In-plane deviations were separated from the detector topography by varying the source–detector distance, resulting in a 3D detector geometry. A correction model for arbitrary source–detector distances was developed, which reduced the maximum errors of sphere centre-to-centre distances in scale-corrected CT measurements from ±3.9 µm to below ±0.8 µm. This fivefold improvement emphasises the importance of such correction for dimensional CT.

ispartof: MEASUREMENT SCIENCE AND TECHNOLOGY vol:30 issue:12 status: published

International audience; The scanning electron microscopy (SEM) technique is widely used for the characterizing of nanoparticle (NP) size, but very few papers deal with NP dimensional metrology. This article reports on a methodology with which to evaluate the uncertainty budget associated with the measurement of the mean diameter of a standard silica NP population by SEM. In this context, the effects of potential error sources have been evaluated though a metrological qualification of the instrument. The measuring method, consisting of determining the area equivalent diameter taken at middle height (D eq-FWHM), has been tested on a reference silica NP with an indicative certification value given by SEM/TEM (number-based modal diameter). Because agglomeration phenomena can cause measurements errors, semi-automatic homemade software has been employed to build the diameter distribution histogram, selecting only isolated particles. Finally, an uncertainty budget, including the main experimental components, has been established for the mean diameter measurement of this silica NP population. The main contributors to this uncertainty budget are the resolution linked to the dimension of the electron beam diameter at the focal plane, the calibration uncertainty on reference NPs, and the measurement repeatability.

Nanopositioning stages are used in many areas of nanotechnology and advanced materials analysis, often being integrated into analytical devices such as scanning probe and optical microscopes and manufacturing devices (e.g. lithographic systems). We present a metrological instrument, together with software, designed for traceable evaluation of stage performance. The system capabilities and performance are illustrated by measurement of stages of different levels of accuracy, including a low cost custom built stage manufactured by 3D printing. The traceability of the system is described and main uncertainty sources are discussed. Guidelines are given for the specification of stage performance.

Six European National Measurement Institutes (NMIs) have joined forces within the European Metrology Research Programme funded project NANOTRACE to develop the next generation of optical interferometers having a target uncertainty of 10 pm. These are needed for NMIs to provide improved traceable dimensional metrology that can be disseminated to the wider nanotechnology community, thereby supporting the growth in nanotechnology. Several approaches were followed in order to develop the interferometers. This paper briefly describes the different interferometers developed by the various partners and presents the results of a comparison of performance of the optical interferometers using an x-ray interferometer to generate traceable reference displacements.

Acoustic thermometry using a gas-filled quasi-spherical resonator (QSR) is one of the most promising techniques for measuring the Boltzmann constant kB with low uncertainty. Dimensional metrology with coordinate measurement machines (CMMs) can be used to determine the resonator's volume, either directly or in combination with measurements of the resonator's microwave spectra. We assessed the uncertainty achievable when using a CMM to characterize the shape and volume of three QSRs. The resonators differed significantly in their design and construction: their inner volumes ranged between 524?cm3 and 2225?cm3, while the QSR geometries ranged from a diamond-turned triaxial ellipsoid to the variable misalignment of spheroidal hemispheres. Comparative coordinate measurements of two solid spherical density standards were used to identify and estimate type B uncertainties.We tested the regression of the CMM data to spherical harmonic expansions and determined the volume of a QSR directly with a relative uncertainty uR < 30 parts in 106. Additionally, spherical harmonic regression of the CMM data can place uncertainty bounds on the eccentricity parameters, ?1 and ?2, typically with a relative uncertainty uR ? 0.02. This is sufficient to determine corrections to both the acoustic and the microwave resonance frequencies of the QSR with a relative uncertainty uR < 1 part in 106 for all resonances. These figures assume that the enclosed volume of an assembled QSR is equal to the sum of the volumes of its two component 'hemispheres'. In practice this cannot be strictly true and the additional uncertainties in the volume of the assembled QSR are discussed.

© 2018 IOP Publishing Ltd. Beam hardening artefacts caused by the polychromatic nature of the x-ray spectra are known to deteriorate the reconstructed image quality in multi-material industrial computed tomography. A variety of beam hardening correction (BHC) algorithms exist. Most of these methods rest on the x-ray spectra to a certain extent, which means their performance may be hindered if the spectral information is not accurate. The dependence of these methods on the spectral information, however, has not been benchmarked. This work addresses the need for such investigation by applying two sets of spectra - (1) a set of the true spectra used to produce the radiography, and (2) a set of approximated spectra acquired from simulation - to three multi-material BHC algorithms of different types. The algorithms are a segmentation based linearisation algorithm, a dual-energy algorithm, and an iterative reconstruction algorithm. Our objective in this study is to estimate the dependence of these three algorithms on spectral information. For comparable accuracy, multiple metrics are employed to quantify the performance of the methods in terms of artefact presence and dimensional metrology. The results show that under the same initial conditions, dual-energy appears to be the most sensitive one to the spectral change. Contrariwise, the segmentation method is least spectrally sensitive. The iterative method is stable over the spectral change, but performs poorly in dimensional metrology. ispartof: MEASUREMENT SCIENCE AND TECHNOLOGY vol:29 issue:9 status: published

The building blocks of particle accelerators are magnets responsible for keeping beams of charged particles at a desired trajectory. Magnets are commonly grouped in support structures named girders, which are mounted on vertical and horizontal stages. The performance of this type of machine is highly dependent on the relative alignment between its main components. The length of particle accelerators ranges from small machines to large-scale national or international facilities, with typical lengths of hundreds of meters to a few kilometers. This relatively large volume together with micrometric positioning tolerances make the alignment activity a classical large-scale dimensional metrology problem. The alignment concept relies on networks of fixed monuments installed on the building structure to which all accelerator components are referred. In this work, the Sirius accelerator is taken as a case study, and an alignment network is optimized via computational methods in terms of geometry, densification, and surveying procedure. Laser trackers are employed to guide the installation and measure the girders' positions, using the optimized network as a reference and applying the metric developed in part I of this paper. Simulations demonstrate the feasibility of aligning the 220 girders of the Sirius synchrotron to better than 0.080 mm, at a coverage probability of 95%.

The aim of this paper is to demonstrate an alternative method of measurement to be used in determining the minimum thickness of insulation on electrical and telecommunications conductors that are circular in section. As such, a critical analysis of the standard that is usually used in this type of measurement is undertaken and a new error-free methodology is proposed. The problem is reduced to obtaining the minimum separation between the two interior, eccentric circumferences. The method proposed indirectly determines this separation from four measurements between tangents to each circumference, two on the X-axis and two on the Y-axis, positioning the test piece to be measured in any position and taking any origin of coordinates at random. As such, errors derived from the skill of the operator are avoided, as the test piece can be positioned in any direction without the need to determine the thinnest section visually. This method does not involve increasing the uncertainty and is carried out using the same measuring instruments that the standard indicates (a microscope or profile projector).

The scanning electron microscope (SEM) and transmission electron microscope (TEM) are very powerful tools for the nanoscale characterization of materials. To make the best use of these capabilities, it is necessary to understand the nature of the uncertainties in the measurement process and to allow for errors during the data capture and data analysis stages of the measurement. By using replicated measurements and statistical analyses, it is possible to address repeatability and reproducibility issues and to assign a precision to the measurements. In general it is much harder to address accuracy issues in the experiment because some of the errors are systematic and non-statistical in nature and in almost all cases the true value of the measurand is unknown. In this work computer simulations are used to understand systematic errors and accuracy concerns in dimensional and chemical metrology in both the SEM and TEM. Multislice high-resolution TEM (HRTEM) simulations are used to produce synthetic cross-section micrographs of SiO2 gate dielectrics on Si substrates. These synthetic images are processed in the same manner as experimental images to extract a film thickness value from the micrographs. The absolute error in the dielectric film thickness measurement is determined by comparing this 'measured' value with the known, true thickness intrinsic to the sample's structural model used for simulation. This process allows the accuracy of the measurement process to be assessed for a given set of microscope, sample, environmental, data capture and data processing parameters. Statistical design of experiment methods is used to screen the influence of variables including beam tilt, along-beam thickness, dielectric thickness, defocus, astigmatism and vibration on the accuracy. The most important main effects are beam tilt, defocus and vibration, and the most significant two-term interactions are (beam tilt–defocus) and (defocus–vibration). Three-dimensional Monte Carlo simulations in Java and Jython are used to simulate the electron transport and x-ray generation of energy-dispersive x-ray (XEDS) experiments in the SEM. This code permits the simulation of synthetic hyperspectral XEDS datasets from complex, chemically heterogeneous nanostructures. Analysis of these datasets reveals the effects of self-absorption, thickness and beam broadening due to multiple scattering on the accuracy of chemical measurements in the SEM and TEM. A synthetic XEDS datacube from a four-phase Raney nickel sample is presented. While the effects mentioned above degrade both TEM-based and SEM-based measurements, their magnitude is larger and more easily visualized in the SEM because of lower beam energies and thicker samples.

Dimensional metrology for micro/nano structure is crucial for addressing quality issues and understanding the performance of micro-fabricated products and micro-fabrication processes. Most of the established methods are based on optical microscopy for planar dimensions and stylus profilometry for out-of-plane dimensions. Contact profilers suffer from slow speed of measurement for three-dimensional profiles and are not suitable for delicate surfaces and parts. Advanced systems using white light interferometer are equipped with CCD cameras and interfaced with a microscope to conduct an array of measurements ranging from two-dimensional to three-dimensional profiles and surface roughness analysis. This paper presents a methodology based on white light interferometer for the dimensional measurement of 3D micro-structures, demonstrated on micro-gears and moulds produced by UV lithography and vacuum casting, respectively. Physical artifacts, such as gauge blocks, are also utilized to verify and validate the measurements on the microcomponents.

A procedure for the calibration of sensors used for the measurement of surface temperature in dimensional metrology is developed. It consists of the utilization of a climate chamber, with an aluminium block inside, to house reference and calibrating sensors. The temperature of the sensors is controlled by the climate chamber and uncertainties are reduced due to the utilization of the aluminium block. The method is demonstrated by comparing the results obtained with those of a water bath calibration.

Often Abbe errors are the most important uncertainty sources in dimensional metrology applications aiming for measurement uncertainties of only a few nanometres. Abbe errors are caused by the angle deviations of relative translations between measurement object and sensing device?either in moving object or moving sensing device configuration?and the offset between the measurement axes of the machine and the measurement point of the structure localization device or the displacement sensor under investigation. The angle deviations of the motion stage can usually be determined, e.g. by an electronic autocollimator with sufficient accuracy. Unfortunately, in many cases, the Abbe offset cannot be estimated with sufficient accuracy or varies over the measurement range. In order to reduce the influence of the Abbe error many length measuring machines are equipped with control loops to reduce the angle deviations. However, in order to specify the uncertainty contribution of the residual Abbe errors, the Abbe offsets are still required. In these cases, in principle, an in situ determination of the Abbe errors is possible by the following method. First the measurement is conducted in the common way. Then two further measurements are performed during which one angle, consecutively the yaw and the pitch angle, is scanned by the angle actuators and measured by the angle sensors of the control loop. The differences of these two measurements from the first should reflect the influence of the Abbe errors and the dependence of the length measurement results on the angles can be determined. This predication was tested during the measurements of a high resolution encoder with the Nanometer Comparator. Contrary to the classical perception, the observed dependence of the Abbe error on the angle variation applied was nonlinear. However, using a polynomial of third order it is possible to correct the artificially introduced Abbe errors of up to 20 nm almost down to the noise level.

METAS developed a new 3D coordinate measuring machine (CMM) dedicated to traceable measurement for small parts with nanometre accuracy. The innovative design of the touch probe is based on a parallel kinematic structure of flexure hinges in order to minimize the moving mass and ensure an isotropic low stiffness. This head features very weak probing forces, below 0.5 mN, and supports exchangeable probes down to 0.1 mm diameter. It was combined with a highly accurate positioning stage developed at Philips CFT. The machine features a 90 mm × 90 mm × 38 mm air bearing stage with interferometric position measurement with no Abbe offset. The relevant calibration measurements reported here proudly highlight a repeatability of about 5 nm achieved by our micro-CMM. At the reached level of precision, the shape deviation of the probing sphere becomes a major contribution to the uncertainty. Therefore a calibration method for spheres based on error separation techniques was implemented. The result of roundness measurements on three calibration spheres is also presented. In addition, a scanning measurement procedure was implemented without any loss of accuracy, as attested by a comparison using a roundness measuring machine.

An atomic force microscope (AFM) has been developed for studying interactions between the AFM tip and the sample. Such interactions need to be taken into account when making quantitative measurements. The microscope reported here has both the conventional beam deflection system and a fibre optical interferometer for measuring the movement of the cantilever. Both can be simultaneously used so as to not only servo control the tip movements, but also detect residual movement of the cantilever. Additionally, a high-resolution homodyne differential optical interferometer is used to measure the vertical displacement between the cantilever holder and the sample, thereby providing traceability for vertical height measurements. The instrument is compatible with an x-ray interferometer, thereby facilitating high resolution one-dimensional scans in the X-direction whose metrology is based on the silicon d220 lattice spacing (0.192 nm). This paper concentrates on the first stage of the instrument's development and presents some preliminary results validating the instrument's performance and showing its potential.

As development of computer vision, stereoscopic vision sensors have been used more and more widely, and double CCD vision sensor with its simplicity of operator, highaccuracy and high-efficiency has been used in many spheres. It can be used in dimensional metrology of large forge piece, which greatly improves the efficiency and accuracy of large forge piece measurement.

Standard least squares algorithms for finding the best-fit geometric surface to coordinate data implicitly assume that the uncertainties associated with the coordinates are uncorrelated and axis-isotropic, i.e., the uncertainties associated with the x-, y- and z-coordinates are equal (but can vary from point to point). Very few coordinate measuring systems have such uncertainty characteristics but, in the absence of quantitative information about the true uncertainty structure, these assumptions can be justified. However, more effort is now being applied to evaluate the uncertainties associated with coordinate measuring systems and the question arises of how best to use this extra information, for example in surface fitting. This paper describes algorithms for fitting geometric surfaces to coordinate data with general uncertainty structure and shows how these algorithms can be implemented efficiently for a class of uncertainty matrices that arise in many practical systems. The fitting algorithms are illustrated on data simulating laser tracker and coordinate measuring machine measurements.

It is now fully appreciated that metrology will play an integral role in the successful development and commercialization of micro- and nanotechnology. To this end, the UK Government, through the National Measurement System, funded several groundbreaking projects in its 2002–2005 Programme for Length. This paper will briefly describe the background of the research, concentrating on the technical details of the projects. The Programme for Length normally only funds work into dimensional metrology but this funding cycle also funded work into low force metrology as this area is crucial to most mechanical probing techniques. The projects described include a traceable areal contacting instrument designed to calibrate areal transfer artefacts and hence offer traceability for industrial areal instruments, the production of the areal transfer artefacts, the development of Internet-based softgauges for profile parameters, a primary low force balance with a force resolution of 50 pN and the development of methods for measuring complex micro-scale structures. Amongst others, the projects involved collaboration with PTB, TNO, Taylor Hobson, AWE, Rubert & Co. and the Universities of Warwick, Huddersfield and Eindhoven.

Nanometrology is the science and practice of measurement of functionally important, mostly dimensional parameters on components with at least one critical dimension which is smaller than 100 nm. Although still called microelectronics, the production of semiconductor devices with smallest feature widths well below 100 nm is the economically most important part of nanotechnology nowadays and presumably in the near future. In parallel with the shrinking dimensions of the components and structures produced in the semiconductor industry, the required measurement uncertainties for dimensional metrology in this important technology field are decreasing too. This contribution will provide an overview on developments in the field of nanometrology with a special focus on the demands from the semiconductor industry from the point of view of a metrology institute.

We propose a sub-nanometric positioning control method for piezoelectric actuators based on a home-made high frequency phase shifting electronic circuit and a heterodyne interferometer. The method has been set up. Using a readily available piezoelectric actuator, we demonstrate that our method allows back and forth displacement without nonlinearities. Repeatability of 0.053 nm has been obtained over 1 µm displacement range. Displacement steps as low as 260 pm are presented. Such a method could be very useful for the nanotechnology and nanometrology communities for nano-scale manipulations or nano-assembly applications.

Metrology is the science and engineering of measurement. It has played a crucial role in the industrial revolution at the milli-inch length scale and in the semiconductor revolution at the micrometre length scale. It is often proclaimed that we are standing at the threshold of another industrial revolution, brought by the advent and maturing of nanotechnology. We argue that for nanotechnology to have a similarly revolutionary effect a metrology infrastructure at and below the nanometre scale is instrumental and has yet to be developed. This paper focuses on dimensional metrology, which concerns itself with the measurement of lengths and its applications such as pattern placement and feature size control. We describe our efforts to develop grating- and grid-based scales with sub-nanometre accuracy over 300 mm dimensions using the nanoruler—a scanning-beam interference lithography tool.

Comparison of independent measurement results allows an assessment of the accuracy of the underlying methods. In this work, four multichannel filter radiometers were calibrated using tunable laser-illuminated and lamp-illuminated integrating sphere sources (ISSs). The determination of the radiance of the laser-illuminated ISS is based on electrical substitution radiometry at cryogenic temperatures and dimensional metrology of circular apertures. The determination of the spectral radiance of the lamp-illuminated ISS is based on blackbody physics, referenced to the freezing temperature of gold. By calibrating the filter radiometers using both methods, we compare the `detector-based' to the `source-based' radiance scale at the National Institute of Standards and Technology (NIST).

In recent years, x-ray computed tomography has been successfully applied as an innovative coordinate measurement technology for dimensional metrology. An important characteristic to be evaluated when testing the metrological performances of computed tomography systems is the metrological structural resolution for dimensional measurements, which describes the size of the smallest structure that can still be measured within error limits to be specified. The 'two-spheres' concept allows for the investigation of the metrological structural resolution by using a simple reference standard consisting of two touching spheres with the same nominal diameter. This work is aimed at defining and validating an enhanced method based on the 'two-spheres' concept and on a new measurement strategy. Advantages in using this method are discussed and a selection of the factors influencing the results are evaluated through experimental and simulation analyses.

The diameter measurement of sphere is very important in dimensional metrology. The measurement of diameter is generally carried out by a comparison method or direct method using 1D linear measuring system. The probes touch both sides of the workpiece and the diameter is determined from displacement of the probes. The contact force is generally operated at 1N which yield deformation due to force of approximately 1 μm with uncertainty of ±0.2 μm. This system provides good performance but has a limitation when workpiece is made from soft matter or sensitive to scratch. National Institute of Metrology (Thailand) developed a laser interferometer system which is equipped with reference spherical lens in order to make non-contact radius measurement of spherical objects possible. Radius of completed sphere and partial sphere with radius range from 1 mm up to 50 mm can be measured with accuracy of ±2.4 μm.

Large-scale dimensional metrology usually requires a combination of multiple measurement systems, such as laser tracking, total station, laser scanning, coordinate measuring arm and video photogrammetry, etc. Often, the results from different measurement systems must be combined to provide useful results. The coordinate transformation is used to unify coordinate frames in combination; however, coordinate transformation uncertainties directly affect the accuracy of the final measurement results. In this paper, a novel method is proposed for improving the accuracy of coordinate transformation, combining the advantages of the best-fit least-square and radial basis function (RBF) neural networks. First of all, the configuration of coordinate transformation is introduced and a transformation matrix containing seven variables is obtained. Second, the 3D uncertainty of the transformation model and the residual error variable vector are established based on the best-fit least-square. Finally, in order to optimize the uncertainty of the developed seven-variable transformation model, we used the RBF neural network to identify the uncertainty of the dynamic, and unstructured, owing to its great ability to approximate any nonlinear function to the designed accuracy. Intensive experimental studies were conducted to check the validity of the theoretical results. The results show that the mean error of coordinate transformation decreased from 0.078 mm to 0.054 mm after using this method in contrast with the GUM method.

International audience; According to the standard ISO 10360-2 (2001 Geometrical product specifications (GPS)-acceptance and reverification tests for coordinate measuring machines (CMM)-part 2: CMMs used for measuring size (ISO 10360-2: 2001)), we verify the coordinate measuring machine (CMM) performance against the manufacturer specification. There are many types of gauges used for the calibration and verification of CMMs. The step gauges with parallel faces (KOBA, MITUTOYO) are well known gauges to perform this test. Often with these gauges, only the unidirectional measurements are considered which avoids having to deal with a residual error that affects the tip radius compensation. However the ISO 10360-2 standard imposes the use of a bidirectional measurement. Thus, the bidirectional measures must be corrected by the residual constant offset probe. In this paper, we optimize the step gauge measurement and a method is given to mathematically avoid the problem of the constant offset of the tip radius. This method involves measuring the step gauge once and to measure it a second time with a shift of one slot in order to obtain a new set of equations. Uncertainties are also presented.

The aim of the paper is to demonstrate the successful operation of a combination of a scanning tunnelling microscope (STM), as a prominent representative of scanning probe microscopes (SPMs), with an x-ray interferometer (XRI). X-ray interferometry provides a means of calibrating nanometric displacement transducers and related instruments using silicon lattice parameters as secondary length standards. On the other hand, SPMs could be used to calibrate standards e.g. diffraction gratings for dimensional metrology. The extent of the measuring ranges covered by these instruments is wide, ranging from the diameters of atoms to dimensions of 100 µm. Some special instruments, so-called metrology SPMs, are calibrated against a laser interferometer and are affected by the laser interferometer's nonlinearity which is in the range of 1-2 nm. This uncertainty is a limit to the SPM and to the samples calibrated. Further improvement is necessary. If use is made of the high resolution of an x-ray interferometer when measuring the displacement of a sample under an SPM, a higher accuracy should be achievable and it should be possible to calibrate transfer standards with subnanometre accuracy. Here we report, for the first time, results of pitch measurements obtained for a structure on a sample, not of ideal shape but available for this experiment. The translation of the sample and the measurement of its profile were performed by a specially developed scanning XRI which uses the almost homogeneous silicon lattice spacing (Δd/d

Primary pressure standards in the atmospheric pressure range are often established using mercury manometers. To a lesser extent, controlled-clearance dead-weight testers, in which one component (normally the piston) has been dimensionally measured, have also been used. The recent advances in technology on two fronts: (i) the fabrication of large-diameter pistons and cylinders with good geometries; and (ii) the dimensional metrology capability of these components, have allowed some dead-weight testers at the National Institute of Standards and Technology (NIST) to achieve total relative uncertainties (2 σ) in generated pressure near 10 × 10-6 (10 ppm). This paper describes recent developments at the NIST in which accurate dimensional measurements have been translated into effective areas. It is anticipated that total relative uncertainties in generated pressure may decrease to 5 ppm (2 σ) when recent dimensional measurements are incorporated in the newest gauges.

In many fields of science and engineering it is important to obtain accurate high-resolution images of underwater objects and scenes to allow precision dimensional measurement and inspection. Optical holography enables true three-dimensional images, with a simultaneous high resolution and large depth of field, to be recorded. The technical challenges of recording such holograms, and their subsequent replay in the laboratory, is considerable as there are increased optical aberrations arising from the change in refractive index when an object recorded in water is replayed in air. Our detailed evaluation of these aberrations, and techniques for their compensation, are described. We have demonstrated a resolution of better than 10 µm using in-line holography and better than 100 µm using off-axis holography in laboratory simulations of underwater scenes. Volumes of water of 2.5 litres (in-line) and up to 100 litres (off-axis) have been recorded. An absolute coordinate accuracy of better than 1% for both in-line and off-axis holograms has been achieved. Results are presented on resolution and coordinate accuracy versus distance, replay wavelength, off-axis angle, and holographic plate misalignment. We discuss the concepts with reference to the design of an underwater holographic camera for the recording of marine organisms and the associated replay of the holograms.

Computed tomography for dimensional metrology has been introduced in quality control loop for about a decade. Due to the complex measurement-error cause system, generally no consistent measurement uncertainty reporting has been made. The ISO 15530-3 experimental approach, which makes use of calibrated parts, has been tested for estimating the uncertainty of CT-based measurements of features of size of a test object made of POM. Particular attention is given to the design of experiment and to the measurement uncertainty components. The most significant experimental findings are outlined and discussed in this paper.

The dark-field microscopy method with alternating grazing incidence UV illumination (UV-AGID) developed at Physikalisch-Technische Bundesanstalt offers the possibility of measuring individual isolated line structures with linewidths down to the sub-wavelength regime. In contrast, scatterometry is able and already widely used to measure average dimensional parameters of periodic structures down to the deep sub-wavelength regime. Both methods can be used for dimensional measurements of micro- and nanostructures, in particular the critical dimensions (CDs) on wafers or photomasks in the semiconductor industry, complementing each other favourably. Based on numerical simulations, we have investigated the ultimate limits of these two methods in the deep sub-wavelength regime. It has been shown that AGID microscopy in the DUV spectral range is in principle capable of measuring line structures with CDs down to a few 10 nm, depending on the structure material. For scatterometry, no fundamental limit has been observed. In practice, a technical limit due to the limited signal-to-noise ratio is expected for CDs of a few nm in width.

Interference microscopy is an important field of dimensional surface metrology because it provides direct traceability of the measurements to the SI base unit definition of the metre. With a typical measurement range from micrometres to nanometres interference microscopy (IM) covers the gap between classic metrology and nanometrology, providing continuous transfer of dimensional metrology into new areas of nanoscience and nanotechnology. Therefore IM is considered to be an indispensable tool for traceable transfer of the metre unit to different instruments. We report here the metrological study of an absolute Linnik interference microscope (IM) based on two frequency stabilized lasers. The design permits the flexible use of both lasers for measurements depending on the demand of the concrete measurement task. By principle of operation IM is combination of imaging and phase-shifting interferometry (PSI). The traceability is provided by the wavelength reference, that is, a He-Ne 633 nm stabilized laser. The second laser source, that is, a Blue-Green 488 nm grating stabilized laser diode, is used for improvements of resolution, and also for resolving integer fringe discontinuities on sharp features of the surface. The IM was optimized for surface height metrology. We have performed the study of the systematic effects of the measurements. This study allowed us to improve the hardware and software of IM and to find corrections for main systematic errors. The IM is purposed for 1D to 3D height metrology and surface topography in an extended range from nanometres to micrometres. The advantages and disadvantages of the design and developed methods are discussed.

In the field of dimensional metrology, significant technical challenges have been encountered with regard to large-scale object assembly, satellite positioning, control of the long-distance precision stage, and inspections of large steps or deep holes on semiconductor devices and multi-layered display panels. The key elements required are high speeds, a long dynamic measurable range, and good precision of measurements, and conventional methods can scarcely meet such requirements simultaneously. Promisingly, the advent of the optical comb has opened up numerous possibilities to break through practical limits by exploiting several of its unique features. These include inter-mode interference, a wide spectral bandwidth with a long coherence length and well-defined longitudinal modes. In this review, various dimensional metrological methods using the optical comb are introduced, describing their basic principles and applications in scientific as well as industrial areas.

Scattered radiation and beam hardening introduce artefacts that degrade the quality of data in x-ray computed tomography (CT). It is unclear how these artefacts influence dimensional measurements evaluated from CT data. Understanding and quantifying the influence of these artefacts on dimensional measurements is required to evaluate the uncertainty of CT-based dimensional measurements. In this work the influence of scatter and beam hardening on dimensional measurements is investigated using the beam stop array scatter correction method and spectrum pre-filtration for the measurement of an object with internal and external cylindrical dimensional features. Scatter and beam hardening are found to influence dimensional measurements when evaluated using the ISO50 surface determination method. On the other hand, a gradient-based surface determination method is found to be robust to the influence of artefacts and leads to more accurate dimensional measurements than those evaluated using the ISO50 method. In addition to these observations the GUM method for evaluating standard measurement uncertainties is applied and the standard measurement uncertainty due to scatter and beam hardening is estimated.

Although the Heydemann correction is widely used to demodulate the phase of quadrature homodyne interferometer and encoder signals, the related measurement uncertainty is considered only in a few publications. The statistical uncertainty of the phase, which is the contribution of the high-frequency noise in the input signals, due to the use of a simplified fitting approach in the Heydemann correction, cannot be determined exactly. Therefore, neglecting the correlation between the input signals and the fit parameters, an approximation is provided and verified using Monte Carlo simulations and an iterative fitting method that allows exact determination of the statistical uncertainty of the phase. For the high-quality signals encountered in dimensional metrology applications, only minor differences of a few percent in the uncertainty estimates are observed. Furthermore, for cases in which a number of points used in the fit is sufficiently large, a new, simple, analytic expression for the statistical uncertainty of the phase is derived. It represents a practical limit of optical quadrature displacement interferometry, which already has been reached experimentally. To achieve an expanded measurement uncertainty of 10 pm a signal-to-noise greater than 104 has to be realized experimentally.

The requirements on the precision lengths and precision load measurement rise due to the rapid technical development, in particular of nanotechnologies and precision optics. According to the roadmap "Dimensional metrology for micro- and nanotechnology" of the European National Metrology Institutes (iMERA)2 in the next few years "traceable 2D (3D) metrology at (sub)-nm accuracy over several 100 mm range" will be required.

With x-ray computed tomography (CT) it is possible to evaluate the dimensions of an object’s internal and external features non-destructively. Dimensional measurements evaluated via x-ray CT require the object’s surfaces first be estimated; this work is concerned with evaluating the uncertainty of this surface estimate and how it impacts the uncertainty of fitted geometric features. The measurement uncertainty due to surface determination is evaluated through the use of a discrete ramp edge model and a Monte Carlo simulation. Based on the results of the Monte Carlo simulation the uncertainty structure of a coordinate set is estimated, allowing individual coordinate uncertainties to be propagated through the geometry fit to the final measurement result. The developed methodology enables the uncertainty due to surface determination to be evaluated for a given measurement task; the method is demonstrated for both measured and simulated data.