Uncertainties in Small-Angle Measurement Systems Used to Calibrate Angle Artifacts

We have studied a number of effects that can give rise to errors in small-angle measurement systems when they are used to calibrate artifacts such as optical polygons. Of these sources of uncertainty, the most difficult to quantify are errors associated with the measurement of imperfect, non-flat faces of the artifact, causing the instrument to misinterpret the average orientation of the surface. In an attempt to shed some light on these errors, we have compared autocollimator measurements to angle measurements made with a Fizeau phase-shifting interferometer. These two instruments have very different operating principles and implement different definitions of the orientation of a surface, but (surprisingly) we have not yet seen any clear differences between results obtained with the autocollimator and with the interferometer. The interferometer is in some respects an attractive alternative to an autocollimator for small-angle measurement; it implements an unambiguous and robust definition of surface orientation in terms of the tilt of a best-fit plane, and it is easier to quantify likely errors of the interferometer measurements than to evaluate autocollimator uncertainty.