The European Synchrotron Radiation Facility (ESRF) located in Grenoble, France is a joint facility supported and shared by 19 European countries. It operates the most powerful synchrotron radiation source in Europe. Synchrotron radiation sources address many important questions in modern science and technology. They can be compared to “super microscopes”, revealing invaluable information in numerous fields of diverse research such as physics, medicine, biology, geophysics and archaeology. For the ESRF accelerators and beam lines to work correctly, alignment is of critical importance. Alignment tolerances are typically much less than one millimetre and often in the order of several micrometers over the 844 m ESRF storage ring circumference. To help maintain these tolerances, the ESRF has, and continues to develop calibration techniques for high precision spherical measurement system (SMS) instruments. SMSs are a family of instruments comprising automated total stations (theodolites equipped with distance meters), referred to here as robotic total stations (RTSs); and laser trackers (LTs). The ESRF has a modern distance meter calibration bench (DCB) used for the calibration of SMS electronic distance meters. At the limit of distance meter precision, the only way to improve positional uncertainty in the ESRF alignment is to improve the angle measuring capacity of these instruments. To this end, the horizontal circle comparator (HCC) and the vertical circle comparator (VCC) have been developed. Specifically, the HCC and VCC are used to calibrate the horizontal and vertical circle readings of SMS instruments under their natural working conditions. Combined with the DCB, the HCC and VCC provide a full calibration suite for SMS instruments. This thesis presents their development, functionality and in depth uncertainty evaluation. Several unique challenges are addressed in this work. The first is the development and characterization of the linked encoders configuration (LEC). This system, based on two continuously rotating angle encoders, is designed improve performance by eliminating residual encoder errors. The LEC can measure angle displacements with an estimated uncertainty of at least 0.044 arc seconds. Its uncertainty is presently limited by the instrumentation used to evaluate it. Secondly, in depth investigation has lead to the discovery of previously undocumented error-motion effects in ultra-precision angle calibration. Finally, methods for rigorous characterisation and extraction of rotary table error motions and their uncertainty evaluation using techniques not previously discussed in the literature have been developed
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