The spatial angle autocollimator calibrator: optimised model, uncertainty budget and experimental validation

The traceable optical measurement of spatial angles is taking on an increasingly important role in the modern form measurement of high quality optical surfaces. In many cases, autocollimators are utilised to measure the local tilt of a surface in two perpendicular directions. Autocollimators have up to now been traceably calibrated using plane angle standards like sine bars or divided circles. Here we present recent advances of the spatial angle autocollimator calibrator (SAAC) of the Physikalisch-Technische Bundesanstalt (PTB). The SAAC consists of an innovative Cartesian arrangement of three autocollimators facing a central reflector cube. This arrangement effectively divides the spatial angle measurement of the autocollimator to be calibrated into two separate measurements of plane angles of the two reference autocollimators. The reference autocollimators serve as transfer standards and are traceably calibrated by using the WMT 220, which is the primary plane angle standard of PTB. We present an optimised mathematical model of the SAAC which features an approximation-free description obtained by using a minimal set of parameters. The model is used for the in situ determination and correction of the alignment errors of the opto-mechanical components. The uncertainty of an autocollimator calibration when using the SAAC is evaluated by means of the Monte Carlo approach. The uncertainty of the calibration of the reference autocollimators is the dominant contribution. In addition, we present an experimental validation of the model and of the uncertainty budget using an error separation technique.