Pushing the limits: latest developments in angle metrology for the inspection of ultra-precise synchrotron optics
The requirements on the quality of ultra-precise X-ray optical components for application in the Synchrotron Radiation (SR) community are increasing continually and strongly depend on the quality of the metrology devices available to measure such optics. To meet the upcoming accuracy goal of 50 nrad rms for slope measuring profilers, a dedicated project, SIB58 Angles, consisting of 16 worldwide partners and supported by the European Metrology Research Programme (EMRP) was started in Sep 2013. The project covers investigations on autocollimators under extremely challenging measuring conditions, ray-tracing models, 2D autocollimator calibration (for the first time worldwide), determination of error sources in angle encoders providing traceability by ‘sub-division of 2π rad’ with nrad uncertainty, angle generation by 'ratio of two lengths' in nrad level, and on the development of portable precise Small Angle Generators (SAGs) for regular in-situ checks of autocollimators’ performance. Highlights from the project will be reported in the paper and the community of metrology for X-Ray and EUV Optics will be informed about its progress and the latest work in angle metrology.
Application of advanced shearing techniques to the calibration of autocollimators with small angle generators and investigation of error sources.
The application of advanced error-separating shearing techniques to the precise calibration of autocollimators with Small Angle Generators (SAGs) was carried out for the first time. The experimental realization was achieved using the High Precision Small Angle Generator (HPSAG) of TUBITAK UME under classical dimensional metrology laboratory environmental conditions. The standard uncertainty value of 5 mas (24.2 nrad) reached by classical calibration method was improved to the level of 1.38 mas (6.7 nrad). Shearing techniques, which offer a unique opportunity to separate the errors of devices without recourse to any external standard, were first adapted by Physikalisch-Technische Bundesanstalt (PTB) to the calibration of autocollimators with angle encoders. It has been demonstrated experimentally in a clean room environment using the primary angle standard of PTB (WMT 220). The application of the technique to a different type of angle measurement system extends the range of the shearing technique further and reveals other advantages. For example, the angular scales of the SAGs are based on linear measurement systems (e.g., capacitive nanosensors for the HPSAG). Therefore, SAGs show different systematic errors when compared to angle encoders. In addition to the error-separation of HPSAG and the autocollimator, detailed investigations on error sources were carried out. Apart from determination of the systematic errors of the capacitive sensor used in the HPSAG, it was also demonstrated that the shearing method enables the unique opportunity to characterize other error sources such as errors due to temperature drift in long term measurements. This proves that the shearing technique is a very powerful method for investigating angle measuring systems, for their improvement, and for specifying precautions to be taken during the measurements.
Calibration of angle encoders using transfer functions
Classical approaches to the calibration of angle encoders typically make use of circle division by means of an auxiliary artefact and apply linear equation systems constrained by circle closure which are solved for the errors of the encoder and those of the artefact simultaneously. Lately, emphasis has been placed on Fourier methods, as Fourier approaches involving transfer functions have proved to be a powerful tool applicable to various high-precision measurement tasks. We present an in-depth treatment of the use of the Fourier approach including transfer functions for the calibration of angle encoders. Different weighting schemes for combining the measurements will be presented by which the uncertainty of the calibration of angle encoders can be substantially reduced. The method utilizes angle difference measurements and it can therefore also be applied to the calibration of angle encoders using suitable arrangements of multiple reading heads. The approach is used for calibrating an angle encoder in an experimental set-up by means of a five-sided calibration polygon with angle differences between the optical faces that are not integer fractions of the full circle. The calibration results, including an evaluation of the measurement uncertainty, are presented for different weighting schemes and it is shown that appropriate weighting leads to a reduction in the uncertainty up to a factor of 4.