Reconstruction of the Image Metric of Periodic Structures in an Opto-Digital Angle Measurement System

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.

The use of two-dimensional scales for measuring angle and linear displacement

“…In the work [19], which was already mentioned above, among other important results on correcting distortions of the mark image in a real measuring system, an estimate of the manufacturing error of the mark photomask was obtained. It is shown that the error of deviation of the coordinates of the mark elements from the calculated values has a distribution close to normal with RMS of about 1 micron.…”

“…The paper also presented experiments with the implementation of the mark on a digital screen (a standard smartphone), significantly expanding the understanding of the possibilities of such measuring procedures. A separate study [19] was devoted to correction of distortions in the brand image to minimize the Δs parameter in formula (1), including correction of the tilt of the mark image, correction of lens distortion, correction of mark manufacturing errors. That corrections reduce the value of Δs by an order of magnitude (from tenths to hundredths of a pixel).…”