Abstract
Measurement of the object angular position and its change is one of the important tasks in measurement technique. Our method is based on determination of the angular position of a 2D periodical optical pattern (2D mark) at the object, captured by the sensor of a digital camera. System performance can be frustrated by errors in determination of the spot coordinates on the camera sensor; by the presence of lens aberrations; by deviations from the parallelism of the pattern planes and the camera sensor; and by differences between the actual spots positions and the ideal grid. In the paper we discuss the effect of these errors and the way to correct or eliminate them. We have developed the mathematical routine and the corresponding numerical codes for correction of the said errors. The code and the routine we checked in a real experiment. It has shown that the correction decreases the standard deviation in 15 times.
Highlights
Academic Editors: Nikolay Kazanskiy, Sergey Odinokov and Vladimir V
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The peculiarity of angle measurements is the fact that the angle, by definition, is a dimensionless quantity, representing a certain fraction of the total angle 2π, which, in turn, is the only obvious natural standard of the angle
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The resolution of the proposed method (without interpolation) in this case is determined by the size of the camera pixel (3–4 μm) divided by the radius of the scale (20 mm) and the root of the number of 2D-pattern elements (100,000) For these values, we get 0.1 arc-sec. The presence of lens aberrations leads to the appearance of additional shifts in the coordinates on the camera sensor, depending on the current position of the spot image xn , yn In this case, the most significant aberration is distortion. If the pattern is perpendicular to the optical axis, and the camera sensor is tilted, the constructions have a similar appearance If both the sensor and the pattern are tilted, the distortions are determined by the total angle between their planes. The calculations are repeated until the correction effect becomes less than a given value
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