The basis of new, parallax-free methods of length measurements by optical interferometry is presented. Two new length specifying parameters of a material end standard, i.e. optical and mechanical lengths of a block are introduced, that give the possibility to realize more accurately the length unit. A traceability of the mechanical and optical lengths, obtained by optical interferometry, to the basic physical quantity, the length of a material artifact, has been established for the first time. We present here the system of equations which shows the inter-relation between these lengths, and links them to the results of the basic interferometric length measurements and to such quantities as skin depth, roughness values of the gauging surfaces, wringing in surface deformations, excessive wringing film thickness, interferometer optics distortions. Experimental confirmation of the main theoretical relations is presented. We discuss in detail the key feature of optical and mechanical length measurements and give examples of their uncertainty budget evaluations.

Modification of an interferometer instrument for highest accuracy calibration of long gauge blocks is presented. The interferometer design employs a Kosters prism, and a built-in 1 metre long vacuum cell for evaluation of refractive index of air in the direct neighborhood of the gauge block. The measurement set-up also includes platinum resistance thermometers and thermocouples for accurate measurements of gauge block temperature. Principles of the measurement method, including the application of phase stepping interferometry to both the length measurement and the correction for refractive index of air, are described in detail.

The main features of the small Carl Zeiss comparator (for the gauge blocks up to 100 mm), and a large Kosters interferometer (for gauge blocks up to 1000mm) are discussed in some detail. Special emphasis is made on the problem, requirements and specific feature of the differntial optical measurements, which become feasible with these new devices. Very high resolution of the instruments, resulting in resolving the oblique incidence effects for "sad" and "smile" type of interferograms, which correspond to different directions in the measurement of the fringe fraction values, imposes some restrictions on the measurement procedure, realized with their use. For example, the the optimum parameters of the interferogram, which are required for the most accurate and reliable operation of the fringe-pattern analyzing comparators, the measurement can be performed for only one type of interferogram ("sad" in our case), and for the measurements of the other type ("smile") a new optical tuning of the interferometer is required. The problems of temperature measurements with a sub-mK accuracy level are formulated, and the ways to overcome them are outlined.

The detailed knowledge of thermal expansion and dimensional stability of low expansion materials is of growing interest and requires measurements of length changes with sub nm uncertainty. In addition to accurately defined environmental conditions the interferometer adjustment, namely the number of fringes covering the sample and also the method of autocollimation adjustment, become more important. Their influence, investigated with PTB's precision interferometer, will be discussed.

The effect of wringing deformations on the result of the main types of measurements by optical interferometry is studied in some detail. The wringing bending deformations can be used to improve by 10-20 times the accuracy of length measurements of gauge blocks with nominal lengths of a few millimeters. The data on the surface deformations of steel and quartz reference plates, resulting from the writing procedure of gauge blocks to their surface, are presented. Ways of crucial reduction of the plate surface deformations are reported. Surface texture deformations, arising in the tight wringing contact, are measured to be about 2.5-3 nm for modern steel and tungsten carbide blocks. Thanks to extremely high level of their reproducibility, the surface texture deformations, practically, do not affect the accuracy of the mechanical length measurements of gauge blocks.

A low-coherence tandem interferometer with a single-mode optical fiber is developed for remote-measurement of length. The optical path difference provided in the first low-coherence interferometer is transmitted through the optical fiber to the second low-coherence interferometer. Low-coherence interference fringes are generated when the optical path difference in the second interferometer, which correspond to the length being measured, compensates that of the first interferometer. A gauge block of 50 mm long has been calibrated remotely through the single-mode optical fiber of 3 km length with a stnadard deviation of 0.12 μm.

An analysis of gauge block calibrations by mechanical comparison carried out at METAS with several sets of gauge blocks during several years has demonstrated very small variations. It is shown, that under optimum conditions with respect to laboratory environment and instrumental equipment as well as by following a suitable handling and measurement procedure, the contribution in the uncertainty budget added by the mechanical comparison process to the uncertainty of the interferometrically calibrated reference gauge blocks can be very small.

Linear variable differential transformer (LVDT) sensors are usually used in precision measurement system for dimensional displacement measurements, especially in long gauge block comparator or gauge block. In order to ensure the accuracy of the LVDT sensor, the research provides static calibration methods to measure the displacement linearity to within ± 12mm. Our experiment structures include a laser interferometer and mechanical devices to setup optical alignments on SIP universal measuring machine. The experiment results show the read values from LVDT sensor and laser interferometer, and the correction values are defined as the read values of LVDT subtracted from the ones of laser interferometer. These corrections were calculated statistically as regression and residual analysis. Statistical results show that correctional error is 0.04 mm in short-term operations, and the displacement linearity is -0.016 mm /1 mm. For precision measuring systems, LVDT sensors should be calibrated periodically and the research results could provide both a static calibration method and plotting linearity curves for users’ references.

Using of length materialized standards is necessary to calibrate CMMs according to ISO 10360 written standard. CEM calibrate this kind of standards till 1200 mm on its fully automatized CEM-TEK 1200 interferometric comparator, obtaining a repeatability of less than 40 nm. It conducts to an uncertainty U = Q [70;0.4 L/mm] nm when calibrating long gauges and to U = Q [0.1;0.4E-3 L/mm] µm for step gauges, both for a coverage factor k = 2, the last being the smallest CMC value approved by RMOs and BIPM among those offered by NMIs calibrating step gauges. It permits to reduce considerably the uncertainty linked to the process of verifying CMMs performance because the low uncertainty associated to the step calibration. Recently this comparator has been improved to obtain for steps an uncertainty closer to that of the long gauges, and updated to calibrate automatically high precision line scales by using optical methods, combining CCD, microscopy and home made software including image analysis and edge recognition. So, this equipment is probably the most universal one in the world, permitting the calibration of many different standards (long gauges, end bars, step gauges and line scales), with a repeatability of less than 40 nm and expanded uncertainties lower than 0.1 μm. On this paper CEM present some of the results obtained in international key comparisons.

An automatic calibration bench to calibrate line scales up to three meters has been developed at the Centro Nacional de Metrologia. It incorporates an heterodyne laser interferometer to follow the position of a carriage that support a microscope with a CCD camera. The images are processed using a novel robust algorithm to determine the center of each line. The carriage travels along guide ways and is commanded by a computer that controls the servomotor that moves it, allowing to complete the calibration automatically. The measurement and control software developed uses an image processing algorithm based on Gabor filters and robust statistics to discriminate between lines and unwanted features that may exist such as stain, scratches, rust, etc. It then calculates the absolute position of each line by coupling the reading of the carriage position given by the interferometer and the centerline position of the line in the image. Additionally, the software corrects the laser readings for ambient condition variations and controls the progress of the carriage. The mechanical design consists of a stiff bench with guide ways on which the carriage travels. Although the carriage travels in non-kinematic guide ways, the microscope and CCD camera sit on a plate that is kinematically supported. The movement is provided by a servomotor and transmitted by means of a screw. Uncertainty is expected to be between 3 and 10 um which is common to other similar systems. The gross advantage is the ability to calibrate automatically and discriminate defects on the scale.

NMIJ line standard interferometer has been modified for measurement of a linear scale module with analog output. The interferometer was developed for line standard calibration. The light source is a stabilized He-Ne laser. Before the modification, a line standard can be calibrated with an uncertainty of about 0.2 micrometer for the total length of 500 mm (k=2). After the modification, a linear scale module can be calibrated as well as a line standard. A linear scale is set in a support on a moving carriage. The displacement of the moving carriage is measured by the interferometer with a sampling frequency of 30 kHz to 300 kHz while the electronic output of the linear scale module is sampled with the same timing. The analog output of the line scale module is used instead of digital output because it is important to assure the simultaneous sampling of the displacement and the scale output.

This contribution will report on the results of the international line scale comparison Nano3, which was carried out between 2000 and 2003. The comparison was initiated by the BIPM working group on nanometrology as one of five comparisons in the field of nanometrology. Two high quality line scales of Zerodur and quartz with 280 mm graduations were chosen as transfer standards. They were measured by 13 national metrology institutes from 4 different metrology regions. The measurement uncertainties which were evaluated by the participants over the 280 mm length showed a variation from about 300 nm down to 30 nm.

Traceable radius of curvature measurements are critical for precision optics manufacture. An optical bench measurement of radius is very repeatable and is the preferred method for low-uncertainty applications. On an optical bench, the displacement of the optic is measured as it is moved between the cat's eye and confocal positions, each identified using a figure measuring interferometer. Traceability requires connection to a basic unit (the meter, here) in addition to a defensible uncertainty analysis, and the identification and proper propagation of all uncertainty sources in this measurement is challenging. Recent work has focused on identifying all uncertainty contributions; measurement biases have been approximately taken into account and uncertainties combined in an RSS sense for a final measurement estimate and uncertainty. In this paper we report on a new mathematical definition of the radius measurand, which is a single function that depends on all uncertainty sources, such as error motions, alignment uncertainty, displacement gauge uncertainty, etc. The method is based on a homogeneous transformation matrix (HTM) formalism, and intrinsically defines an unbiased estimate for radius, providing a single mathematical expression for uncertainty propagation through a Taylor-series expansion.

The highest accuracy method for angle measurement employed at NIST (National Institute of Standards and Technology) makes use of an automated stack of three indexing tables--our Advanced Automated Master Angle Calibration System (AAMACS)--in conjunction with one of two possible instruments for small-angle measurement. The small-angle measurement system is usually an autocollimator, but we have also used a Fizeau phase-stepping interferometer in this role. We have performed numerous experiments to characterize the performance of the Fizeau interferometer for angle measurement. The two small-angle measurement systems are subject to a variety of potential errors when measuring imperfectly flat surfaces or imperfectly mounted artifacts, and we have quantified many of these sources of error. Potential errors of the Fizeau system, such as diffraction and various aberration effects, are small relative to potential errors associated with the measurement of non-flat artifact faces. Furthermore, when measuring the angle between imperfect surfaces, our two instruments implement slightly different definitions of the "average angle", and we might expect to see a significant difference in results from the two instruments. In actuality we have seen only very small differences when measuring typical artifacts.

The pitch calibration by a single wavelength laser and Littrow configuration laser diffractometer was presented. The calibration system consists of a green He-Ne laser, a precision angular positioning state, a four-quadrant detector, a beam splitter, and some optics. The measurement principles was based on the Littrow configuation that the reflective diffraction beam coincides with the incident beam. The pitch value was determined by the diffraction angle α and laser wavelength λ. A pitch standard, with nominal value of 292 nm, was measured by a wavelength of 543 nm green He-Ne laser diffractometer. The average pitch value was 292.10 nm. According to the "Guide to the expression of uncertainty in measurement", the system uncertainty was evaluated. The error sources included laser wavelength, refractive index of air, angular state, temperature, and coefficient of thermal expansion. The expanded uncertainty was 0.03 nm at a confidence level of 95% and 15 degrees of freedom. The main contributor of uncertainy was the positioning deviation of angular stage. Although the laser diffractometer had a high-accuracy ability, the measurement capability of Laser diffractometer was limited by the laser wavelength. The pitch p should be large than a half of laser wavelength.

Two types of film thickness standards have been developed, manufactured and investigated - for X-ray reflectometry (XRR), X-ray fluorescence analysis (XRR), electron probe microanalysis (EMPA) on the one hand, and ellipsometry on the other. Metrological characterisation of both specific kinds of material measures and investigation results achieved are reported. The standards for XRR, XRF, EMPA consist of quarts substrate coated with Pt resp. a C-Ni-C-layer-system with a nominal metal layers thickness of 10 nm alternatively 50 nm. An established process for manufacture of X-ray mirrors was used for coating. XRR proved to be the dominant investigation method. Apart from film thickness characteristics like film thickness variances, interdiffusion between substrate and film have been analysed. In conclusion it can be estimated that the expanded measurement uncertainty of the film thickness for XRR applications is less than 0.5 nm. The standards for calibration of ellipsometer used for film thickness determination consist of an Si-substrate and an SiO₂-film. They are provided with an additional topographic structure making a topographic film thickness determination (approximately) possible. The nominal values of film thicknesses are between 6 nm and 900 nm. Film thickness determinations were effected by XRR, Scanning Force Microscopy in combination with Transmission Electron Microscopy as well as various ellipsometrical techniques. The consistency of results found by different measurement techniques is discussed.

We will report on the progress of our project to realize a traceable Scanning Probe Microscope at the Van Swinden Laboratorium of the Nederlands Meetinstituut in the Netherlands. The traceable Atomic Force Microscope (AFM) is constructed from a separate AFM head, a 3D translation stage and an accurate 3D laser interferometer system. Nanometer uncertainty can be maintained in the entire scanning volume of 100 μm × 100 μm × 20 μm. Apart from providing direct traceability to the SI unit of length, the coordinates provided by the laser interferometer are also used in a closed loop position feedback controller to realize accurate positioning at arbitrary locations within the volume provided by the translation stage. In this paper we will emphasize the development of the control system.

A monolithic x-ray interferometer manufactured at KRISS has been used to provide a means for the calibration of transducers with the traceability to the standards of length in the sub-nanometer region. Such calibration by the monolithic x-ray interferometer using the lattice spacing of silicon is directly traceable to primary standards. The lattice plane used for diffraction was (220) with lattice parameter of 0.192 nm. One period of the x-ray interference fringe corresponds to the lattice parameter. We could achieve a resolution of less than 0.01 nm by detecting the phase of the x-ray interference signal. A monolithic x-ray interferometer was made from a silicon single crystal. It comprises three thin lamellas called splitter, mirror, and analyzer, and it incorporates a double parallel spring structure for the translation of the analyzer lamella. The x-ray interferometer has been applied to the measurements of displacements at sub-nanometer levels. The displacements of linear transducers have been measured using the x-ray interferometer. Several capacitive sensors were also calibrated and the results of these measurements are reported in the paper.

An initial description of the design and operation of compact miniature interferometers that employ fiberoptic lightguides for all of their optical couplings and are suitable for general-purpose use is followed by a metrological analysis of their mode of operation and examples of their broad applicability, based on several typical instrumental setups.

The precision of interferometric measurements strongly depends on the system's calibration procedure, the stability of the illumination source and the quality of the scanner that moves the objective through focus. Typically, a calibration procedure is done prior to measurement and these measurement conditions are then assumed to be constant over time. Any variation in these conditons introduces errors into the measurement. Veeco's NT8000 optical profiler employs a calibration procedure that sharply decreases the system's sensitivity to changes in measurement conditions. It is a system that is independent of any geometrical standards and one that is capable of self-calibration during each measurement. This hands-off self-calibrating feature allows for high repeatability, reproducibility and accuracy of measurements and excellent sytem to system correlation. These measurement features make such a system ideally suited for production lines, laboratories and standardization institutes.

In form and roughness measurements, often surfaces are measured which are approximately straight, round, or smooth. Measuring such surfaces often gives measurement results in which noise plays a role. This noise may give an offset in measurement parameter as the noise makes the parameter, e.g. the flatness deviation of the Ra-value, deviate away from zero. In this paper we propose a method to correct for this noise bias for the roughness parameter Rq which is equivalent to the standard deviation. By considering the decrease in Rq once an average over multiple measurements is made, an unbiased value for Rq is estimated by extrapolating the value to an infinite amount of measurements. It is shown that using this method for two profile measurements only, the true measurand is approached better than with averaging dozens of measurements. This principle is extended to obtain a complete 'noise-corrected' profile by considering the power spectrum and the change of each Fourier component with averaging. As for each Fourier component few estimations are available, the method only has advantages when many measurements are taken. Combining the two methods and considering the statistical significance of each Fourier component enables a further reduction. Simulation and measurement examples are shown for roughness and roundness measurments.

Surfaces as needed in optical systems, ranging from the visible even into the EUV region, become larger and often have a length or diameter of 500 mm and more. The form of these surfaces, describing the surface spatial frequency content with components below 1 mm-1, has to be characterized on the nanometer and sometimes even on the sub-nanometer scale. The extendibility of the measuring systems accuracy to large specimen dimensions basically depends on the method of the measurement and the scaling of different systematic uncertainty components with lateral coordinate values. This is analyzed for flatness and sphericity measuring systems, with a focus on the systems for Extended Shear Angle Difference (ESAD) and Large Area Curvature Scanning (LACS) used at PTB. Both are scanning methods working absolute and with a good natured scalability to large dimensions. For the measurement of optical flats the dominant uncertainty of topography is in the quadratic or spherical contribution of the surface in terms of a polynomial description. For calibration flats, as used for large interferometers, this often cannot be measured absolutely with sufficient accuracy. The potential of ESAD and other methods is analyzed with respect to this uncertainty component. Uncertainty considerations and measurement results for large flats are presented. For the form measuremetn of largely extended convex or concave surfaces, where classical interferometric set-ups are not possible due to the lack of a master surface or the extrme costs incurred for large optical components, the potential of LACS is presented.

Form Measurements used to lie somewhere between the macroscopic CMM and the microscopic surface measurement. But there are some specific details that should be treated differently. And one of these is the effect of the probe on the measurement. In the new standards, this appears already as a morphological filter. But there are still some aspects that may be considered also, for instance, the possibility of deformation the contact between the probe and workpiece. In this work, we developed a mathematical model (experimentally proven) to evaluate this effect during a form measurement in a reference laboratory, while performign the usual measurement procedures for roundness, cylindricity, straightness evaluation, among others. It could be considered either in the uncertainty budget or the measurement itself. This model may be extrapolated to other fields, although it was restricted to form measurements at the beginning, where the conditions differ, for example, on the number of points measured, filters and algorithms, etc. Its implementation in other more sophisticated algorithms developed, will not complicate the theoretical model, but may be helpful when comparing the results obtained from different reference laboratories.

Any measurement of an artefact on a CMM will include contributions from the systematic errors of the machine, the random errors in the machine and also the actual geometry of the artifact. If an artifact is rotated (or translated) within the CMM measuring volume, such that the chosen measurement points on the artifact continue to map onto the same machine coordinates, then the component of the measurement due to the artifact geometry will rotate, whilst the component due to the machine systematic errors will remain in the same position. In the self-calibration technique, a set of measurements of this type is made, and from these the systematic errors of the machine can be identified. The measurement accuracy of the artifact geometry is then only limited by the random component of the machine error, which is generally smaller than the systematic errors of the machine. This paper reviews self-calibration techniques and assesses their feasibility for improving the uncertainty of form measurement of large optical surfaces on a coordinate measuring machine.

The development of a canister-free videogrammetry system is presented. Applications in view, are coordinate measurements during thermal vacuum test and on-baord space flight metrology of mechanical structures, reflectors and antenna's. The paper presents the breadboard system architecture. Two breadboards have been developed. One is based on a space-qualified micro-imager camera. Lenses and flashers are all commercial components and have been made vacuum compatible. Results of accuracy (typically 50ppm) and resolution (typically 25 ppm) tests, in ambient and in vacuum are also presented.

The Wide Field Camera 3 (WFC3) instrument for the Hubble Space Telescope (HST) will replace the current Wide Field and Planetary Camera 2 (WFPC2). By providing higher throughput and sensitivity than WFPC2, and operating from the near-IR to the near-UV, WFC3 will once again bring the performance of HST above that from ground-based observatories. Crucial to the integration of the WFC3 optical bench is a pair of 2-axis cathetometers used to view targets which cannot be seen by other means when the bench is loaded into its enclosure. The setup and calibration of these cathetometers is described, along with results from a comparison of the cathetometer system with other metrology techniques.

A CMM has been developed which operates over a working volume of 50 × 50 × 50 mm, and achieves an uncertainty in 3D probing of ~100 nm. This miniature CMM is based around the concept of a metrology frame, mounted on a host CMM, with a miniature probe system held on the host CMM's ram. The probing system is rigidly connected to 3 orthogonal mirrors, the positions and rotations of which are measured using 3 dual axis interferometers (length, angle) and 3 dual axis angular sensors. Corrections for the mis-alignments of the interferometers, flatness errors of the mirrors and the performance of the miniature probe system are all determined in situ, by reference to the calibrated laser wavelength. This process performs a full error map of the CMM and requires only two artefacts: a precision sphere and a good quality optical cube. The error map is used online to determine the 3D position of the probe tip, based on measurements of the interferometers and angle sensing systems. The CMM is fully programmable and operates as a normal CMM, albeit with considerably improved accuracy. The design, manufacture and calibration of the CMM are described, followed by examples of measurements made with the machine and a determination of the uncertainty sources. This CMM is designed as the first step in bridging the gap between conventional (millimetre scale metrology) and nanometrology.

The NIST M48 coordinate measuring machine (CMM) was used to measure the average diameter of two precision, silicon spheres of nominal diameter near 93.6mm. A measurement technique was devised that took advantage of the specific strengths of the machine and the artifacts while restricting the influences derived from the machine's few weaknesses. This effort resulted in measurements with unprecedented accuracy and uncertainty levels for CMM style instruments. The results were confirmed through a blind comparison with another national measurement institute (NMI) that used special apparatus specifically designed for the measurement of these silicon spheres and employed very different measurement techniques. The standard uncertainty of the average diameter measurements was less than 20 nanometers. This paper will describe the measurement techniques along with the decision-making processes used to develop these specific methods. The measurement uncertainty of the measurements will also be rigorously examined.

Electronic distance measuring instruments (EDMs) are devices used by surveyors where calibrated tape measures are not adequate or appropriate. Modern EDMs are generally accurate and reliable, are commonly capable of measuring up to 6 km, and may be combined with an electronic theodolite in a total station unit. Precise traceable calibration of EDMs is possible using a linear displacement interferometer, for example, with the respective reflectors in back-to-back configuration. Calibration data may be analysed for scale error and cyclical error. The distances so calibrated are usually constrained by the length of laboratory (and/or straight rails) available, as well as by the maximum working distance of the interferometer, but may be extended further with caution by the introduction of mirrors to fold the EDM beam. This paper describes the apparatus used to calibrate an EDM up to 200 m in a 60 m laboratory, and investigates some of the problems and artefacts that can arise, for example, from unwanted intermediate reflections of the EDM beam.

For dimensional measurements and positioning, laser interferometers are often used to obtain highly accurate readings. To service their reliability, a system of laser interferometry standards is made available at the National Measurement Laboratory to offer instrument calibration as well as to ensure their traceability to the SI units. Owing much to their great sensitivity, the accuracy of laser interferometers undergoing calibration is strictly influenced by surrounding conditions, especially the correction parameter in the refractive index of air - a complex combination of ambient temperature, humidity, and atmosphere pressure. In order to minimize the deviation, an automated calibration system is constructed by employing a computer-controlled driver stage to perform linear displacement and data acquisition in the absence of operator intervention. A supplementary displacement measurement sub-system was set up to serve as an independent control on the stage. An average of 12 data points were taken at each predefined positions along the 20-m travel to support the comparison between the original system and the automated one. Several test runs from the calibration operation showed a standard deviation of 2.4×10^-8 for the automated system and 6.5×10^-8 for the previous. In addition to lower operational cost, experimental data also indicated improved calibration reliability benefited from the automation.

High-accuracy long-distance is performed using a broad and stable femtosecond frequency comb. Cyclic-error, which has been the main source of inaccuracy in conventional measurements, is reduced more than tenfold, directly achieving high accuracies of 50 μm at 1-GHz frequency and 14 μm at 10-GHz frequency in a 240-m distance measurement using the phase measurement of intermode beats of a femtosecond frequency comb. Traceability of distance meters is discussed.

An acoustic method for measurement of the effective temperature and refractive index of air along a laser beam path is described. The method can be used to improve the accuracy of interferometric length measurements outside the best laboratories, and even in severe environmental conditions. The method is based on the measurement of the speed of ultrasound over the same distance measured with a laser interferometer. The effectiveness of the method derives from the fact that the relative effect of a change in air temperature is about two thousand times greater on the speed of sound than on the refractive index of air. Experimental equations for the effective temperature or refractive index of air as a function of the speed of sound, pressure, humidity and CO₂ concentration are fitted using the measured speed of sound, the Cramer equation, the dispersion correction and Edlén equations. The standard uncertainties of the effective temperature and the refractive index of air equations are estimated to be 15 mK and 1.7×10^-8, respectively. The uncertainties of the effective temperature and refractive index of air measured with the test setup were 25 mK and 2.6×10^-8 (for L = ~5 m), respectively.

We have characterized the accuracy of atmospheric wavelength tracking based on a laser servolocked to a simple Fabry-Perot cavity. The motivations are (1) to explore a method for air refractive index measurement and (2) to determine the stability and accuracy of these cavities when employed as a length reference, with potential application to absolute distance interferometry, air-wavelength stabilized lasers, or similar applications. The Fabry-Perot cavity consists of mirrors optically contacted to an ultra-low-expansion spacer with the interior of the cavity open along its length to the surrounding air. Changes in laser frequency are monitored to determine changes in the refractive index of the gas in the cavity. We have studied limitations of this technique that arise from humidity effects, thermal distortion, and (for absolute refractive index measurements where the cavity must be evacuated) pressure-induced distortions. Comparing results from two cavities with very different lengths gives us a very sensitive probe of errors associated with end effects, and pressure-induced distortions can be measured by filling the cavity with helium, whose index of refraction is believed to be well known from ab initio calculations. The uncertainty of refractive index measurements can be greatly reduced when these sources of error are measured and corrected.

Refractive index fluctuations due to changing environmental conditions or due to air turbulence can significantly influence the measurement uncertainty of interferometric length measurements in air ambiance. A two wavelength interferometer is to some extend capable of measuring synchronously a path difference and the integral refractive index along this path difference. The best performance is achieved using two harmonically correlated optical fields like in a second harmonic interferometer. We developed a new type of a second harmonic two wavelength interferometer based on a double heterodyne interferometer with electronic frequency multiplication of one heterodyne frequency. The optical setup of the interferometer uses a measurement and a reference interferometer, both with spatially separated measurement and reference beam to avoid optical nonlinearities and reduce the influence of mechanical vibrations. The phase difference between measurement and reference interferometer is kept constant which reduces possible nonlinearities of the phase analysis. The system is capable of measuring the integral index of refraction without any effect modulation like e.g. a variation of the path difference which makes the design also applicable for absolute measuring interferometry. First experimental results will be presented

Laser interferometer systems are known for their high resolution, and especially for their high range/resolution ratio. In dimensional metrology laboratories, laser interferometers are popular workhorses for the calibration of displacements. The uncertainty is usually limited to about 10 nm due to polarization- and frequency mixing. For demanding applications however nanometer uncertainty is desired. We adapted a commercially available heterodyne laser interferometer by feeding the measurement signal into a fast lock-in amplifier and use the laser interferometer reference signal as a reference. By measuring both the in-phase and quadrature component an uncorrected phase can be directly measured. By recording both components while the phase changes between 0 and 2π a typical ellipse is recorded from which the first and second harmonics of periodic deviations can be derived. These can be corrected independent of their origin. Measurements show that this method can reduce severe non-linearities (40 nm top-bottom) to a standard deviation of about 0.02 nm. Also, optical set-ups can be analysed to predict the non-linearities when a non-compensated standard interferometer is used.

The interferometer set-up in use at IMGC for the calibration of microdisplacement actuators is driven by a computer-based loop control of the out-of-phase between the reference and the measuring signal of the interferometer. In such a way, the displacements are changed in steps of λ of the optical path difference (OPD) and the periodic non-linearity error of the heterodyne interferometer is minimised. Nevertheless, with a double-pass optical configuration a few sampling points are available for the calibration of small displacements in the sub-wavelength range. The non-linearity has a period of λ in terms of optical path change and is due to optical mixing of the two beam frequency components in the two arms of the interferometer. Some methods have been proposed to compensate the optical non-linearity. An approach based on fast phase-shifting to zero-fill the phase difference of the heterodyne beat signals at each sub-wavelength displacement to be measured, is discussed in this contribution. Use is made of a transverse electro-optic modulator for phase shifting the path of the measuring beam of the heterodyne interferometer. The preliminary results shows a significant reduction of the non-linearity in the full sub-wavelength range.

The MSTAR sensor (Modulation Sideband Technology for Absolute Ranging) is a new system for measuring absolute distance, capable of resolving the integer cycle ambiguity of standard intrferometers, and making it possible to measure distance with sub-nanometer accuracy. The sensor uses a single laser in conjugation with fast phase modulators and low-frequency detectors. We describe the design of the system - the principle of operation, the metrology source, beam-launching optics, and signal processing - and show results for target distance up to 1 meter. We then demonstrate how the system can be scaled to kilometer-scale distances.

A universal method for precision lenght measurements, called "excess fractions" was proposed at the end of the 18th century for the precise calibration of gauges. In this method, the interferometer compares an unknown gauge with the number of known wavelengths. The array of φ_i; which consists of the remainders of an integer number of wavelengths in the length of the gauges, was obtained and analyzed. For the measurement of gauge lengths that were small enough, the integer number of wavelengths can be found heuristically. With the development of lasers technique, the possibility of applying this idea to the measurement of large distances, such as the distance to the moon, appeared. With the imminent number of wavelengths in the distance, the heuistic solution is not possible. In this paper the solution based on Chinese Remainder Theorem is proposed. The Chinese Remainder Theorem is developed for use in the case, when wavelengths are not mutually prime numbers, and metrological aspects of this solution will be analyzed.

Electronic distance measuring instruments (EDM) are now universally used for measuring large engineering structures such as ships, dams and tunnels and still have a key role for establishing position in land surveying where the Global Positioning System (GPS) is not effective or requires too much time to achieve the required accuracy. EDM instruments are difficult to calibrate at most national measurement institutes as they are designed for large scale measurement and not for laboratory scales. The Natioanl Measurement Laboratory in Australia has a legal responsibility to provide traceabiltiy for EDM instruments and has developed two specialized facilities, a 650 m baseline and a 70 m optical bench, in order to establish EDM traceability to the Australian standard of length. The paper describes cyclic error and scale factor measurements on the baseline and on the optical bench. The conclusion is that the two techniques test different aspects of the EDM performance; short and long range performance. For the EDM instruments studied there are significant differences.

The PTB in cooperation with the Dr. Johannes Heidenhain GmbH built up a new length comparator with a measurement range of 610 mm for 1D length measurements on line scales, linear encoders and interferometers. The PTB nanometer comparator was retrofitted and now allows a stable operation of the interferometer. To investigate the actual measurement performance a few line scales and a linear encoder were measured and compared with results from other comparators. The results are discussed and recent developments at the nanometer comparator are described.

This paper describes the automatic calibration system for an angle encode which is installed at the AIST (National Institute of Advanced Industrial Science and Technology). The system uses the Equal-Division-Averaged (EDA) method that is one kind of the self-checking method. This system has great performance of the calibration with small uncertainty. In this paper we try to explain the factor of uncertainty of this system. The dominant uncertainty factor is the eccentricity of shaft between the system and an external rotary encoder. The influence from other factors is very small about 0.01" or less.

GPS is already a main method of positioning measurement in geodesy and is applied widely in many fields. For maintaining and ensuring the accuracy of positioning, an accurate and efficient system for calibration the GPS receivers must be established. A highly accurate GPS calibration network tied to the ITRF coordinates of IGS stations, can be effectively used to evaluate the performance of GPS receivers. This study addresses the feasibility of establishing a system for calibrating GPS receivers and the system's traceabilty in metrology. Uncertainties of the GPS calibration network established and maintained by NML (National Measurement Laboratory, Taiwan) are evaluated based on the method suggested by the ISO (International Organization for Standardization). The uncertainties of NML network coordinates are obtained and used as a basis for calibration. The results of the slope distances between pillars measured by the GPS processing units and the precise EDM units are discussed. Analytical results indicate that the 3D expanded uncertainty of the main station TNML of the network in the ITRF system is around 33.2 mm at the 95% confidence level. The 3D expanded uncertainties of the calibration points of ultra-short distance network and short distance network are evaluated to be about 22.2 mm and 3.4 mm in relation to the main station TNML, respectively, at the 95% confidence level. The precision of the NML network coordinates suffices to calibrate the geodetic and navigational GPS receivers of regional users and is available through the Internet.

Measurement uncertainty is an important topic for traceable measurements. Nevertheless not many literatures on the uncertainty of flatness measurements have been reported. In this paper, we report on this issue according to the Guide to the Expression fo Uncertainty in Measurements (GUM). First stability of the reference optical flat used in Fizeau interferometer is discussed analytically, numerically, and experimentally. Then other uncertainty sources in actual measurements are investigated. As a result the uncertainty of flatness measurement of a large aperture flatness interferometer made by National Metrology Institute of Japan is 1/77 wavelength.

To calibrate a squareness standard and a height micrometer, the Korea Research Institute of Standards and Science (KRISS) has built a new linear measuring machine moving vertically. The main requirement on design of the machine is to achieve the flexibility to calibrate several kinds of standards such as square master, cylindrical square, height micrometer and linear height gauge which are positioned vertically on the surface plate. The system consists of a precision granite column with an air bearing state, a laser interferometer and two electronic probes. In order to calibrate the squareness standards, the granite beam is used as a reference of squareness and a guide of vertical movement. The instrument incorporates a frequency stabilized He-Ne laser. The vertical movement is measured by a laser interferometer whose operation is based on the heterodyne measurement technique. Positioning for calibrating the height micrometer is undertaken by using a vertical state and a horizontal stage, and its measurement range of 0-700 mm. The paper gives a description of the system and a preliminary measurement results.

To calibrate a squareness standard and a height micrometer, the Korea Research Institute of Standards and Science (KRISS) has built a new linear measuring machine moving vertically. The main requirement on design of the machine is to achieve the flexibility to calibrate several kinds of standards such as square master, cylindrical square, height micrometer and linear height gauge which are positioned vertically on the surface plate. The system consists of a precision granite column with an air bearing state, a laser interferometer and two electronic probes. In order to calibrate the squareness standards, the granite beam is used as a reference of squareness and a guide of vertical movement. The instrument incorporates a frequency stabilized He-Ne laser. The vertical movement is measured by a laser interferometer whose operation is based on the heterodyne measurement technique. Positioning for calibrating the height micrometer is undertaken by using a vertical stage and a horizontal stage, and its measurement is performed by combining the laser interferometer reading and the electronic probe readings. The paper gives a description of the system and a preliminary measurement results.

A simple rubidium stabilized diode laser has been developed for a gauge block interferometer. The laser light source is a commercially available external-cavity tunable diode laser (New Focus Inc.). Laser frequency stabilization is realized by the third-harmonic technique, where a fast frequency modulation (10 kHz) is applied on the current. The absolute laser frequency was calibrated by an absolute optical frequency measurement system using a femtosecond mode-locked laser. The relative uncertainty of the laser frequency reached 4.3×10^-10 for an averaging time of 0.01 s. The phase error in the interferometeric measurement due to the optical frequency modulation is theoretically indicated to be small enough to measure long gauge blocks of up to 1000 mm. Long gauge block measurement of up to 1000 mm was successfully demonstrated using the developed rubidium stabilized diode laser and the I₂-stabilized offset locked He-Ne laser (633 nm).

The need for fast and accurate inspection of small sample features is eminent considering the developments in micro and nano technology. The scanning probe microscope (SPM) offers extreme resolution and even accuracy when properly calibrated but the principle of operation result in inherently slow acquisition of the measurement data. Therefore scanning probe microscopes are rarely deployed in industrial in-line inspection and quality control where the time aspect usually is critical. We propose an alternative mode of operation that can considerably speed up SPM measurements. In this mode only the areas of interest are probe with maximum accuracy while the rest of the imaging is ignored. The measuring mode is best suited when a-priori information of the surface is available, like in an industrial production line.

We have developed a digital controller to stabilize one of NMi's iodine stabilized helium-neon lasers using the third harmonic technique. The controller is proven to be a suitable replacement of the analogue electronics, as demonstrated by internal comparisons and a calibration against the frequency comb of the Bureau International des Poids et Mesures.

A new optical encoder which measures absolute, true-Cartesian displacement with ultra-high sensitivity and linearity has been developed at NASA's Goddard Space Flight Center. The device is the two-dimensional analog of recently developed linear and rotary encoders based on optical pattern recognition. In this encoder, a glass scale carrying absolute Cartesian position information travels with the payload in an X-Y motion system. Because the scale comprises the entire measurement coordinate system in a monolithic form, motion control axes can be skew to one another to an arbitrary degree and can exhibit substantial lateral drift with no effect on the correctness of X-Y readout, thus eliminating challenges of orthogonal mounting for motion axes and challenges of mounting independent encoders parallel to the directions of travel for each constituent X and Y axis. Prototype devices with ranges of 30 x 30 mm and 150 x 150 mm with 5 nm and 50 nm resolutions, respectively, have been built in the laboratory. Performance data from the Cartesian encoder in the Point Target Assembly for the optical calibration stimulus for Hubble Space Telescope's Wide Field Camera 3 are presented.

The development of a compact, ultra-high resolution, electronic autocollimator with excellent readout stability, linearity, and coordinate orthogonality is presented. This optical metrology tool relies on new advances in Cartesian optical encoders based on pattern recognition technology. Readout instabilities characteristic of conventional electronic autocollimators whose lateral effect photodetectors and operational amplifiers exhibit temporal and thermal drifts, are absent in this new technology. An autocollimator with a form factor similar to conventional alignment telescopes has been demonstrated with an angular resolution of 0.02 arcseconds peak-to-peak and less than 0.01 arcseconds rms. Various optical metrology applications for the laboratory and for space flight, including cryostatic ones, are described.