We have established a portable I₂-stabilized Nd:YAG laser for the purpose of making wavelength standards at 532 nm and 1064 nm. All the optical parts of the laser systems were arranged on a 45 cm X 45 cm breadboard. The system was transported from NRLM to JILA for frequency comparison. The results of the comparison show that the Allan Variance of the portable laser reached < 3 X 10^-13 when the integration time (tau) is larger than 100 s. The frequency differences between the NRLM and JILA lasers during 3-day measurements were consistent within +/- 35 Hz, but the matrix-averaged standard deviation of about 310 Hz, and offset are regarded as not yet fully satisfactory. The stability of the portable laser was further improved to about 3 X 10^-14 by using a longer iodine cell and several frequency stabilization techniques.

We have developed a laser interferometer to calibrate gauge block utilizing 2 lasers, 633 nm He-Ne and 1,064 nm Nd:YAG. At only 633 nm of wavelength, several kinds of practical He- Ne lasers have been developed and manufactured, while there is not practical laser light source for interferometer other than at 633 nm. To realize practical light source in addition to 633 nm, we stabilized the wavelength of 1,064 nm Nd:YAG laser, utilizing linear absorption of iodine at 532 nm. The iodine cell was inserted between two non linear crystals for second harmonic generation and first derivative signal was generated by dispersion effect near the absorption line of iodine, without electric circuit for modulation or for phase sensitive detection. Gauge blocks were measured with the two wavelengths of 633 and 1,064 nm. The fringe pattern was detected by CCD camera and the length was estimated by excess fraction method. It is easy to determine the integer part of the fringe order, since the wavelength difference between these two is large and the wavelength ratio is not expressed by a simple combination on integers. The results agreed with those obtained by conventional method with ¹⁹⁸Hg isotope lamp.

A simple stabilizer for locking 543 nm, 612 nm and 633 nm helium-neon lasers to iodine is described. When applied to a 543 nm laser, a long term frequency stability of 1.4 X 10^-12 was observed. One stabilizer can lock three lasers simultaneously to iodine references with relative uncertainties better than 2 X 10^-10 for sample times greater than 1 s, providing primary frequency references that can be used for gauge block measurements.

An interferometer is realized, based on the Twyman-Green Interferometer principle for the calibration of long gauge blocks and length bars in the 100-1000 mm range with an uncertainty of 0.02 micrometers + 0,1 micrometers /m. Also the expansion coefficient of gauge blocks and even of rod-shaped materials with non-optical flat faces can be calibrated in the 18-22 degrees C range with an uncertainty below 1 X 10^-7/K. The set-up basically follows the most commonly used interferometer arrangements for long gauge blocks as they are described by Darnedde, Ikonen and Lewis where the most similarities with the latter occur. The set- up has some peculiarities which make the measurement straightforward, accurate and reliable.

The design and construction of a laser interferometer using the method of exact fractions for high-accuracy calibration of gauge blocks up to about one meter in length, are described. The interferometer is based on the classical Michelson arrangement. A two-mode stabilized He-Ne laser emitting light at a wavelength of 633 nm is the primary wavelength reference for the interferometric length measurement, since its frequency is calibrated by heterodyne measurement with an iodine-stabilized He-Ne laser at 633 nm which is used to maintain the national meter standard. A second two-mode stabilized He-Ne laser, at a wavelength of 543 nm, is used in order define the absolute length. The estimated standard uncertainty for interferometric length measurements is about 50 nm for a 1 meter gauge block. Results from trial measurements made on various gauge blocks, including a bilateral comparison, are reported.

When optical techniques are applied to high precision length measurement in the free atmosphere, it is essential to correct the wavelength of the radiation for the refractive index of the air. The two most widely employed techniques for determining the refractive index of the air ar the calculation of a value using the Elden equation from the measurements of atmospheric parameters and direct measurement using a refractometer.

A new design for a variable length vacuum path air refractometer is developed. The device has some advantages as compared with traditional gas refractometers. It measures directly the refractive index of laboratory air. Hence it is not necessary to move air to or form any separate cavity. The optical construction of the device is simple. The device utilizes two Michelson type interferometers. One interferometer has fixed mechanical lengths in both arms. The optical length of one arm can be altered by changing the proportion between air and vacuum lengths of the beam path. This is realized by a variable length vacuum cylinder. The other interferometer measures the displacement of the vacuum window of the cylinder. The interference signals caused by the change of optical path change and by displacement of the vacuum window are digitalized and analyzed to give the refractive index of ambient air. The Abbe error is eliminated by using a glass corner cube with hole through the center that allows symmetric alignment of the beams of the two interferometers. Difference of refractive index values measured by the refractometer and calculated with updated Edlen's formula form experimental data was 1.2 X 10^-8 when standard deviation of the difference was 4 X 10^-8.

For accurate interferometric length measurements, the accurately determined value of the refractive index of air is required. In many cases the refractive index is evaluated from measured air parameters. A widely applied set of formulae for this evaluation has been provided by Edlen who fitted existing experimental data. Modified Edlen's formulae are presented which were fitted to values obtained by an air refractometer situated in an environmental chamber. This chamber allows stabilization of the air parameters. A new series of measurements has been performed with three laser wavelengths at 543 nm, 633 nm, and 780 nm and good agreement with the results previously reported has been obtained.

It is difficult to measure efficiently long gauge blocks by the interferometric method because long time is necessary for temperature run-in of long gauge blocks. The interferometer which can measure long gauge blocks up to 1000 mm has been developed by Mitutoyo Corporation. This interferometer is constructed with the optical system which can measure four gauge blocks one after another setting them once. The optical system of this interferometer can be easily adjusted and comparison measurements of gauge blocks by interferometry is also possible. As its light source, isotope lam p and laser are used. When the laser used, it is possible to measure directly 1000 mm. The uncertainty in measurement with this interferometer is evaluated as U equals 0.225 micrometers (k equals 2) for the case of 1000 mm long gauge block.

An interferometer has been developed by Mitutoyo Corporation which automatically measures with the optical sensor the fraction of interference fringe. The optical fiber sensor is fixed around the center position of gauge block and central both sides of platen, and the fraction is measured the interference fringe by scanning of optical wedge, which is put between half-reflection-mirror and gauge block. The light source uses both 633 nm and 543 nm He-Ne lasers stabilized within 1 X 10^-9. The gauge block length can be determined by means of coincidence method. A set of 12 gauge blocks placed on the table and can be measured one by one in turn. For the refractive index of surrounding air, temperature, atmospheric pressure and humidity are measured by sensor in the interferometer. A personal bias by interference fringe reading is eliminated and measurement is carried out with easy operation and high precision. Repeatability of reading of interference fringe fraction.

A new fringe-pattern analyzing interferometer, featuring ultimate resolution of a few parts in 10⁹, stability of readings of about 0.1 nm and non-excluded systematic uncertainties due to optic effects of less than 1 nm, has been study some systematic effects in gauge block length measurements. Measurements on steep and quartz plates are analyzed. Limitations of the present definition of the length of the block are outlined. Stability and reproducibility of the wringing procedure for steel and quartz plates are reported. A new double-ended method in length measurements of gauge blocks has been realized. It includes determination of the corrections for non-ideal optics of the interferometer, curvature of the pate and deformations of the quartz plate due to wringing of the block to its surface. The result of the length measurement is not affected, in the first approximation, by deformation of the pate and the quality of wringing.

Interferometric image-analyzing comparator for gauge blocks of 1-100 mm length is reported. Sophisticated image processing software, that supports 0.1 nm resolution in central length and 1 nm in 3D surface measurements, has been developed. Resolution of the comparator reaches the value of 1 X 10^-9 for 100 mm blocks. Inclination error is reduced to the value of 8 X 10^-9. The relative uncertainty for inclination correction can be statistically diminished to about 2 X 10^-9. The instrument and a new method have been used to study the deformations of steel plates, caused by wringing forces. In these experiments, 3D surface profiles of plates and blocks are being recorded while gradually diminishing the wringing forces by the oil, that slowly penetrates into the wringing contact. Shorter blocks are shown to be significantly deformed by the steel plate, while the deformations of the plate are quite negligible. This allows to realize reproducible wringing, and to perform precise correction on interferometer optics and curvature of the base plate. Blocks longer than 25 mm are shown not to be deformed, practically, by the plate.

An instrument for the measurement of ball diameters in the 0.5-20 mm range in a gauge block interferometer is realized. The measurement principle is that the ball is positioned between an optical flat and a calibrated gauge block. The total length is measured in a gauge block relative to the optical flat and proper measurement of the deformations due to the measuring force. The parallelism is adjusted while viewing the interference patterns on the gauge block and the optical flat. The measuring force can be varied in the 0.03- 2.35 N range. The applied force is calibrated. Experiments show that commonly used formulas to calculate the ball indentation as a function of the applied force are approximately correct; this instrument however provides a direct means to measure this dependence and to apply a proper extrapolation to zero measuring force. The design is rather compact so it will fit in commonly used gauge block interferometers. The uncertainty which can be achieved is less than 0.1 micrometer.

Double-ended Fizzeau type interferometers can be applied advantageously for direct dimensional measurements of regular bodies with parallel, flat measuring surfaces. At PTB, such an interferometer with specific equipment for phase stepping interferometry has been developed. The basic interferometer or etalon consists of two parallel, semi- reflecting reference plates. The symmetrical arrangement of two optical systems for illumination and observation of the interference pattern allows alternating measurements from both sides. The interference systems are observed in reflection and focused onto CCD-cameras. The optical pates are attached to a rigid frame, so that both an adjustment of the interference and a parallel displacement for the phase stepping technique is obtained. Servo-control units allow a precise value of 1/4 interference order for the displacement to be adjusted, which is necessary for a special Fizzeau algorithm. The dimensions of the interferometer are designed for volume measurements of cubes of about 80 mm, which are used as density standards. The distance topography between two opposed surfaces of the cubes are derived from measurements of the empty etalon and measurements with the cube inserted. The interferometer can also measure gauge blocks which are not wrung to a base plate by direct optical probing of the free surfaces and explore the influence of roughness and optical phase shift.

Several standard and measures laboratories are using typical Koester interferometers (KI) and routine measurement procedures for evaluating the practical length of block gauges. In the paper the modification of KI by introducing laser light source and phase shifting element for automatization of interferogram analysis by temporal phase shifting method are presented. From phase data obtained the flatness, parallelism and length deviation of gauge block are automatically determined. The methodology and software procedures for this process are introduced and the examples of measurement are shown.

This paper describes improvements to a Hilger gauge block interferometer, including a fiber optic feed for a traceable laser radiation, automatic wavelength selection, and a CCD camera for fringe observation. The gauge measuring process is now semi-automated, computer controlled, more accurate and significantly faster and easier to operate than the original design.

Error sources in gage block mechanical comparisons can range from classical textbook examples to a completely counter- intuitive example of diamond probe tip wear at low applied force. Fortunately, there are methods available to metrologists that can successfully be applied to minimize these and other effects. Techniques such as statistical process control, use of check standards, thermal drift eliminating measurement algorithms, improved sensor calibration, and well-tested deformation modeling are used at the National Institute of Standards and Technology to minimize errors. These same methods can be applied by anyone making mechanical comparison gage block measurements.

A system has been developed at the National Physics Laboratory that measures a correction for the phase change on reflection due to surface roughness when measuring the length of a gauge block by optical interferometry. The system uses an integrating sphere and photodetectors to measure the intensity of the light that is both diffusely and specularly reflected at a surface. From these intensities the system calculates a surface roughness parameter that is proportional to the phase change on reflection due to surface roughness. The operating principle of the system along with the uncertainties and bandwidth limitations of an integrating sphere are discussed. An interferometric system has also been developed to calibrate the integrating sphere method, but it was found that effects due to wringing caused such high uncertainties that it was necessary to use the well-established phase stack method instead. The new method is quick and easy to use and measures a roughness correction for every gauge in a set.

Determination of the roughness correction with a scattering light method is preformed at PTB since more than forty years for measurements of gauge blocks by interferometry. Setting up of a new integrating sphere initiated investigations on calibration methods. The coupled interferometer method and the Newton's ring method are described and compared. For the coupled interferometer method, the gauge blocks are wrung to an optical flat and the phase of reflection for the gauge- flat interface is determined in a Twyman-Green interferometer. Satisfactory agreement is obtained for the result with both methods.

One of the most elusive measurement elements in gage block interferometry is the correction for the phase change on reflection. Techniques used to quantify this correction have improved over the year, but the measurement uncertainty has remained relatively constant because some error sources have proven historically difficult to reduce. The precision engineering division at the National Institute of Standards and Technology has recently developed a measurement technique that can quantify the phase change on reflection correction directly for individual gage blocks and eliminates some of the fundamental problems with historical measurement methods. Since only the top surface of the gage block is used in the measurement, wringing film inconsistencies are eliminated with this technique thereby drastically reducing the measurement uncertainty for the correction. However, block geometry and thermal issues still exist. This paper will describe the methods used to minimize the measurement uncertainty of the phase change on reflection evaluation using a spherical contact technique. The work focuses on gage block surface topography and drift eliminating algorithms for the data collection. The extrapolation of the data to an undeformed condition and the failure of these curves to follow theoretical estimates are also discussed. The wavelength dependence of the correction was directly measured for different gage block materials and manufacturers and the data will be presented.

Phase correction in measured lengths of gauge blocks was researched. It has been known that the phase correction depends on the surface roughens of the gauge and the shift of the effective plane of reflection caused by penetration, due to the complex refractive index.

The gauge block can realize the length of an object with the interferometric method.When light reflects on the measuring surface, the lag of phase occurs due to optical characteristics and surface roughness of the test piece. It is necessary to ad this correction value to the optical length obtained by the measurement. The investigation is carried out whether the phase shift correction used for steel gauge block to gauge block made of new material 'ceramics'.

The current definition of the length of a gage block is a very clever attempt to evade the systematic errors associated with the wringing layer thickness and optical phase corrections. In practice, most laboratories wring to quartz or fused silica reference plates, and in addition there are very large systematic operator and surface effects. We present quantitative data on these effects and how that the current definition of gage block length is a primary source of measurement uncertainty.

The length of a gauge block is defined as the distance of a selected point of the measuring face to the plane surface of a platen which consists of the same material and has the same surface texture as the gauge block. With these idealized conditions of the definition, the probing errors due to opposed surfaces and due to the roughness are eliminated. It is assumed implicitly that the surface of the gauge is sufficiently flat so that symmetry in the wringing area is maintained. The assembly of gauge block and platen can be directly measured with an optical wave in an interferometer, and the measurement closely follows to the definition of the length unit>In practice, however, there are always deviations from these idealized conditions and corrections have to be applied. In particular, the wringing influence is important and effects are demonstrated by examples. Results obtained by interferometry are checked by comparison. Under optimum conditions, the comparison method allows nanometer accuracy to be achieved in the determination of length differences if gauges of the same material are compared so that probing errors are eliminated. Both methods have complementary properties and can be applied to systematic investigations. The aim is to obtain a system of gauge block standards consistent within the quoted uncertainties, independent of the method used.

The concept of the traceability in length measurement standard is described and the present traceability system in Japan is discussed first. The calibration data of commercial stabilized He-Ne laser wavelength are shown and the suitable usage of the laser interferometer is given. The round robin gauge block measurement by comparator that is carried out among the calibration laboratories positioned several countries inside worldwide corporation are described with focusing on the consistency and the compatibility of the calibration accuracy. The contribution to traceability and consistency in length standard measurements is explained through two measurements mentioned above.

International measurement comparisons are important to demonstrate the technical competence of calibration laboratories, to experimentally confirm the measurement uncertainties and to demonstrate the equivalence of national measurement standards and traceability schemes in accreditation systems. The network of international comparison schemes in general and the specific issues of gauge block comparisons in particular are presented. An overview on different comparisons which were carried out in the past few years on a regional and a worldwide scale is given for both, gauge block measurements by interferometry and by comparison.

The definition of gauge black length,and the lowest- uncertainty gauge block calibrations, derive their link to the definition of the meter through the technique of optical interferometry using calibrated optical wavelengths. Following interferometric calibration of gauge blocks, the technique of mechanical comparison of gauge blocks is largely used for the dissemination of the meter. A measurement scenario for the case of low-uncertainty gauge block calibration in which the working standard and client gauge blocks are made of dissimilar materials is described. The correction for stylus deformation is determined experimentally. A detailed tutorial on evaluating the uncertainties for this gauge block calibration in accordance with the ISO Guide to the expression of uncertainty in measurement is reported, including discussion of degrees of freedom and correlations.

The uncertainties in the measurement of gauge blocks by interferometry based on the official publication of the ISO 'Guide to the Expression of Uncertainty in Measurement', are evaluated. The effects caused by a variety of factors such as laser frequency, refractive index of air, temperature and wringing film thickness are analyzed. The evaluation results how that for steel gauge blocks of grade 00, the expanded uncertainty is 0.04 micrometers + 14 X 10^-7L where L is the length of the gauge block. The reported uncertainty is based on a standard uncertainty multiplied by a coverage factor of k equals 1.96, which provides a level of confidence of 95 percent.

This paper deals with some practical aspects of the calibration of long gauge blocks. Particular attention is given to the thermal aspects of the calibration, including the in situ calibration of the thermometers according to the ITS-90, the procedure which frees from the need of external traceability to electrical SI units, the optimal disposition of the thermometers on the gauge block, and the clamping technique which prevents distortion of the gauge and minimizes the probability of mechanical shocks to the thermometers. Experimental data are reported which shows a sub-millikelvin uniformity of the gauge block. The stress- free gauge block supports are also descried, optimized to compensate for the bending due to the weight of the platen wrung to the block end, to allow accurate face parallelism measurements. The procedures for measuring the deviation from planarity and the variation of length are described, which implement the ISO 3650 definitions with no approximate image processing of the interferograms.

An instrument for the measurement of the thermal expansion coefficient near room temperature of gauge blocks and other samples of similar shape and size has been developed. The length dilation is measured by a differentia plane mirror interferometer. A special interference phase detection technique compensates for non-linearity errors caused by polarization mixing. In combination with an electronic phase meter this allows to achieve nanometer accuracy. Since the measurements are done in vacuum, no compensation for the refractive index of air has to be made. For samples with good thermal conductivity the slow heat exchange by thermal radiation allows for a small temperature gradient of the sample and a good stability in the thermal equilibrium. From the thermal expansion curve, measured in a temperature range typically between 10 degrees C and 30 degrees C, the linear and quadratic expansion coefficients are evaluated at 20 degrees C, the reference temperature for length. It is shown, that for the investigated gauge block materials the room temperature expansion can be very accurately described with two coefficients within a few parts in 10⁹ per degree. A detailed analysis of the measurement uncertainty demonstrates the capability of the measurement instrument, which is confirmed by the results of an international comparison.

Linear thermal expansion coefficients (LTECs) of two kinds of partially stabilized zirconica (PSZ) gauge blocks were measured in the range from -10 to 60 degrees C with an optical heterodyne interferometric dilatometer. The dilatometer provides an order of 1 X 10^-9 K^-1 uncertainty and reproducibility in LTEC measurement. LTEC of (9.230 +/- 0.012) X 10^-6 K^-1 were obtained for four 2 percent Al₂O₃- PSZ gauge blocks, and (9.383 +/- 0.001) X K^-1 for one 99.9 percent PSZ gauge block. These differences are discussed, together with the compositions and production lots.

Correct shaft alignment is vital for most rotating machines. Several shaft alignment instruments, ranging form dial indicator based to laser based, are commercially available. At VTT Manufacturing Technology a device for calibration of shaft alignment instruments was developed during 1997. A feature of the developed device is the similarity to the typical use of shaft alignment instruments i.e. the rotation of two shafts during the calibration. The benefit of the rotation is that all errors of the shaft alignment instrument, for example the deformations of the suspension bars, are included. However, the rotation increases significantly the uncertainty of calibration because of errors in the suspension of the shafts in the developed device for calibration of shaft alignment instruments. Without rotation the uncertainty of calibration is 0.001 mm for the parallel offset scale and 0,003 mm/m for the angular scale. With rotation the uncertainty of calibration is 0.002 mm for the scale and 0.004 mm/m for the angular scale.

The domestic round-robin testing for interferometric length measurements of gauge blocks was initiated in 1960 in Japan, to evaluate and also to improve the proficiency of calibration laboratories. It had been arranged by the National Research Laboratory of Metrology (NRLM) and Japan Precision Measuring Instrument Association 16 times prior to 1992. A 100 mm gauge block was used as the test object on each occasion and measurement result of the NRLM was used as the reference value. When the difference between the result of each laboratory and the NRLM was larger than 30 nm, the laboratory repeated the measurement and the reason for the discrepancy was investigated. About 10 laboratories, including those of local governments, private companies and semigovernment organizations, participated regularly and many of them maintained their proficiency in the measurement of gauge blocks.

A comparison of phase correction measurements by the stack method and by roughness measurements has been performed by the National Metrology Institutes of Sweden, Denmark, Norway and Finland. For a given technique the agreement between the participants is good, but the roughness measurements give consistently lower results for the phase correction than the stack method. This may be due to a systematic error in the stack results, originating from form errors.