For an absolute measurement of a density standard, mass and volume are measured separately. The absolute determination of the volume is still the quantity limiting the uncertainty. Lowest uncertainties are achieved by interferometric measurements of the diameter of spheres made from a silicon single crystal. So far, measurements have been based on a plane interferometer. At PTB, we demonstrate a new method of determining the diameter using a spherical interferometer, which yields more and particular information about the resulting volume.

Gauge blocks are still used as length standards in industry and trade primarily because they are easier and less expensive to handle than laser-based instruments.

One important prerequisite for interferometric length measurements of high accuracy is autocollimation adjustment. This guarantees that the direction of the length scale represented by light waves is parallel to the length direction of the object investigated. First we describe the conventional visual autocollimation adjustment method used at Physikalisch-Technische Bundesanstalt since the beginning of interferometric length measurements. Then a new autocollimation method based on scanning the retroreflection from the interferometer is described. Check measurements are performed in order to investigate the quality of the adjustment. As a result of the method applied the uncertainty contribution originating from the cosine error could be reduced drastically for the interferometer used.

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.

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.

Phase errors that arise in phase-stepping interferometry are discussed. Investigations were performed by use of a Twyman-Green interferometer equipped with a compensation plate with a variable and servo-controlled tilt angle. With this instrument, phase-stepping errors can be reduced to a negligible level. There are, however, phase errors that are caused by camera nonlinearities. Two methods for minimizing these errors are presented. The first method is based on the simple idea that the interference intensity at the output of a two-beam interferometer has an exact cosine shape. The camera signals were monitored as a function of the tilt angle of the compensation plate, and the deviation from the cosine form was used to produce a correction. The second method is based on the idea that, under specific conditions, errors of an average of two phase measurements may compensate for each other. Numerical calculations were performed and give evidence of this hypothesis. Each method, the signal-correction and the averaging method, drastically reduces errors in evaluation of phases. The combination of both methods is a powerful tool that allows precise phase data to be obtained with an uncertainty, in the range lambda/2000 approximately 0.3 nm, that is caused mainly by signal noise.

Two publications on interferometric gauge block measurements claiming extraordinarily low uncertainties gave rise to some critical considerations. For such interferometric measurements, wringing of the gauge block to a platen is a basic element in the measurement process. Among the effects limiting the attainable uncertainty level, the elastic deformation of the gauge block by the wringing process has to be included in the evaluation model and to be appropriately taken into account in the uncertainty budget.

For the new determination of Avogadro's constant, N/sub A/, one part of the measuring task consists in the high accuracy determination of the volume of a silicon sphere with a mass of 1 kg and a diameter of about 90 mm. An interferometer with spherical reference surfaces has been designed for this specific purpose. The measuring principle of the interferometer and first measurements on silicon spheres are described.

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.

Ein Temperaturmesssystem wird beschrieben, mit dem Unsicherheiten < 1 mK erreicht werden. Mit einer Messbrücke (mit Pt-25-Fühler und Referenzwiderstand) wird die Temperatur eines Kupferblockes, der als Bezugspunkt dient, genau bestimmt. Die geringe Temperaturdifferenz zum Probekörper wird mit Thermoelementen gemessen. Das speziell hierfür entwickelte elektronische System, der Aufbau der Sensoren sowie die Kalibrierung des Thermoelement-Messsystems werden am Beispiel der Temperaturmessung an Endmaßen erläutert.

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 degreesC to 28 degreesC with uncertainties from about 0.01 % to 0.03 %. 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 %. 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 phase-stepping interferometer designed for dimensional measurements of bodies with parallel, flat measuring surfaces is described. The special Fizeau-algorithm used requires a step-width of exactly 1/4 interference order which is achieved by means of piezoactuators with an integrated capacitive sensor. Two interferometric procedures have been developed to calibrate the capacitive sensors. The remaining step-with errors are much below 1 nm.

A digital piezo system comprises a PZT and a capacitive sensor combined in a single unit. The desired displacement can be achieved by simply inputting the displacement value into the software. However, when target value of /spl lambda//8 was input to the three PZT's, the Fizeau plate did not show parallel movement, resulting in tilt to the linear fringes of the interferogram, In order to measure the length of the gauge block with high accuracy, this non-parallel movement of the Fizeau plate should be corrected precisely. This could be accomplished by multiplying correction factors to the target values of the piezo systems, which are self-measured by the phase shifting Fizeau interferometer.

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.

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.

An air refractometer has been developed for accurate measurements of the refractive index of gases under well-defined conditions. Measurements have been performed for dry and moist air at four wavelengths distributed over the visible part of the spectrum. The measured values have been compared with values determined by modified Edlén's formulae and measured parameters. A fitting procedure is described to adjust the humidity dependence and the constant term of the dispersion formula so that optimum agreement is obtained. A standard deviation of 3 × 10-9 for the residuals describes the reproducibility of the measurements and the success of fitting. For 50 % relative humidity, a standard uncertainty of 10-8 for the fitted formulae is claimed, arising mainly from the uncertainty contributions of the air parameters.

The vacuum wavelength of a 544 nm iodine-stabilised He-Ne laser was measured by means of the PTB's Michelson interferometer, which had been designed for highly accurate wavelength comparisons. One of the two longitudinal models of the internal mirror He-Ne laser was selected and frequency stabilised using FM saturation spectroscopy at iodine by means of an external cell. Reference wavelengths were obtained from an I-2-stabilised He-Ne laser at 633 nm and an I-2-stabilised Ar+-laser at 515 nm. The wavelength of the 544 nm I-2-stabilised He-Ne laser was found to be lambda = 543,516 333 04 nm with a relative standard uncertainty of 8,4 . 10(-11).

Determination of the roughness correction with a scattering light method is performed 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 results with both methods.

The vacuum wavelengths of hyperfine components of three different rovibronic transitions of the B 0u+ - X 1Eg+ spectrum of molecular 127I2 in the near-infrared were determined with a relative standard uncertainty of δλ/λ = 1.3 × 10-10. The measurements were performed by interferometric wavelength comparison using as standards an iodine-stabilized He-Ne laser at 633 nm and a dye laser stabilized to the intercombination line of Ca at 657 nm. The vacuum wavelengths of hyperfine component a10 of the R(96) lines of both the (0-14) and (0-15) bands and the component a of the P(166) line of the (0-14) band were determined to be 781.488 441 03(10) nm, 793.527 910 44(10) nm and 790.109 812 76(10) nm, respectively.

Material standards of volume or length can be measured with highest accuracy, when double-ended Fizeau interferometers with phase stepping evaluation are used. The technique is suitable for regular bodies with reflecting flat or spherical surfaces. For the measurements, the bodies are included in the interferometer system, so that light waves of appropriated wavefronts and known wavelengths can directly be used for probing their surfaces. Interferometers for measurement of spheres and cubes including the necessary servo control units and data evaluation systems are described. Experimental material is presented to demontrate the properties of a special Fizeau algorithm and the features of a particular interferometer.