The PTB developed a new optical heterodyne interferometer in the context of the European joint research project ‘Nanotrace’. A new optical concept using plane-parallel plates and spatially separated input beams to minimize the periodic nonlinearities was realized. Furthermore, the interferometer has the resolution of a double-path interferometer, compensates for possible angle variations between the mirrors and the interferometer optics and offers a minimal path difference between the reference and the measurement arm. Additionally, a new heterodyne phase evaluation based on an analogue to digital converter board with embedded field programmable gate arrays was developed, providing a high-resolving capability in the single-digit picometre range. The nonlinearities were characterized by a comparison with an x-ray interferometer, over a measurement range of 2.2 periods of the optical interferometer. Assuming an error-free x-ray interferometer, the nonlinearities are considered to be the deviation of the measured displacement from a best-fit line. For the proposed interferometer, nonlinearities smaller than ±10 pm were observed without any quadrature fringe correction.

Often Abbe errors are the most important uncertainty sources in dimensional metrology applications aiming for measurement uncertainties of only a few nanometres. Abbe errors are caused by the angle deviations of relative translations between measurement object and sensing device—either in moving object or moving sensing device configuration—and the offset between the measurement axes of the machine and the measurement point of the structure localization device or the displacement sensor under investigation. The angle deviations of the motion stage can usually be determined, e.g. by an electronic autocollimator with sufficient accuracy. Unfortunately, in many cases, the Abbe offset cannot be estimated with sufficient accuracy or varies over the measurement range. In order to reduce the influence of the Abbe error many length measuring machines are equipped with control loops to reduce the angle deviations. However, in order to specify the uncertainty contribution of the residual Abbe errors, the Abbe offsets are still required. In these cases, in principle, an in situ determination of the Abbe errors is possible by the following method. First the measurement is conducted in the common way. Then two further measurements are performed during which one angle, consecutively the yaw and the pitch angle, is scanned by the angle actuators and measured by the angle sensors of the control loop. The differences of these two measurements from the first should reflect the influence of the Abbe errors and the dependence of the length measurement results on the angles can be determined. This predication was tested during the measurements of a high resolution encoder with the Nanometer Comparator. Contrary to the classical perception, the observed dependence of the Abbe error on the angle variation applied was nonlinear. However, using a polynomial of third order it is possible to correct the artificially introduced Abbe errors of up to 20 nm almost down to the noise level.

In order to be able to resolve displacements of a picometer with widely used commercially available heterodyne interferometers, an advanced phase meter was developed at PTB. Key to this level of accuracy is the use of a state-of-the-art analogue-to-digital converter (ADC) board enabling the implementation of a phase-evaluation method by using embedded field programmable gate arrays. Experimental results obtained with commercially available heterodyne laser interferometer components prove that the proposed phase-evaluation procedure is capable of interpolating an optical fringe down into the picometer regime. The phase evaluation was moreover extended to track simultaneously two heterodyne beat frequencies with only two photodetectors and ADCs. Potential limitations of the long-term stability of heterodyne interferometers are discussed. The phase meter was tested, has been readily applied, can be easily adapted and is therefore to be used in a wide field of applications.

Optical interferometers are widely used in dimensional metrology applications. Among them are many quadrature homodyne interferometers. These exhibit two sinusoidal interference signals shifted, in the ideal case, by 90° to allow a direction sensitive detection of the motion responsible for the actual phase change. But practically encountered signals exhibit additional offsets, unequal amplitudes and a phase shift that differs from 90°. In order to demodulate the interference signals the so called Heydemann correction is used in almost all cases, i.e. an ellipse is fitted to both signals simultaneously to obtain the offsets, amplitude and the phase lag. Such methods are typically based on a simplified least squares fit that leads to a system of linear equations, which can be solved directly in one step. Although many papers related to this subject have been published already only a few of them consider the uncertainties related to this demodulation scheme. In this paper we propose a new method for fitting the ellipse, based on minimization of the geometric distance between the measured and fitted signal values, which provides locally best linear unbiased estimators (BLUEs) of the unknown model parameters, and simultaneously also estimates of the related statistical uncertainties, including the uncertainties of estimated phases and/or displacements.

This report describes the results of the international line scale comparison Nano3, which was carried out between 2000 and 2003 and which was accepted as supplementary comparison CCL-S3. This comparison was initiated by the BIPM working group on nanometrology as one of five international comparisons in the field of dimensional nanometrology. Two high quality line scales, one made of Zerodur and one made of fused silica (quartz), with 280 mm main graduation length and additional smaller graduations of only a few mm were chosen as transfer standards. These scales were produced using advanced and optimized lithography and processing technologies by the Dr Johannes Heidenhain GmbH, Germany. A considerable number of characterizations of the graduations were performed in order to ensure an optimized line edge quality of the scales used in the comparison. Moreover, it was decided to have long gauge blocks manufactured out of the same piece of substrate material as was used for the scales. In this way, it was possible to independently determine important substrate material parameters like thermal expansion, compressibility and to investigate the long-term stability of the substrate materials.The Zerodur line scale standard revealed a small length reduction of about (−7 ± 4)×10-8/a, which was confirmed by the measurements on the long gauge blocks. This length change of the Zerodur line scale could be taken into account for the comparison of participant's data by the application of a linear drift model. On the quartz samples and linescales no comparable effects were observed.The line scales were measured by 13 national metrology institutes from four different metrology regions. Two institutes decided to withdraw from Nano3 after the measurements were performed, but before Draft A was circulated. The measurement uncertainties that were evaluated by the participants over the 280 mm length of the graduations showed a variation from about 300 nm down to 30 nm.The good line edge quality of both scales allowed a meaningful separation of the length-dependent and length-independent deviations from the weighted mean values. Therefore a meaningful comparison of these deviations with the evaluated uncertainty contributions of the participating institutes was possible.For the most important measurand of this comparison, namely the position deviations of the line structures on the 280 mm main graduation, three results out of the 11 data sets provided had to be excluded by application of the En-criterion for the quartz and Zerodur scales respectively. Investigations of the reasons for the deviations have already been started by the respective institutes, including bilateral follow-up line scale comparisons with the Nano3 pilot laboratory.Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCL, according to the provisions of the Mutua...