We describe the application of a vector-based radius approach to optical bench radius measurements in the presence of imperfect stage motions. In this approach, the radius is defined using a vector equation and homogeneous transformation matrix formulism. This is in contrast to the typical technique, where the displacement between the confocal and cat’s eye null positions alone is used to determine the test optic radius. An important aspect of the vector-based radius definition is the intrinsic correction for measurement biases, such as straightness errors in the stage motion and cosine misalignment between the stage and displacement gauge axis, which lead to an artificially small radius value if the traditional approach is employed. Measurement techniques and results are provided for the stage error motions, which are then combined with the setup geometry through the analysis to determine the radius of curvature for a spherical artifact. Comparisons are shown between the new vector-based radius calculation, traditional radius computation, and a low uncertainty mechanical measurement. Additionally, the measurement uncertainty for the vector-based approach is determined using Monte Carlo simulation and compared to experimental results.
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