A Model of Angle Measurement Using an Autocollimator and Optical Polygon

Abstract

The significance of an autocollimator in angular metrology cannot be overestimated: in many countries, it is either included as part of the primary plane angle standard or is involved in transferring the unit of plane angle from this standard to less accurate measuring instruments. This paper presents a historical overview of the problems encountered when using an autocollimator in angular metrology, as well as of proposed solutions. Not for the first time, the problem of the theoretical definition of the angle being measured between surfaces that are not perfectly flat is raised. In addition, the authors attempt to compile a complete list of factors affecting angular measurements using an autocollimator and to build a model that allows some of these factors to be taken into account for a subsequent algorithmic compensation of their influence. To assess the level of accuracy of angular measurements at which the use of the proposed model is reasonable, a simplified simulation example is presented. In an attempt to confirm the validity of the proposed model, a corresponding analysis of experimental data is provided. The applicability and limitations of the proposed model are discussed in the conclusion.