Geometrical Characterisation of a 2D Laser System and Calibration of a Cross-Grid Encoder by Means of a Self-Calibration Methodology

Abstract

This article presents a self-calibration procedure and the experimental results for the geometrical characterisation of a 2D laser system operating along a large working range (50 mm × 50 mm) with submicrometre uncertainty. Its purpose is to correct the geometric errors of the 2D laser system setup generated when positioning the two laser heads and the plane mirrors used as reflectors. The non-calibrated artefact used in this procedure is a commercial grid encoder that is also a measuring instrument. Therefore, the self-calibration procedure also allows the determination of the geometrical errors of the grid encoder, including its squareness error. The precision of the proposed algorithm is tested using virtual data. Actual measurements are subsequently registered, and the algorithm is applied. Once the laser system is characterised, the error of the grid encoder is calculated along the working range, resulting in an expanded submicrometre calibration uncertainty (k = 2) for the X and Y axes. The results of the grid encoder calibration are comparable to the errors provided by the calibration certificate for its main central axes. It is, therefore, possible to confirm the suitability of the self-calibration methodology proposed in this article.

2D Positioning Control System for the Planar Motion of a Nanopositioning Platform

“…To minimise this contributor, a low-noise power supply, with a peak-to-peak noise of 10 mV, has been used. In a previous study [16], a self-calibration procedure for the geometrical characterization of the 2D laser system of the NanoPla was proposed. The standard uncertainty of the calibrated laser system, after correcting for geometrical errors, was calculated to be 99 nm on the X-and Y-axes.…”

“…Even though the laser system's resolution is included inside the standard uncertainty of the laser system, its value is also shown separately in the table, so it can be compared to the magnitude of the other contributors. In a previous study [16], a self-calibration procedure for the geometrical characterization of the 2D laser system of the NanoPla was proposed. The standard uncertainty of the calibrated laser system, after correcting for geometrical errors, was calculated to be 99 nm on the X-and Y-axes.…”

“…NanoPla positioning uncertainty contributors can be divided into two categories: Ones whose contribution to the final positioning error in an open loop is known, like the resolution of the phase voltage generation (analysed in [14]) and the laser system (analysed in [16]); and the errors in the laser system that are still present after correcting for the geometrical errors obtained by the self-calibration procedure defined in [16]. The other types of errors are those whose contributions to the final positioning error cannot be calculated separately and cause RMS deviations of the positioning errors.…”

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

“…These errors cause root mean square (RMS) deviations of the positioning error in the open-loop, which can be experimentally measured. In addition, the geometrical errors of the 2D laser system have been characterized by a self-calibration procedure, as defined in [26], and corrected in the measurements. The uncertainty of the calibrated laser system also contributes to the final positioning uncertainty.…”