Mathematical model analyzes image changes from rotation angles in cylindrical reflectors, suggesting improved measurement methods.
The control element of the autocollimation system (reflector) is considered, which is a mirror tetrahedron, the lower face of which is replaced by a cylindrical surface, while the angle between the flat faces is not equal to 90 °. A mathematical model of this reflector is synthesized, describing the image change depended on the rotation angles. The possibility of using the model to measure characteristic image parameters is analyzed. A computer model of the autocollimation system (ACT-60 autocollimator) is created with Zemax software tool. An algorithm for measuring the rotation angles of a control element based on determining the characteristic image parameters is presented. Based on the simulation results, the consistency of mathematical and computer models is proved using the overlay method. The results obtained can be applied in systems requiring precise angular positioning of elements, for example, in the study of deflections and deformations of experimental structures, installation and assembly of large-sized parts of products, installation of aircraft and ship slipways.
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Nikitin et al. (2025) studied this question.
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