The Project


Although a sub-nm uncertainty of a measured length or displacement appears to be rather small and one tends to think it may be negligible, there are already important applications in metrology and industry where accuracies in this range are needed or will be needed in the very near future. It is therefore necessary for national metrology institutes to address this issue.

Today, accurate measurements of displacements or the dimensions of macroscopic bodies are usually made with optical interferometers that measure the sought quantity in terms of the wavelength of light. The wavelength λ of an electromagnetic plane wave, that is an infinitely extended wave with plane parallel wavefronts, is related to its frequency ν via the speed of light c in the respective medium by λ = c / ν. Therefore, by knowing the exact frequency of a laser and the speed of light, which depends on the medium’s refractive index, a wavelength can be calculated. However, this wavelength is only an approximation to the real wavelength. The wavefronts in real interferometers are curved and never infinitely extended. Although the plane wave approximation can be quite good in some cases, real wavelengths differ typically by parts per million up to parts per thousand depending on the wavefront curvature and position in relation to the light source. This means, for a wavelength in the visible light region (between 380 nm and 780 nm), the real wavelength differences can reach picometre level (10-12...10-10 m). In order to measure displacements or lengths with sub-nm accuracy theoretical models which consider the actual shape of the wavefront must be used to calculate a correction to a measured value. Up to now, appropriate models are neither readily available nor validated.

Another class of devices widely used to measure displacements are capacitive sensors. The measurement principle is based on the capacitance of a plate capacitor. By knowing the area of the electrodes, the permittivity of the medium between the electrodes and by measuring the capacitance in principle one can calculate the distance between the electrodes. However, the precision of such a measurement (the number of digits which can repeatedly be resolved) can be much better than the accuracy (small deviation from the real value) of the quantities needed to calculate the absolute distance. Therefore, although the precision is very high, accurate measurements depend on calibration and may drift in time and change with environmental conditions like humidity and temperature.

Scientific Objectives

The purpose of this JRP is to enable traceable measurements in the sub-nm range for optical interferometers as well as improved capacitive sensors. Traceability of sub-nm length measurements requires consistent modelling of the measurement system as well as cross validation between different measurement principles. For this purpose the measurements have to be improved regarding uncertainty, resolution and dynamic range of displacement. Models for the propagation of aberrated wavefronts in optical interferometers as well as a model based correction of alignment errors and environmental effects of capacitive sensors and a traceable wavefront sensor with an uncertainty better than λ/30 and only limited by its repeatability will be developed. The influence of roughness and drift in optical interferometers will be investigated which will result in improved uncertainty budgets. The FPI displacement measurement and related sensor calibration will be improved to sub-nm uncertainty by means of a detailed uncertainty budget, with particular attention for environmental effects, sensor referencing, alignment, noise and drift of the FPI. The target uncertainty for an existing metrological FPI is sub-nm for a displacement stroke of 1 µm and 10 nm for a stroke of 100 µm. A proper sensor calibration methodology using the FPI and supporting sub-nm uncertainty, specifically investigated for selected capacitive sensors has to be found. A picometer-range uncertainty for the FPI is targeted by means of improved ambient stability, referencing compatibility and optical frequency comb traceability to the time standard. Target uncertainty is 10 pm for a displacement stroke of 1 µm. Quantized positioning of x-ray interferometer (XRI) measurements with an resolution of 24 pm, quadrature counting of x-ray fringes and scanning ranges up to 10 mm will be enabled. An improved sensor design for capacitive sensors with lower sensitivity to alignment and environment effects will be developed. Alignment errors in the arcmin region and environment effects on capacitive sensors by referencing to optical interferometers and XRI will be analyzed. The requirements for a displacement transfer standard will be specified and the available technology will be reviewed. Eventually, a prototype of a displacement transfer standard facilitating cross-validation of at least 2 different types of interferometers with sub-nm uncertainty [10 pm (1 nm) for a stroke of 1 µm (100 µm)] will be suggested by a feasibility study.


Software that models the propagation of experimentally detected laser-beam wavefronts will be developed. Therefore, accurate measurement of wavefronts is a premise which is addressed by the development of a flexible and traceable wavefront sensor. A combined optical and x-ray interferometer set-up is then used to validate the theoretical prediction for the optical displacement measurement. For the capacitive sensors new technological methods as well as the influence of environmental effects on the reproducibility are studied in direct comparison to sophisticated Fabry-Pérot and x-ray interferometers. The scientific and technological output is also evaluated in a feasibility study about a transfer standard for length measurements with sub-nm traceability.


The project aims to develop improved traceability of dimensional nanometrology in high end instrumentation used at NMIs and in high tech industries. Applications include e.g. metrology for the semiconductor fabrication and lithography, and nanopositioning industries as well as other industries with challenging requirements such as the space instrumentation industry that requires a one-off calibration that must be valid for the lifetime of the instrument. Cutting edge NMI metrology projects, e.g. the re-definition of the kilogram, will benefit from this project. The results will lead to standardised, traceable and validated measurement methods for calibrating precision instruments; will enhance the quality assurance of national metrology institutes, the calibrations they perform for customers and will improve ultimate quality of the products manufactured in Europe, thereby enhancing the competitiveness of European industry. Precision engineering is an important technology for the manufacturing of medical equipment especially in the nano medicine. Therefore advancements in these fields could have impact on medical technology leading to better healthcare. Improved accuracy in manufacturing could potentially lead to more efficient production thereby reducing waste and energy consumption. Further social benefits may emerge from impact of improved uncertainties in production engineering providing new information technology components and consumer electronics.