26 June 2017 Autocollimation system for measuring angular deformations with reflector designed by quaternionic method
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Autocollimators are widely used for angular measurements in instrument-making and the manufacture of elements of optical systems (wedges, prisms, plane-parallel plates) to check their shape parameters (rectilinearity, parallelism and planarity) and retrieve their optical parameters (curvature radii, measure and test their flange focusing). Autocollimator efficiency is due to the high sensitivity of the autocollimation method to minor rotations of the reflecting control element or the controlled surface itself. We consider using quaternions to optimize reflector parameters during autocollimation measurements as compared to the matrix technique. Mathematical model studies have demonstrated that the orthogonal positioning of the two basic unchanged directions of the tetrahedral reflector of the autocollimator is optimal by the criterion of reducing measurement errors where the axis of actual rotation is in a bisecting position towards them. Computer results are presented of running quaternion models that yielded conditions for diminishing measurement errors provided apriori information is available on the position of rotation axis.

A practical technique is considered for synthesizing the parameters of the tetrahedral reflector that employs the newly-retrieved relationships. Following the relationships found between the angles of the tetrahedral reflector and the angles of the parameters of its initial orientation, an applied technique was developed to synthesize the control element for autocollimation measurements in case apriori information is available on the axis of actual rotation during monitoring measurements of shaft or pipeline deformation.
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Phong V. Hoang and Igor A. Konyakhin "Autocollimation system for measuring angular deformations with reflector designed by quaternionic method", Proc. SPIE 10329, Optical Measurement Systems for Industrial Inspection X, 1032938 (26 June 2017); doi: 10.1117/12.2269118; https://doi.org/10.1117/12.2269118

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