An evaluation system for automatic measurements of short gauge blocks by interferometry is described. The system is based on a commercially available Twyman-Green interferometer which has been modified so that phase stepping interferometry can be applied. Three stabilized lasers are used to determine the gauge block length by the method of exact fractions. The data of the evaluated interference phase have to be processed to enable automatic identification of the gauge block's measuring face in the interference pattern and to determine characteristic quantities of the gauge block under test. The uncertainty contribution of the interference evaluation for the central length is approximately 1,5 nm which is sufficiently small compared with other uncertainty contributions of the measurement process.

This paper deals with some basic problems of interferometric length measurements. Traditionally, all the deformations of a material artifacts, associated with the wringing procedure, were included into the length of a block, as there were no reliable ways to measure these deformations and to apply the corresponding corrections. Here, we present the first measurements of the surface texture deformations, arising in the wringing contact between the two gauging surfaces of similar materials and surface finish. The deformation value is obtained as a result of the measurements of the peak-to-peak length value of a free, unperturbed block and of the mechanical length of the block, which is obtained with the reproducible wiring technique and the slave-block method. Basically new concept for the optical length metrology - the physical length of a free artifact has been introduced in to the measuring practice. The way for crucial improvement of the realization of the SI length unit in the corresponding range has been outlined.

Mechanical comparison calibration of gauge blocks using reference standards that are a different material from the client gauge block can be problematic. This two-part study investigates some of the dominant influences identified in the mechanical comparison calibration of ceramic gauge blocks using steel reference standards. The goal is to develop techniques for lowest uncertainty mechanical comparison calibration in the application of two dissimilar gauge block materials. Of primary interest are: correction for differences in mechanical stylus deformation, and length equivalent thermal corrections in the different materials. In our model, mechanical stylus deformation is evaluated using gauge blocks of known length, calibrated by optical interferometry. The optical phase correction applied in this initial interferometric determination of gauge block length is an important first step. In the first part of this study, optical phase correction for ceramic gauge blocks has been determined using similar techniques by three labs, all of them applying the method of stack experiments using the same gauge blocks, and similar platens. One of the platens is of the same material and made by the same manufacturer as the ceramic gauge blocks. Temperature effects dominate the mechanical comparison calibration of dissimilar materials. In the second part of this study, the importance of the approach to length corrections as a result of temperature variation is demonstrated.

New parallax-free methods of interferometric length measurements, developed recently at INMETRO, give the possibility to exclude, practically completely, the uncertainties related to the wringing procedure of a gauge block to a reference plate. It is shown experimentally that the uncertainty of the length measurement by optical interferometry can be reduced to the value of about 1 angstrom. The temperature measurements of a material artifact are demonstrated with the uncertainty of less than 0.1 milli-Kelvin. There are no basic restrictions for the improvement of the practical realization of the SI length unit, based on the measurements of material length standards by optical interferometry to the level of approximately 0.001 ppm. Two new, independent length specifying parameter fora gauge block are introduced, i.e. the mechanical and optical lengths of a block, which correspond to the length measurements with the uncertainty level indicated above. Parallax-free measurements of the optical length of the block has been performed for a 'free' block in unperturbed state. Basically new concept for length metrology, i.e. the concept of a free, unperturbed artifact, has been introduced into the length measurements.

In the quest for a better measurement quality, a reduction of the measurement uncertainty must be foreseen. Gauge block calibration by interferometry is an unavoidable link in the traceability chain of most dimensional measurements and it has an impact in the uncertainty budget of all measurements that derive from it. Length-dependent effects of this calibration contribute largely to the combined uncertainty and therefore, its reduction must be expected to improve the combined uncertainty of gauge block calibration by interferometry. The thermal expansivity expressed as a linear thermal expansion coefficient (LTEC) is one of the main sources of uncertainty in the uncertainty budget. The gauge block manufacturer commonly quotes this number with an uncertainty of about one part in 10^-6 degrees C^-1. A reduction of the LTEC uncertainty to one third of the quoted value would provide a decease of at least 25 percent in the combined uncertainty of gauge blocks longer than 50 mm calibrated by interferometry.

Inductance probes are widely used in gauge block comparators. They have to be calibrated by interferometer to fulfill the traceability. To avoid the nonlinearity of interferometer within one interference fringe, a combination of digital and analog servo driving device with integer number of fringe orders of Fizeau interferometer is used to provide the movement for probe calibration. The standard deviation of positioning repeatability of the driving device is about 1 nm. Calibration is performed with double probe arrangement to simulate the actual condition of probes used in gauge block comparators. Typical sensitivity of probes is about 0.3412 V/micrometers with standard deviation of 0.087 percent while nonlinearity is about 9 nm over measuring range of +/- 10 micrometers . A 0.33 percent difference of sensitivity is observed if single probe is arranged in the calibration.

This presentation describes an investigation into the interferometric measurement of the length spacing of the faces of a step gauge using the fringe fraction method. The system used was originally developed to measure the flatness and parallelism of the faces.

Japanese Ultimate Flatness Interferometer (FUJI) is a Fizeau type flatness interferometer that is capable of measuring flatness over 310 mm diameter. The concept and technologies applied to FUJI are explained. To demonstrate the performance of FUJI, an international comparison was held with Australia, and the difference of two independent measurements were smaller than four nanometers.

To calibrate dial indicators, gage blocks or dial indicator calibrators are usually used. For better accuracy and resolution, interferometers are used to calibrate dial indicator calibrators. Systematic errors of laser interferometers can be classified into three categories of intrinsic errors, environment errors and installation errors. Intrinsic errors include laser wavelength error, electronic error and optics nonlinearity. In order to achieve nanometer accuracy, minimizing intrinsic error is crucial. In this paper, we will address the problems of minimizing the optics nonlinearity error and describe the discrete-time signal processing method to minimize the electronic error, nonlinearity error and drift by simply using quadrature phase interferometer for nanometer accuracy and linearity.

This paper describes the design of a facility to calibrate electronic distance measuring instruments (EDMs), as used in surveying (electronic theodolites) and large scale industrial measurement, over the range of 0 to 60 m. The combined uncertainty of the system at 60 m, estimated at the 95 percent confidence level, is expected to be 0.4 mm. The EDM is compared with a heterodyne laser measurement system in a back-to-back configuration. The trolley carrying the optics travels on aluminium rails. In order to improve the straightness of the path followed by the reflectors during measurement, the trolley optics are mounted on a two-axis motorized translation stage which uses a quadrant diode to track an additional guiding laser beam parallel to the required path. Once programmed, the trolley tracking electronics are autonomous and no connection is necessary to external power or control sources for that. However, radio frequency remote control of the motor propelling trolley motor would assist the measurements.

Laser interferometers provide an easy path for traceable measurements as most commercial instruments are inherently accurate to better than 10-7. The main problem with using these interferometers over an extended path can be the alignment requirements which can only be met with a precision rail system. Tape benches are typically 50 m (or more) long and are easily affected by building movement, requiring frequent re-alignment. An interferometer with an expanded measurement beam has significantly reduced alignment requirements and one with a beam diameter of 45 mm was used by the author to measure survey pillars. This had an alignment tolerance of +/- 10 mm allowing the use of a simple stretched wire rail system. This paper describes a simple adaptation that can be made to a commercial interferometer to expand the measurement beam without interfering with its normal operation.

Line scales such as engineering rules and steel tapes are still used for many routine measurements despite the existence of more sophisticated devices. MSLNZ's Automatic Line Scale Measuring Instrument is based on a heterodyne laser interferometer used in a configuration that compensates for Abbe errors. The position of each scale graduation is detected by monitoring the change in the diffuse reflection of a focused line of diode laser light, as a motorized trolley travels along above the scale. The signal from the diffuse reflection is used to trigger the laser measurement system at the edge of each graduation. The instrument is capable of measuring the position of every graduation on a rigid scale up to four meters in length with an uncertainty of Q(10e-6 m, 7.5e-6L) (95% confidence level). Measurement time (after set up) for a one-meter scale is less than 2 minutes.

The invention ofthe gas laser in the 1960's provided a robust and relatively inexpensive radiation source, which frirnished an intense collimated coherent beam ideally suited for use in optical mterferometer systems. The inherent accuracy and resolution ofthese laser based instmments making them the ultimate tool both for the precision measurement of geometric parameters and motion control. At the Conference Generate des Poids et Mesures in 1983 the International standard oflength the Metre was redefmed as the distance travelled by light in free space during 1/c of a second, where c is the defmed speed of light [ 299,792,458 Kms ]. Optical mterferometers are employed worldwide for precision positioning and calibration, achieving direct traceability to this length standard by using lasers as precision reference standards of frequency. The source most commonly utilised in commercial interferometers is the red Helium-Neon laser with a wavelength of633nm. The coherence ofthe light emitted from frequency stabilised versions ofthese lasers permits bi-directional fringe counting interferometer systems with measurement ranges ofup to 50 metres or more in the free atmosphere and experience has shown that the frequencies ofthese lasers do not change by more than a few parts in ten to the eight over the lifetime ofthe tube [Typically several years ]. The coherence length of the light emitted from the lower cost nonfrequency stabilised Helium-Neon tubes provides a measurement range of several centimetres with a frequency known to better than one part in ten to the six, properties which make these lasers a suitable source for short range interferometric metrology applications.

A laser tracking interferometer system (LTS), which can measure 3D coordinates, has been developed in our laboratory. The LTS makes use of the principle of laser trilateration. The principle satisfies Abbe's principles and the coordinates are calculated solely form length measurements. Consequently, measurements directly traceable to length standard can be achieved. The first generation trackers, however, were large, heavy and not so accurate. So, we developed a compact, accurate laser tracker. It has a hemisphere mirror, which is used as a tracking mirror and is driven by an X-Y moving table. The performance of this laser tracker was checked by a high precision coordinate measuring machine. The results of the experiments show that the displacement measuring error of this laser tracker is below 0.6 micrometers , which is much better than any other conventional laser trackers.

The NIST Is continuing to develop the ability to perform accurate, traceable measurements on a wide range of artifacts using a very precise, error-mapped coordinate measuring machine (CMM). The NIST M48 CMM has promised accuracy and versatility for many ears. Recently, these promises have been realized in a reliable, reproducible way for many types of 1D, 2D, and 3D engineering metrology artifacts. The versatility of the machine has permitted state-of-the-art, accurate measurements of one meter step gages and precision ball plates as well as 500 micrometer holes and small precision parts made of aluminum or glass. To accomplish this wide range of measurements the CMM has required extensive assessment of machine positioning and straightness errors, probe response, machine motion control and speed, environmental stability, and measurement procedures. The CMM has been used as an absolute instrument and as a very complicated comparator. The data collection techniques have been designed to acquire statistical information on the machine and probe performance and to evaluate and remove any potential thermal drift in the machine coordinate system during operation. This paper will present the data collection and measurement techniques used by NIST to achieve excellent measurement results for gage blocks, long end standards, step gages, ring and plug gages, small holes, ball plates, and angular artifacts. Comparison data with existing independent primary measuring instruments will also be presented to show agreement and correlation with those historical methods. Current plans for incorporating the CMM into existing measurement services, such as plain ring gages, large plug gages, and long end standards, will be presented along with other proposed development of this CMM.

For the calibration of length standards and instruments, various methods are available for which usually an uncertainty according to the GUM [1] can be set up. However, from calibration data of a measuring instrument it is not always evident what the uncertainty will be in an actual measurement (or calibration) using that calibrated instrument. Especially where many measured data are involved, such as in CMM measurements, but also in typical dimensional geometry measurements such as roughness, roundness and flatness measurements, setting up an uncertainty budget according to the GUM for each measurement can be tedious and even impossible. On the other hand, international standards require that for a proof of the conformance to specifications, the measurement uncertainty must be taken into account. Apart from this it is not so consistent that a lot is invested in the calibration of instruments where it is still unclear what the uncertainty is of measurements carried out with these 'calibrated' instruments. In this paper it is shown that the 'standard' GUM-uncertainty budget can be modified in several ways to accommodate more complicated measurements. Also, it is shown how this budget can be generated automatically by the measuring instrument, by the simulation of measurements by instruments with alternative metrological characteristics, so called virtual instruments. This can lead to a measuring instrument where, next to the measured value, also the uncertainty is displayed. It is shown how these principles are already used for roughness instruments, and how they can be used as well for e.g. roundness, cylindricity, flatness and CMM measurements.

In coordinate measurement metrology, assessment of the measurement uncertainty of a particular measurement is not a straight forward task. A feasible way for calculation of the measurement uncertainty seems to be the use of a Monte Carlo method. In recent years, a number of Monte Carlo methods have been developed for this purpose, we have developed a Monte Carlo method that can be used on CMM's that takes into account, among other factors, the auto correlation of the error signal. We have separated the errors in linearity errors, rotational errors, straightness errors and squareness errors. Special measurement tools have been developed and applied to measure the required parameters. The short-wave as well as the long-wave behavior of the errors of a specific machine have been calibrated. A machine model that takes these effects into account is presented here. The relevant errors of a Zeiss Prismo were measured, and these data were used to calculate the measurement uncertainty of a measurement of a ring gauge. These calculations were compared to real measurements.

The mechanical probing system is often one of the limiting factors in the calibration of length standards. It has been shown, that for highly accurate applications a particular effect, which is often not considered, has to be taken into account: a spherical probe on a stylus undergoes a small rotation due to the angular stylus deflection, which creates friction and potentially stick slip during the probing process and may thus lead to non-reproducible probing. A novel probe has been built which avoids this effect by an additional degree of freedom, providing a small vertical movement of the stylus. The probe is of a monolithic flexure hinge design with a ridge connection of the stylus and the mirror reflector for the plane mirror interferometer, which measures the displacement. Them measurement force, which is proportional to the deflection of the hinges, is measured with a capacitive probe. The probing procedure generates the force/deflection curve and allows for the measurement force to be extrapolated to zero. The presented test results show the system's capability for a probing accuracy in the nanometer range.

Very recently, in the context of measuring aspheres and complex surfaces with ultra-precision, a particular measurement principle was developed which determines the form (topography) of extended test samples by scanning measurements of curvature, being the reciprocal of the radius of curvature. The curvature sensor must be traceably calibrated with a low uncertainty. This back tracing can be done, first, by measuring radius of full spheres with a highly accurate sphere interferometer, second, by measuring roundness with highly accurate methods, and third, by measuring specially designed calibration aspheres. These procedures for traceably calibrating the curvature sensor will be described.

Recently, a novel scanning principle (ESAD - Extended Shear Angle Difference) has been presented for the ultra-precise determination of slope and topography of near-plane surfaces which is based on the measurement of differences of reflection angles with an autocollimator. It uses large lateral displacements (shears) of the order of mm to cm, and a newly developed algorithm allows the exact reconstruction of the slope from the angle differences with two different shears. The topography is then derived from the slope by an accurate integration procedure. Reproducibility of the reconstructed topography of the order of below 1 nm for scans over a near-flat surface has already been achieved. In contrast to interferometric techniques, this scanning method does not rely on an external reference surface of matched topography. The measurands are directly traced back to the base units of angle and length. Therefore, this technique is well suited for creating a very precise standard for straightness and flatness. A central element considerably influencing the overall uncertainty is the autocollimator itself, making a high-accuracy traceable calibration of the device necessary. Autocollimators are calibrated at the PTB by the use of a primary standard angle comparator which is traced back to the natural standard of the full angle of 2Pi rad. The traceable calibration is realized by an incremental circular scale, incorporated into a highly precise rotary table as a measuring system, consisting of a radial optical phase grating and several photoelectric reading heads, thus reaching an angular resolution of approximately 0.001 arcsec. With this comparator, calibration of an electronic autocollimator with 0.001 arcsec resolution and a measurement range of (150 arcsec with an uncertainty of 0.007 arcsec has currently been achieved. The autocollimator type to be used in the ESAD scanning facility was calibrated and investigated with respect to its resolution, reproducibility and accuracy in the range of 0.01 arcsec over a variety of measurement ranges. These experiences will be described. Methods to avoid or control error influences are discussed.

Gauge blocks, line scales and polygons are precision dimensional standards widely used for the dissemination of linear and angular quantities. Comparisons on these standards have been carried out among Singapore Productivity and Standards Board in Singapore, Commonwealth Scientific and Industrial Research Organization in Australia and National Metrology Institute of Japan/National Institute of Advanced Industrial Science and Technology in Japan. The standards include a set of five ceramic gauge blocks with sizes of 1 mm, 3 mm, 6 mm, 25 mm and 100 mm, a 100 mm and 200 mm glass scales, and an eight-sided 45 degrees glass polygon. The results of comparisons are described in this paper.

A multi-functional microscope named Morphininscope, which was designed to switch between various measurement functions by simply rotating its turret or turning on some sub-systems, was presented. Some of the various built-in functions of this microscope, including a confocal microscope, a photon-tunneling microscope, a laser based phase-shifting interferometry microscope, a Linnik interference microscope, and an ellipsometer, etc. are examined. The opportunity to bring traceability to thin-film or nano-materials metrology, which is an issue under extensive investigations now, offered by the multi-functional microscope were also detailed. Design thinking, optical and opto-mechanical configurations adopted, and experimental results of this newly multi-functional microscope were examined. Measurement of a grating surface, the real and the imaginary complex refractive indices, and the corrected surface profile of an inhomogeneous specimen were used to demonstrate the performance and advantages of this type of multi-functional microscope. Potential to achieve and transfer traceability of the primary standard in Morphinscope was also discussed.

Nanosensors are a new class of sensors that has recently appeared. These sensors are characterized by nanometer or sub-nanometer resolution over a range of at least several micrometers. The most well known examples are capacitive and inductive sensors but also laser interferometers, holographic scales, and scanning probe microscopes (SPM's) belong to the class of nanosensors. The accuracy of these nanosensors is not necessarily of the same level as the resolution. Effects like sensitivity errors, non-linearity, hysteresis and drift may cause deviations of many nanometers. In order to determine these errors in a traceable way, a new measuring instrument was developed. The heart of the system is a Fabry-Perot interferometer, which consists of two parallel mirrors separated by a distance L from each other. Light of a so-called slave laser is directed into this Fabry-Perot cavity and stabilized to the cavity length L. When one of the mirrors of this cavity is displaced the frequency of the slave-laser will follow its movement. The frequency of this slave-laser is then compared to the frequency of a primary length standard. In this way the displacement of the mirror is measured. When a nanosensor is placed on top of the mirror it will also follow the movement of the mirror. In this way the nanosensor is calibrated. The range of the instrument is 300 micrometers and the uncertainty is approximately 1 nm. Measurements of different sensors, such as an inductive and a capacitive sensor as well as a laserinterferometer will be presented. A detailed description of the uncertainty budget will also be given.

Interferometrically measured length changes of a silicon gauge block were performed under well defined environmental conditions. Special efforts - described in this paper - were made to reduce the uncertainties of the measurements. The used silicon crystal is of high purity and dislocation free. Expansion coefficients were obtained from thermal induced length changes in the range from 12 degrees C to 28 degrees C with uncertainties from about 0.01 percent to 0.03 percent. This corresponds to an uncertainty reduction by a factor of ten compared with earlier studies in this temperature range. The length change of the silicon gauge block induced by pressure variations from vacuum to atmospheric pressure provides a value for the compressibility of crystalline silicon with an uncertainty of about 1.5 percent. This directly measured compressibility slightly differs from literature data obtained from indirect measurements via ultrasonic wave velocities. The possible nature of this deviation is briefly discussed.

A photomask measuring instrument was developed and built at METAS. The instrument consists of an air bearing x-y stage for the positioning of the mask with a range of 400 mm by 300 mm, a digital video microscope system for the localization of the structures and a differential two axis plane mirror interferometer. The interferometric measurements are made with respect to an x-y reference mirror system made out of Zerodur. The uncertainty for 2D measurements is directly influenced by the shape of the reference system i.e. by the straightness and orthogonality of the mirrors. Through a precise characterization of the reference system its imperfections can be corrected numerically. An initial determination of the mirror shape was performed on a straightness measurement instrument consisting of a granite beam with an air bearing carriage and an inductive touch probe system. The method delivered initial flatness data with a high positional resolution but with some low order distortion due to a circular bending of the used granite beam which was induced by small temperature gradients. An in-situ calibration of the reference system on the photomask measuring instrument itself was used to improve these initial measurements. This second calibration was made by measurements of a 400 mm quartz line scale in axial and in two diagonal directions. By numerical simulation of these measurements of the x- and y- mirror shapes and the angle between the mirrors were determined. Circular and sinusoidal functions were used for the additional mirror form corrections, which were up to 40 nm for the y-axis and up to 140 nm for the x-axis. A final verification measurement showed that the agreement between the axial and the diagonal line scale measurements is now better than 10 nm.

This paper reports to the international community on recent developments in technical policies, programs, and capabilities at the U.S. (United States) National Institute of Standards and Technology (NIST) related to traceability in dimensional measurements. These developments include: formal NIST policies on traceability and assuring quality in the results of the measurements it delivers to customers in calibration and measurement certificates, and a program to support the achievement of traceability to the SI (International System of Units) unit of length in dimensional measurements by manufacturers without direct recourse to a National Metrology Institute (NMI) for dimensional calibrations.

The paper deals with a problem of increasing importance. That is in which way the technologies and formalism can be changed to establish traceability in a reasonable and worldwide acceptable direction in future. Until 1960, when the Pt-Ir-protype in the BIPM was the definition and realization of the SI-unit 'metre', formal and physical reasons called for hierarchical calibration chains from the BIPM via the National Metrology Institutes into the national societies and industries. The procedure is well proven and formally well accepted. Since the definition of wavelengths of discharge lamps- and moreover of laser wavelengths of frequency stabilized lasers - there is no physical reason further on to stay with the traditional way of realizing traceability for length and dimensional metrology. Physical principles and well proven of technologies (mise en pratique) allow to everybody , everywhere at any time to realize the SI unit for length. Experiences of NMI's show that the vacuum wavelength of lasers has never been an accuracy limiting factor for shop floor measurements. Other technical and formal aspects are of more relevance and need to be dealt with successfully to realize direct traceability as an acceptable alternative to the hierarchical calibration chain.

We have designed and tested a portable Nd:YVO₄/KTP/I₂ laser system at 532 nm. Using a conventional third- harmonic-locking servo system, Allan variances less than 1 10^-12 have been obtained for time interval s greater than 100 s.

This paper describes the automatic calibration system for angle encoders which is installed at the AIST. The system uses the Equal-Division-Averaged (EDA) method that is one kind of the self-checking method. Both of the reference standard and the object angle encoders are calibrated at the same time against all encoders graduations within only one hour. The resolution and an uncertainty are 0.001 inch and approximately +/- 0.05 inch, respectively. This equal- division-averaged method is hoped to become the national standard method for the calibration of angle encoders.

Due to increasing demands on the photolithography of integrated circuits and the progress of interferometric linear encoders, length measurement systems with a reproducibility under 3 nm are used in industry today, whereas the connection to the unit of length exhibits an uncertainty of about 25 nm. To resolve this problem a new one dimensional length comparator, the nanometer comparator, was developed in a cooperation between the Physikalisch-Technische Bundesanstalt (PTB), the Dr. Johannes Heidenhain GmbH and Werth Me#technik GmbH. The nanometer comparator will be able to perform one dimensional calibrations of photo masks, line-graduation scales, incremental linear encoders and laser interferometers in one axis up to a maximum length of 610 mm. To ensure the highest level of measurement performance, the interferometer is completely located in vacuum using metal bellows, whilst the calibration objects can be mounted under atmospheric conditions. The interferometer set-up compensates the dilatation and the bending of the granite base and minimizes the measurement circle of the comparator. This will minimize the influence of thermal and mechanical distortions. The interferometer design can be used with a heterodyne or a homodyne signal detection electronics. Due to their high power dissipation, the laser is arranged far apart from the comparator and light is fed to the interferometers by means of glass fibers. The light source is a frequency-doubled Nd:YAG laser frequency stabilized by an iodine absorption line. Different measuring systems for the structure localization can be attached to an universal sensor carrier on a solid bridge above the measuring carriage. Incremental reading heads and two photoelectric microscopes are now available for this purpose.

Relating two different methods of data analysis for assessing the absolute planarity of reference flats is reported. Considered methods are based on Zernike representation and pixel handling, respectively. Operations to be implemented on interferometric systems to use the same data set for comparative processing are described.

We have developed a gauge block measurement system that uses three frequency-stabilized lasers. The stabilized lasers are as follows: an I₂ stabilized offset locked He-Ne laser, an I₂-stabilized Nd:YAG laser, and a Rb-stabilized diode laser. The I₂-stabilized offset locked He-Ne laser is commercially available and its relative wavelength uncertainty is 2.5 X 10^-11. An I₂-stabilized Nd:YAG laser and a Rb-stabilized diode laser was developed in our institute and their relative wavelength uncertainties are 5 X 10^-12 and 1 X 10^-9, respectively. In the measurement system, laser beams were introduced to the interferometer using an optical multimode fiber. An interferometer fringe pattern was taken using a CCD camera and the excess fraction parts were calculated from the fringe pattern using the Fourier transform method. The excess fraction part obtained from the Rb-stabilized semiconductor laser was used only to determine the integer part of the fringe order, because the accuracy and stability of the wavelength were not sufficient for the long gauge block measurements. This interferometer can measure gauge blocks of up to 1000 nm long and the standard uncertainty of the interferometer is about 75 nm for a 1000 mm long gauge block.

The calibration of our interference microscope is currently performed by an elaborate multi step process. As a result the total uncertainty of a measurement performed with the interference microscope is much larger than the intrinsic repeatability of the microscope which is of the order of 1 nm. A major contribution to the total uncertainty is a length dependent factor, resulting from a calibration step using gauge blocks that finally yields 8 nm uncertainty for a step height of 2 micrometers . In order to reduce the total uncertainty we propose a novel step-height standard and calibration procedure. The standard is adjustable and can be simultaneously measured with the interference microscope and a laser interferometer allowing calibration of the entire dynamic range of the microscope with a single artefact. The new calibration method eliminates the process that contributes most to the total uncertainty budget in the current procedure. A possible implementation of the step-height standard is presented.

The setup of the common-path laser heterodyne interferometer (CLHI) with Wollaston Prism is introduced. The nonlinear error of this CLHI is frequency mixing. The concept of frequency mixing and the general principle of nonlinear error are studied by vector and interference theory. The error sources in the interferometer are the orientation of Wollaston Prism and metal mirror. When the polarization direction of the laser beam is not parallel to the axis of Wollaston prism, frequency mixing occurred in the output light. The vector of interference signal of the system is analyzed and the equation of nonlinear error is given. The law of the error is studied. On the other hand, the metal reflection theory is used to study the eccentricity and orientation error in the reflected light of linear polarized laser from metal mirror. Then the vector theory is used to determine the frequency mixing vector of the two reflected beams. The formula of the interference signal and nonlinear error are concluded. The simulation error is presented. Finally, the error compensation methods are discussed. The results of the research show that it is of great importance to improve the accuracy of heterodyne interferometer.

An update is given of recent advances in digital in-line holography with numerical reconstruction. It is shown that lateral resolution in the submicron regime can now be achieved routinely and that depth resolution is improved to the point that tracking of submicron particles is feasible in three dimensions.

A new instrument capable of measuring the diameter and form of cylinders up to 10 mm diameter with uncertainties at the +/- 10 nanometer level is being developed. The primary purpose of the instrument will be to characterize the geometry of pistons used in realizing high-pressure standards, but the instrument will have general applicability. The measurement of diameter is achieved by continuously and independently measuring the positions of two mutually opposed contact probes, using two sub-nanometric displacement measuring laser interferometers.

We propose a modified Michelson's interferometer with some applications in dimensional metrology. The configuration of a Michelson's interferometer using corner cubes instead of pane mirrors is further modified in a rectangular parallelogram. A double prism is introduced in one of the branches of the device in order to obtain a precision of (lambda) /4 and an accuracy of +/- (lambda) /8. The same scheme can be applied to develop absolute portable gravimeters. We present an interferometer version enabling reducing the free fall dropping height less than 25 cm, which is half size of any available device of the same class. Another version of the same interferometer enables a theoretical doubling of the dropping rate and a reduced dropping length with an effective improvement of the measurement precision of g. This solution may lead to a portable absolute dynamic gravimeter. The paper discusses the mathematical model in terms of transfer function of 'g' and describes the modified Michelson's interferometer with a 'futuristic' solution for a dynamic portable absolute gravimeter.