Table of contents

The MacroScale 2011 conference was held at the Swiss Federal Office of Metrology METAS from 4–6 October 2011, and was jointly organized by METAS and the Physikalisch-Technische Bundesanstalt PTB. The conference subtitle 'Recent Developments in Traceable Dimensional Measurements' is reminiscent of a conference series which most recently took place in San Diego in 2005. It is intended that the MacroScale conference be held every three years at different locations worldwide. As the conference was organized under the auspices of CCL, the Consultative Committee for Length within the Metre Convention, it brought together 70 participants, mainly researchers from national metrology institutes, but also from academia and industry, representing 32 countries all together. It provided a forum for experts and scientists in the area of dimensional metrology for an exchange of information, for discussions and for the transfer of new results to the scientific community. The participants were encouraged to submit their papers to Measurement Science and Technology, and as a result we are delighted to present a selection in this special issue of MacroScale 2011.

As in the previous conferences on 'Recent Developments in Traceable Dimensional Measurements' the focus of the MacroScale is on the highest level length measurements of objects ranging from µm to km in size and on their traceability to the SI unit of length. At the MacroScale 2011 the following fields were addressed: interferometry, calibration of length standards, coordinate metrology, form measurements, surface texture measurements, tactile, optical and electronic sensors for surface or structure localization, temperature and force measurements and angle metrology. A total of 31 oral and 17 poster presentations were given during the conference, demonstrating the progress in the development of instruments, in methods and algorithms, in the determination of measurement uncertainty as well as on results of international comparison measurements. During the conference many enthusiastic discussions took place and a huge interest was shown in the future progression of the MacroScale conference series.

From the total of 48 contributions presented at the MacroScale 2011, a relatively large number of peer-reviewed articles (18) now finally appear in the present special issue of Measurement Science and Technology. The production of this issue has involved considerable effort made by many contributors. We would like to thank all the authors for their contributions, the referees for the time spent reviewing the contributions and their valuable comments, and the editor and publishing team of MST for their great support.

In this paper we describe the progress we have made in our simultaneous length measurement and the femtosecond comb interferometric spectroscopy in a conventional arrangement with a moving mirror. Scanning and detection over an interval longer than the distance between two consecutive pulses of the frequency comb allow for a spectral resolution of the individual frequency modes of the comb. Precise knowledge of comb mode frequency leads to a precise estimation of the spectral characteristics of inspected phenomena. Using the pulse train of the frequency comb allows for measurement with highly unbalanced lengths of interferometer arms, i.e. an absolute long distance measurement. Further, we present a non-contact (double sided) method of measurement of the length/thickness of plane-parallel objects (gauge blocks, glass samples) by combining the fs comb (white light) with single frequency laser interferometry. The position of a fringe packet is evaluated by estimating the stationary phase position for any wavelength in the spectral band used. The repeatability of this position estimation is a few nanometres regardless of whether dispersion of the arms is compensated (transform limited fringe packet ∼10 fringes FWHM) or highly different (fringe packet stretched to >200 fringes FWHM). The measurement of steel gauge block by this method was compared with the standard method, and deviation (+13 ± 12) nm for gauge blocks (2 to 100) mm was found. The measurement of low reflecting ceramic gauges or clear glass samples was also tested. In the case of glass, it becomes possible to measure simultaneously both the thickness and the refractive index (and dispersion) of flat samples.

Determination of a phase correction is necessary when making interferometric measurements of gauge blocks with an auxiliary platen. The phase correction compensates for the differences in the reflecting properties of the gauge block and the platen surfaces. Different phase corrections are reported for gauge blocks of different manufacturers, made from different materials and with different surface roughness compared to the platen. In this paper, the process of selection of the best surface roughness parameter and the influence of different complex refractive indices of the same type of material are analysed. The new surface roughness parameter based on the difference between the weighted mean of maximum and minimum asperities of 3D surface roughness measured by a modernized Linnik phase shifting interferometer is introduced. The results of comparison of the phase correction values calculated from the difference between the weighted mean values and calculated from stack method measurements are presented and discussed. The complementary method of phase correction measurement based on the cross-wringing method with the use of the modernized phase shifting Kösters interferometer is proposed.

This paper is a study on the determination of the measurement uncertainty for a relatively simple and widespread calibration task. The measurement of a special form deviation of gauge blocks using the so-called five-point technique is discussed in detail. It is shown that the mainstream treatment of the measurement uncertainty (i.e. propagation of uncertainties) cannot be applied to this problem for principal reasons; the use of supplement 1 of the GUM (Monte Carlo method) is mandatory. The proposed model equation is probably the simplest 'real world' example where the use of supplement 1 of the GUM not only gives better results, but gives results at all. The model is simple enough to serve as a didactical example. Explicit analytical expressions for the probability density functions, expectation values, uncertainties and coverage intervals are given which is helpful for the validation of dedicated software products. Eventually a complete avoidance of the standardized form parameters in calibration certificates is proposed. The statement of 'corner-deviations' would be much more useful, especially for the evaluation of key comparisons.

A new Ultra Precision Interferometer (UPI) was built at Physikalisch-Technische Bundesanstalt. As its precursor, the precision interferometer, it was designed for highly precise absolute length measurements of prismatic bodies, e.g. gauge blocks, under well-defined temperature conditions and pressure, making use of phase stepping imaging interferometry. The UPI enables a number of enhanced features, e.g. it is designed for a much better lateral resolution and better temperature stability. In addition to the original concept, the UPI is equipped with an external measurement pathway (EMP) in which a prismatic body can be placed alternatively. The temperature of the EMP can be controlled in a much wider range compared to the temperature of the interferometer's main chamber. An appropriate cryostat system, a precision temperature measurement system and improved imaging interferometry were established to permit absolute length measurements down to cryogenic temperature, demonstrated for the first time ever. Results of such measurements are important for studying thermal expansion of materials from room temperature towards less than 10 K.

The PTB developed a new optical heterodyne interferometer in the context of the European joint research project 'Nanotrace'. A new optical concept using plane-parallel plates and spatially separated input beams to minimize the periodic nonlinearities was realized. Furthermore, the interferometer has the resolution of a double-path interferometer, compensates for possible angle variations between the mirrors and the interferometer optics and offers a minimal path difference between the reference and the measurement arm. Additionally, a new heterodyne phase evaluation based on an analogue to digital converter board with embedded field programmable gate arrays was developed, providing a high-resolving capability in the single-digit picometre range. The nonlinearities were characterized by a comparison with an x-ray interferometer, over a measurement range of 2.2 periods of the optical interferometer. Assuming an error-free x-ray interferometer, the nonlinearities are considered to be the deviation of the measured displacement from a best-fit line. For the proposed interferometer, nonlinearities smaller than ±10 pm were observed without any quadrature fringe correction.

A highly precise small angle generator (HPSAG) has been developed in UME to realize the SI unit of plane angle, radian (rad), more precisely and calibrate high precision autocollimators. The device can easily generate small angles in measurement steps of 0.001 arcsec in the measurement range of ±8 arcsec. This enables calibration of high-resolution electronic autocollimators in very small measurement steps close to the autocollimators' resolution with an expanded uncertainty of 0.01 arcsec (k = 2). Description of the device, method, uncertainty budget and the first results are reported.

Recently, two new scanning deflectometric flatness reference (DFR) measurement systems were installed at the Physikalisch-Technische Bundesanstalt. These instruments are aimed at measurements of the absolute flatness of optical surfaces with sub-nanometre uncertainties. System 1 is mainly designed for horizontal specimens with sizes up to 1 m and weights up to 120 kg. The other setup, i.e. system 2, is designed for vertical specimens. The two DFR systems use three different deflectometric procedures, which are based on scanning a pentaprism or the so-called double mirror unit (DMU) across the specimen. These 90° beam deflectors eliminate—to a great extent—residual guidance errors of the scanning stages, which is required to attain topography measurements with sub-nanometre uncertainty. The setups of the two new systems, the principles of the three different measurement modes, the alignment procedures, simulation results and first measurements are presented.

Flick standards or magnification standards are widely used for an efficient and functional calibration of the sensitivity of form measuring instruments. The results of a recent measurement comparison have shown to be partially unsatisfactory and revealed problems related to the calibration of these standards. In this paper the influence factors for the calibration of Flick standards using roundness measurement instruments are discussed in detail, in particular the bandwidth of the measurement chain, residual form errors of the device under test, profile distortions due to the diameter of the probing element and questions related to the definition of the measurand. The different contributions are estimated using simulations and are experimentally verified. Also alternative methods to calibrate Flick standards are investigated. Finally the practical limitations of Flick standard calibration are shown and the usability of Flick standards both to calibrate the sensitivity of roundness instruments and to check the filter function of such instruments is analysed.

In dimensional metrology, the measurement of squareness is a basic task for many purposes. At the Centre for Metrology and Accreditation (MIKES), a squareness measuring machine for traceable calibration of squares has been developed. The machine is able to measure a squareness standard of 1000 mm × 1000 mm maximum size. The system consists of a rotary table and a tactile displacement transducer with horizontal and vertical linear guides. The error sources of the developed equipment are presented together with a brief description of the calibration procedure. Implemented error compensation of the rotary table and one linear guide is described. The uncertainty estimate is presented for squareness angle measurement. The standard measurement uncertainty for steel or granite squares is 0.2''. We also present the results of an internal comparison of squareness measurements made with the developed machine and a high accuracy coordinate measuring machine. The results show good agreement.

Due to the introduction of double patterning schemes in the production processes of the semiconductor industry and the corresponding stringent specifications of the placement errors of the optical images of mask features (1.2 nm (3σ)) in the lithographic projection process, significant improvements of the registration measurements on photomasks are required. The Nanometer Comparator of the PTB, a one-dimensional vacuum-interference length comparator, has already demonstrated measurement reproducibility at this level on line scales and linear encoders, and therefore this comparator should also be applied for placement metrology on photomasks. Because a photomask is a relatively thin plate which is supported almost at its ends, the bending influence is much larger than for line scales and precautions had to be taken to reduce the influence of the sample support on the measurements results. A new sample mount was built, which exhibits mechanical alignment aids. In addition the position deviations caused by the mask bending were corrected by means of finite element calculations. Measurements performed with the Nanometer Comparator on a high-quality mask showed a maximum deviation of measured feature positions from the common mean of below 0.5 nm and a reproducibility of 0.2 nm. These results suggest that the use of a one-dimensional calibration of mask measuring machines allows us to perform traceable registration measurements with sufficient accuracy.

An instrument developed for high accuracy calibration of line scales up to 1.16 m is described. The instrument is based on an earlier design from the early 1990s. Since then, in order to improve performance and achieve smaller uncertainty, large portions of software, mechanics and optics have been redesigned and several uncertainty components better characterized. The software has been developed to be less sensitive to imperfections of the line mark. In order to decrease noise and deformation coupling in interferometric measurement, the interferometer operating principle has been designed to use a fibre-coupled laser light, interferometer optics have been improved for better phase adjustment and detection and a differential interferometer principle has been taken into use. In order to minimize the effects due to deformations of the stone table rail with moving heavy carriage, a separate bed has been designed under line scale supports. The bed with fixed differential reflector prevents deformations of the table from affecting the line scale versus interferometer position. The main properties of the instrument are described and an uncertainty estimate is presented. The expanded uncertainty (k = 2) for line distance calibration of high-quality low-thermal-expansion line scale is U = [(4.5 nm)² + (43 × 10⁻⁹ L)²]^½, where L is the measured length. The results of international comparisons support the uncertainty estimate.

The use of optical coordinate measuring machines (CMMs) in industrial metrology shows great potential due to a high measurement speed and non-contact working principle. However, at present measurements performed by different users present too large variations. The uncertainty contributions are difficult to quantify and standard uncertainty evaluation procedures are needed. In order to address this issue, we have investigated the uncertainty sources of commercial optical CMMs. We present a comparison on chessboard standards between three different vision systems. The influence of critical measurement parameters on image formation and analysis is discussed.

For decades three-dimensional (3D) measurements of engineering components have been made using fixed metrology-room based coordinate measuring machines (CMMs) fitted most commonly with single point or to a much lesser extent, scanning tactile probes. Over the past decade there has been a rapid uptake in development and subsequent use of portable optical-based 3D coordinate measuring systems. These optical-based systems capture vast quantities of point data in a very short time, often permitting freeform surfaces to be digitized. Documented standards, for example ISO 10360, for the verification of fixed CMMs fitted with tactile probes are now widely available, whereas verification procedures and more specifically verification artefacts for optical-based systems are still in their infancy. Furthermore, the industry is seeking traceability in 3D measurements of high precision components. A recent requirement is the demand for highly accurate measurements of large gears with diameters up to 1000 mm as used in gear boxes of wind turbines. Up until now it has been impossible to ensure traceability of 3D measurements of big gears, since no traceable standards were available. This paper describes three different types of artefacts that were developed during the project, namely tetrahedron artefacts for testing the basic measurement capability of optical 3D devices, freeform verification artefacts for testing the capability of measuring complex geometry, and a large gear artefact for task related calibration of different types of CMMs. In addition, artefact calibration data and associated measurement uncertainties and international intercomparisons are presented. These developments will be of considerable value to end users, calibration laboratories and producers of optical and tactile CMMs.

In relation to the industrial need and to the progress of technology, Laboratoire National de Métrologie et d'Essais (LNE) would like to improve the measurement of its primary pressure standards, spherical and flick standards. The spherical and flick standards are, respectively, used to calibrate the spindle motion error and the probe, which equip commercial conventional cylindricity-measuring machines. The primary pressure standards are obtained using pressure balances equipped with rotary pistons. To reach a relative uncertainty of 10⁻⁶ in the pressure measurement, it is necessary to know the diameters of both the piston and the cylinder with an uncertainty of 5 nm for a piston diameter of 10 mm. Conventional machines are not able to reach such an uncertainty level. That is why the development of a new machine is necessary. The purpose of this paper is to present the concepts and the architecture adopted in the development of the new equipment dedicated to cylindricity measurement at a nanometric level of a accuracy. The choice of these concepts is based on the analysis of the uncertainty sources encountered in conventional architectures. The architecture of the new ultra-high equipment as well as the associated calibration procedures will be described and detailed.

Advanced manufacturing processes require improving dimensional metrology applications to reach a nanometric accuracy level. Such measurements may be carried out using conventional highly accurate roundness measuring machines. On these machines, the metrology loop goes through the probing and the mechanical guiding elements. Hence, external forces, strain and thermal expansion are transmitted to the metrological structure through the supporting structure, thereby reducing measurement quality. The obtained measurement also combines both the motion error of the guiding system and the form error of the artifact. Detailed uncertainty budgeting might be improved, using error separation methods (multi-step, reversal and multi-probe error separation methods, etc), enabling identification of the systematic (synchronous or repeatable) guiding system motion errors as well as form error of the artifact. Nevertheless, the performance of this kind of machine is limited by the repeatability level of the mechanical guiding elements, which usually exceeds 25 nm (in the case of an air bearing spindle and a linear bearing). In order to guarantee a 5 nm measurement uncertainty level, LNE is currently developing an original machine dedicated to form measurement on cylindrical and spherical artifacts with an ultra-high level of accuracy. The architecture of this machine is based on the 'dissociated metrological technique' principle and contains reference probes and cylinder. The form errors of both cylindrical artifact and reference cylinder are obtained after a mathematical combination between the information given by the probe sensing the artifact and the information given by the probe sensing the reference cylinder by applying the modified multi-step separation method.

The accuracy of today's coordinate measuring machines (CMM) has reached a level at which exact knowledge of each component is required. The role of the probe tip is particularly crucial as it is in contact with the sample surface. Understanding how the probe tip wears off will help to narrow the measurement errors. In this work, wear of a sapphire sphere was studied for different scanning conditions and with different sample materials. Wear depth on the probe was investigated using an automated process in situ on the METAS micro-CMM and completed by measurements with an atomic force microscope. We often found a linear dependence between the wear depth and the scan length ranging from 0.5 to 9 nm m⁻¹, due to variations in scan speed, contact force or sample material. In the case of steel, the wear rate is proportional to the scan speed, while for aluminum several processes seem to interact. A large amount of debris was visible after the tests. Except for aluminum, wear was visible only on the sphere and not on the sample. Sapphire/steel is the worst combination in terms of wear, whereas the combination sapphire/ceramic exhibits almost no wear.

During construction of a new metrology building for MIKES, a 30 m interferometric bench was designed. The objective was to implement a straight, stable, adjustable and multifunctional 30 m measuring bench for calibrations. Special attention was paid to eliminating the effects of thermal expansion and inevitable concrete shrinkage. The linear guide, situated on top of a monolithic concrete beam, comprises two parallel round shafts with adjustable fixtures every 1 m. A carriage is moved along the rail and its position is followed by a reference interferometer. Depending on the measurement task, one or two retro-reflectors are fixed on the carriage. A microscope with a CCD camera and a monitor can be used to detect line mark positions on different line standards. When calibrating optical distance measuring instruments, various targets can be fixed to the carriage. For the most accurate measurements an online Abbe-error correction based on simultaneous carriage pitch measurement by a separate laser interferometer is applied. The bench is used for calibrations of machinist scales, tapes, circometers, electronic distance meters, total stations and laser trackers. The estimated expanded uncertainty for 30 m displacement for highest accuracy calibrations is 2.6 µm.

The calibration and verification of high-precision electronic distance meters (EDMs) requires well-characterized and calibrated geodetic baselines. As the length measurements are performed typically over several hundred metres in air, a thorough understanding of the environmental conditions is necessary. In the course of a major refurbishment, the 600 m baseline of the Physikalisch-Technische Bundesanstalt at Braunschweig, Germany, was equipped with a dense environmental sensor network. This paper presents the characterization of this novel reference baseline, including the calibration of the inter-pillar distances, and identifies the major sources of uncertainty for such a length standard. A preliminary expanded standard uncertainty (k = 2) of $U ( l ) _{k=2}=\sqrt{( 6.2 \times 10^{-4} \: {\rm m} )^2 + ( 7.6 \times 10^{-7} \, l )^2}$ is deduced for single-slope distance comparisons on the baseline. In the course of a full calibration, the additive constant c_EDM of an EDM can currently be determined with an expanded uncertainty of U(c_EDM)_{k = 2} = 6.1 × 10⁻⁵ m, and its scale correction s_EDM with an expanded uncertainty of U(s_EDM)_{k = 2} = 8.2 × 10⁻⁷. As an example, a femtosecond laser-based distance measurement over 600 m on this baseline is presented.