Table of contents

High-accuracy dimensional metrology plays a vital role in the manufacturing, aerospace and precision engineering industries through its provision of national and international traceability and conformity. The measurement of length, displacement, distance and angle, for example, and the characterization of surfaces and three-dimensional shape and form, find application across a very wide range of magnitudes, from sub-atomic displacements to large engineering structures.

This special issue on dimensional metrology covers a multitude of new and recent metrological research techniques and applications within this broad subject area, from a variety of international precision metrology laboratories. The papers are loosely grouped according to their particular field of dimensional metrology. Early on in the issue, there are a number of papers dealing with interferometrically based measurements for high-accuracy length, displacement and distance measurements, with an emphasis on heterodyne, modulated and swept-frequency approaches. These papers target a variety of range measurements from 100 metres down to 100 millimetres, with accuracies in the micrometre range for the air-based distance measurements, to sub-nanometre accuracies and picometre-type resolution for environmentally shielded etalons. Following on from these, we have papers concerned with the measurement of diameter and angle to various accuracies, by means of different techniques including precision rotary tables, ring laser goniometry and x-ray interferometry with nanoradian resolution.

Another group of papers addresses the measurement of dimensional properties such as length, grating pitch and indenter geometry, by recourse to scanning force microscopy. These lead on naturally to diode-laser-based surface profilometry and surface characterization by confocal optical microscopy, high-resolution two-dimensional calibration and pattern generation techniques. Accuracies here are in the nanometre to sub-nanometre range. In addition, there are papers on experimental techniques for large-scale surface flatness measurement, interferometric lens testing, triangulation sensor error analysis, computer-based aberration compensation and modelling of three-dimensional surface contact in abrasive machining.

As guest editors of this special issue, we are pleased that the contributed papers are able, in general, to offer different perspectives of metrological problems within the various subject areas of the issue. These all go toward providing the reader with a wide-ranging view of current international capabilities in dimensional metrology. In recognition of this, we would like to offer our thanks to all the contributing authors, the referees engaged in the review process, and the IOP Publishing team for making this a successful special issue.

Horst Kunzmann, Physikalisch-Technische Bundesanstalt, Germany Patrick Gill, National Physical Laboratory, UK Guest Editors July 1998

Optical sensors are increasingly being employed for quality assurance tasks. Such tasks require metrologically safe tools, which means that the measuring uncertainty of the employed sensors has to be quantified, compared and minimized. The measuring uncertainties of optical triangulation sensors have been found to increase up to a factor of ten, if typical industrially used surfaces, such as steel, are probed under unfortunate angles.

This paper proposes three techniques for reducing errors incurred in measurements of triangulation sensors when the surface of the specimen is not perpendicular to the incident light beam, and when the characteristics of the specimen surface vary. The relative merits of the three techniques are discussed, enabling choices to be made in respect of sensor cost, size of error reduction and speed of operation. The third and most robust technique involves several detectors viewing from different directions in combination with the use of principal component analysis. Principal component analysis is a statistical method to obtain a robust average of all signals of the several detectors.

An advanced displacement measuring interferometer system has been developed to satisfy the needs of semiconductor manufacturing and lithography. The system electronics provides a position resolution of 0.31 nm at velocities up to 2.1 m when the system is used with a double-pass interferometer. Output data rates up to samples per second are available. The data age, which is the delay from the interferometer optics to the measurement sample, can be adjusted to equalize differences between axes to within 1 ns. This low data age uncertainty is necessary for high-resolution, high-speed, multiple-axis measurements.

It is easy to measure length accurately by means of optical interferometry. However, the measurement range of a single-frequency interferometer is limited to less than half the wavelength without a moving carriage to count interference fringes. To resolve this problem, a frequency scanning method had been developed. However, its phase resolution is not so high that the integer part of the order of the interference fringe can be accurately determined. We proposed a method to measure any length absolutely and accurately, by combining a high-resolution phase measurement technique with a frequency scanning technique. In this paper, this method was investigated by using a frequency scanning heterodyne interferometer. With heterodyne phase measurement, we achieved high resolution, higher than quarter wavelength, using the wide-range frequency scanning method. This means that we can measure the absolute length with nanometre accuracy, since the integer part of the order of the interference fringe for a wavelength is determined with the frequency scanning. We measured distances up to about 4 mm with an accuracy of about 3 nm.

The optical length of a 1 m Fabry-Pérot etalon has been determined by swept-frequency interferometry using laser diodes. The method involves progressively building up the measurement accuracy using frequency sweeps over increasing ranges, from 150 MHz (one optical fringe) to 19 GHz and 7 THz. The 7 THz sweep is referenced to the splitting of the rubidium D lines at 780 nm and 795 nm. The result from the 7 THz sweep is sufficiently accurate to use the known frequency of either end point of the scan to determine the length to a few parts in , without the need for any further measurement. The scope for further development of this technique to a range of interferometric systems is discussed.

The dimensional stability of glass ceramic materials has been investigated using two interferometric methods and optical frequency standards. The most sensitive method uses the specimen as the spacer of an optical high-finesse Fabry-Pérot interferometer. It is shown experimentally that a relative length contraction of due to ageing of the material can be determined within a measurement time of 2 min. The requirements and the limitations of the method are derived on the basis of experimental data.

A high-resolution distance meter was fabricated using optical waveguide modulators. An optical intensity modulation frequency of 28 GHz was utilized for the displacement measurement when the driving frequencies to the optical modulators were around 14 GHz. The distance meter was evaluated in the National Research Laboratory of Metrology (NRLM) tunnel, which is a semi-underground tunnel. The measurement resolution is 1 and for a distance of 5 and 100 m, respectively, in one standard deviation after correction of the cyclic error. Furthermore, cyclic errors are examined for 28 GHz optical intensity modulation.

The PTB's new comparator for diameter and form was investigated and optimized with the aim of reducing step by step the uncertainty of outer diameter measurements to U = 10 nm per 100 mm measuring length. This paper presents the measurement procedure, an error analysis and results of outer diameter measurements on a cylindrical standard of a pressure balance.

A new highly precise angle measuring table has been developed for the Physikalisch-Technische Bundesanstalt, which is to be used as a comparator to calibrate angle standards. First results of the determination of the comparator's errors of measurement obtained by two calibration methods are reported. Considering the results obtained, it is to be expected that the desired uncertainty of measurement of can be achieved.

The measurement of radiation diffraction angles in spectrometers is usually carried out by means of optical encoders or laser interferometers. An angle measurement system based on a ring laser (RL) is described in this paper. The main feature of the RL is that a standing electromagnetic wave in the RL cavity can be considered as a high-precision circular scale. Systems incorporating RLs usually provide an accuracy of angle measurements of several hundredths of an arcsecond in the measurement range 0-.

The system described here consists of a RL and an optical interference null-indicator located on a rotary platform optically connected to the crystal of the diffractional spectrometer. An analysis of the measurement principle and measurement errors is presented. It is shown that the main sources of error are the random drift of the phase of the RL output signal and the wideband fluctuation of the null-indicator output signal. Results of measurements of the x-ray line of radiation with an energy of radiation E = 17.47334 keV and corresponding wavelength Å are shown. The angle measurement error of the described system turned out to be about 0.05 arcsecond.

X-ray interferometry is a crystallographic diffraction technique utilizing a moiré effect generated by the lattice. If almost perfect silicon single crystals are employed, scanning of the periodic moiré can be used for the calibration of translation or rotation on a nanometric scale since the lattice parameter is well known in terms of the SI unit of length.

A monolithic x-ray angle interferometer consisting of two crystal blocks and a connecting flexure spring allowing relative rotation was manufactured. Each block supports two x-ray optical lamellae. Their optimum thickness for good visibility of the angular moiré fringes during rotation was calculated using the dynamical theory of x-ray diffraction. The main block serves as the base of the interferometer and also incorporates the piezoelectric drive. This arrangement of three bimorph actuator blades allows angular scanning through the zero degree position in order to use the full Bragg reflection width. Pre-tensioning of the flexure spring, balancing of the rotating part and angular scanning are possible simultaneously. Different operating modes, free-running and locked to the fringe slope, were tested.

This very compact device can be used as a stand-alone instrument or as a fine scale in a large angle measuring calibrating facility.

This paper describes length measurements using a regular crystalline lattice as a reference scale and a dual tunnelling unit scanning tunnelling microscope (DTU-STM) as a detector in a thermo-stabilized cell. Direct length comparisons between a certified standard scanning electron microscope (SEM) grating with an average pitch of 240 nm and a highly oriented pyrolytic graphite (HOPG) lattice spacing, which is 0.246 nm, were performed. Images of the grating and the HOPG were simultaneously obtained in the range of m using the DTU-STM. The thermo-stabilized cell was developed to suppress any thermal drift error. In order to shorten the measurement time and thus reduce the thermal drift error, lengths of m for the two samples were measured along the fast scanning axis. Rapid scanning, in which the tip speed was up to , was also utilized to shorten the measurement time. The grating pitch obtained by comparison with the HOPG lattice spacing agreed with that calibrated by the conventional diffraction method within an error of 2%.

In this paper, experience gathered during the measurement of the geometry of microhardness indenters using a scanning force microscope is discussed. Reasonable accuracy of the geometrical parameters of a microhardness indenter can be obtained only if the scanning force microscope has been calibrated. The effect of the geometrical deviations on the result measured for the universal hardness is discussed.

A long-range atomic force microscope (AFM) profiler system was built based on a commercial metrology AFM and a home-made linear sample displacement stage. The AFM head includes a parallelogram-type scanner with capacitive position sensors for all three axes. A reference cube located close to the tip acts as the counter electrode for the capacitive sensors. Below this metrology AFM head we placed a linear sample displacement stage, consisting of monolithic flexures forming a double parallelogram. This piezo actuated stage provides a highly linear motion over m. Its displacement is simultaneously measured by a capacitive position sensor and a differential double-pass plane mirror interferometer; both measuring systems have subnanometre resolution capability.

For the measurement of periodical structures two operating modes are possible: a direct scanning mode, in which the position of the displacement stage is increased point by point while the AFM head measures the height, and a combined scanning mode where the displacement stage produces offsets which are multiples of the pitch to be measured while the AFM head is simultaneously scanning to locate an edge or a line centre position.

Construction details, system characteristics and results from first pitch measurements are presented. The estimated relative combined uncertainties for pitch values on different standards are in the range to . Laser diffraction measurements of comparable uncertainty were performed on the same standards and show a very good agreement.

This paper discusses rough surfaces contact phenomena and in particular examines surfaces machined with abrasive instruments. The nature of surface roughness obtained as a result of this type of mechanical treatment can be described by the random field of two variables. Attention is paid to three-dimensional surface roughness parameters whose statistical characteristics are determined by the simple rough surface model: for an anisotropic random field obtained by mathematical stretching of an isotropic random field. Consideration is given to surface contacts: rough and smooth surface interaction and the contact of two rough surfaces. Two types of asperities contact are examined: plastic and elastic. The criteria for contact type have been developed. Contact theory is used for the calculation of contact resistance in welding and of wear intensity. The equations obtained reveal that all of them contain one surface roughness height parameter and two spacing parameters.

A displacement generator is realized which enables the calibration of a wide variety of displacement-measuring probes, such as probes of roundness testers, roughness testers and stand-alone type scanning probe microscopes (SPMs), in the range of with a standard uncertainty below 1 nm. A digital piezo translator (DPT) drives a flat mirror which serves as the calibration platform. This mirror is locked to an elastic, hysteresis-free, monolithic parallel guide. Calibration of the platform displacement is carried out by various methods including tunable and stabilized lasers, Fabry-Pérot interferometry and laser interferometry. The system is calibrated with a standard uncertainty of about 0.1 nm using three independent methods. As an example the calibration of an SPM using generated steps is shown.

An interference profilometer has been developed which uses a diode laser as a non-expensive, compact and wavelength tunable light source. The profilometer works like an optical stylus and can be realized at relatively low expense. Two different methods of interference signal processing have been worked out. Both methods take advantage of the wavelength tunability of the diode laser. In connection with the development of the profilometer the spectral properties of different types of diode laser in the wavelength range from 780 nm down to 633 nm have been measured. The performance of the profilometer was proved by comparison measurements with a HeNe laser interferometer and by the measurement of well known surfaces. A measurement range of up to 100 m and a measurement uncertainty of better than 10 nm can be achieved.

In order to realize the performance limits of dimensional measuring machines, `measurement redundancy' calibration techniques are widely employed. The method involves the measurement of a reference object at several different positions within the area or volume to be calibrated and the measurement data are then mathematically analysed to identify and map the systematic errors in the machine. A small-area, two-dimensional position measurement system developed at the NPL was calibrated with a `neutral axis' mm optical scale using a redundancy technique. The scale consisted of a symmetrical array of location features and the method employed required the scale to be measured at eight different positions involving the rotation and inversion of the scale. Mathematical analysis of the measurements provided two-dimensional systematic error maps both for the system and for the scale with a dimensional accuracy of nearly one quarter of the value for the repeatability of the system's setting. This improvement was achieved by a combination of the metrology strategy employed and an innovative approach for the isolation of the machine errors. The design and construction of the instrumentation will be described together with the results of the calibration with the optical scale.

A laser reference plane for measurement of the flatness of large-scale dimensional surfaces has been proposed. A finely collimated laser beam is swept by rotating a pentaprism in an ideal plane parallel to the surface to be measured. The apex angle error of the pentaprism is the most effective one for measurement of the flatness. In this paper, a practical method of compensating the apex angle error for a precision laser reference plane is presented. The measurement of the flatness of the Japanese Industrial Standard zeroth grade precision surface plate, whose deviation from flatness should be less than m in an area of m, was performed using the proposed and conventional (Union Jack) methods. The results of the two methods coincided with each other and this clarified the feasibility of the proposed method.

The demands on the uncertainties of pattern placement and overlay measurements in lithography are constantly growing due to the continuing reduction of feature size which allows higher density integration. Although nowadays optical projection lithography plays the dominant role in lithography and will continue to do so in the near future other technologies will be developed further in order to replace optical lithography soon after the beginning of the next century. A pattern placement metrology instrument should be able to perform measurements on the masks used today as well as on future types of lithography masks. The PTB has developed a new pattern placement metrology instrument using a high-resolution electron beam probe. The electron optical metrology system consists of a low-voltage scanning electron microscope with a large vacuum chamber and a 300 mm x-y-positioning stage, controlled by vacuum laser interferometry. The design principles of the instrument will be described and a comparison of measurements with those of an optical mask measuring system will be presented.

We present a lateral-shearing interferometer specially devised for production-line inspection of aspheric lenses. The interferometer constitutes four right-angle prisms, whose relative sliding motions provide the lateral shearing and phase shifts necessary for measuring the beam wavefront collimated by the lens under test. The prisms are held together face to face using index-matching oil, so environmental disturbances from external vibration and atmospheric turbulence can be minimized. Furthermore, a special phase-measuring algorithm of least-squares type is adopted to compensate for the phase shift error caused by the variation in thickness of the index-matching oil holding the prisms. Experimental results prove that the interferometer provides a measuring reproducibility of the order of one hundredth of the light's wavelength.

One of the main problems in interferometric form testing is to distinguish form defects of the tested mirror from wavefront aberrations due to bad adjustment of the experimental set-up (Tutsch R 1994). When testing planar and spherical mirrors, an interpretation of the result is achieved using Zernike polynominals, for example, and fitting them to the measured wavefront. With increasing complexity of the measuring task (for example the interferometrical examination of hyperbolic or parabolic mirrors) it becomes more complicated to differentiate between defects of the mirror and those of the interferometer. This paper presents research work concerning the application of computer-based adjustments to various complex types of interferometers with the objective of increasing the reliability and, finally, the accuracy of interferometric measurements.

Optical non-contact techniques are very interesting for 3D characterization of sensitive and complex engineering surfaces. Unfortunately, the application of optical techniques was for many years restricted to selected types of surfaces which have only moderate variations of height and surface slope relative to their lateral resolution and measurement field. Owing to the fact that artefacts and form deviations occur with high spatial frequencies in optically measured topographs, there were some difficulties in interpreting the results and comparing them with the tactile standard techniques for surface characterization. Furthermore, artefacts in optically measured profiles have often been misinterpreted in terms of the resolution of optical techniques being higher than that of the tactile techniques. This paper presents two optical methods of confocal microscopy for highly accurate characterization of surfaces. The first method works on measurement fields of less than 1 and is in practice absolutely comparable to the mechanical stylus instrument, even on rough surfaces. For this method results compare very well not only in surface statistics but also in topographic raw data, as will be demonstrated for the PTB roughness standards. The second method works on measurement fields up to square centimetres.