Marta Torralba

Design Optimization for the Measurement Accuracy Improvement of a Large Range Nanopositioning Stage

Both an accurate machine design and an adequate metrology loop definition are critical factors when precision positioning represents a key issue for the final system performance. This article discusses the error budget methodology as an advantageous technique to improve the measurement accuracy of a 2D-long range stage during its design phase. The nanopositioning platform NanoPla is here presented. Its specifications, e.g., XY-travel range of 50 mm × 50 mm and sub-micrometric accuracy; and some novel designed solutions, e.g., a three-layer and two-stage architecture are described. Once defined the prototype, an error analysis is performed to propose improvement design features. Then, the metrology loop of the system is mathematically modelled to define the propagation of the different sources. Several simplifications and design hypothesis are justified and validated, including the assumption of rigid body behavior, which is demonstrated after a finite element analysis verification. The different error sources and their estimated contributions are enumerated in order to conclude with the final error values obtained from the error budget. The measurement deviations obtained demonstrate the important influence of the working environmental conditions, the flatness error of the plane mirror reflectors and the accurate manufacture and assembly of the components forming the metrological loop. Thus, a temperature control of ±0.1 °C results in an acceptable maximum positioning error for the developed NanoPla stage, i.e., 41 nm, 36 nm and 48 nm in X-, Y- and Z-axis, respectively.

Experimental Approach for the Uncertainty Assessment of 3D Complex Geometry Dimensional Measurements Using Computed Tomography at the mm and Sub-mm Scales

The dimensional verification of miniaturized components with 3D complex geometries is particularly challenging. Computed Tomography (CT) can represent a suitable alternative solution to micro metrology tools based on optical and tactile techniques. However, the establishment of CT systems’ traceability when measuring 3D complex geometries is still an open issue. In this work, an alternative method for the measurement uncertainty assessment of 3D complex geometries by using CT is presented. The method is based on the micro-CT system Maximum Permissible Error (MPE) estimation, determined experimentally by using several calibrated reference artefacts. The main advantage of the presented method is that a previous calibration of the component by a more accurate Coordinate Measuring System (CMS) is not needed. In fact, such CMS would still hold all the typical limitations of optical and tactile techniques, particularly when measuring miniaturized components with complex 3D geometries and their inability to measure inner parts. To validate the presented method, the most accepted standard currently available for CT sensors, the Verein Deutscher Ingenieure/Verband Deutscher Elektrotechniker (VDI/VDE) guideline 2630-2.1 is applied. Considering the high number of influence factors in CT and their impact on the measuring result, two different techniques for surface extraction are also considered to obtain a realistic determination of the influence of data processing on uncertainty. The uncertainty assessment of a workpiece used for micro mechanical material testing is firstly used to confirm the method, due to its feasible calibration by an optical CMS. Secondly, the measurement of a miniaturized dental file with 3D complex geometry is carried out. The estimated uncertainties are eventually compared with the component’s calibration and the micro manufacturing tolerances to demonstrate the suitability of the presented CT calibration procedure. The 2U/T ratios resulting from the validation workpiece are, respectively, 0.27 (VDI) and 0.35 (MPE), by assuring tolerances in the range of ± 20–30 µm. For the dental file, the EN < 1 value analysis is favorable in the majority of the cases (70.4%) and 2U/T is equal to 0.31 for sub-mm measurands (L < 1 mm and tolerance intervals of ± 40–80 µm).

Analysis of Surface Extraction Methods Based on Gradient Operators for Computed Tomography in Metrology Applications

Among the multiple factors influencing the accuracy of Computed Tomography measurements, the surface extraction process is a significant contributor. The location of the surface for metrological applications is generally based on the definition of a gray value as a characteristic of similarity to define the regions of interest. A different approach is to perform the detection or location of the surface based on the discontinuity or gradient. In this paper, an adapted 3D Deriche algorithm based on gradient information is presented and compared with a previously developed adapted Canny algorithm for different surface types. Both algorithms have been applied to nine calibrated workpieces with different geometries and materials. Both the systematic error and measurement uncertainty have been determined. The results show a significant reduction of the deviations obtained with the Deriche-based algorithm in the dimensions defined by flat surfaces.

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

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.

Development of the control strategy of a 2D nanopositioning long-range stage

In order to provide an effective positioning along a wide working range with nanometre resolution, a two-dimensional stage platform has been designed and manufactured. In view of the demanding metrological performance, the drive system and control strategy are being analysed and developed. Thus, this paper describes the preliminary modelling of the control when using four custom-made Halbach linear motors as a driving system. Firstly, the 1D control case is defined and validated by simulation. The different required blocks of the loop are presented and an initial controller solution is proposed to achieve the established positioning features. Secondly, the 2D scheme is presented to define all the needs of the whole control, including all sensors and actuators of the system. In addition, this work justifies the hardware and software selected, as an optimal low-cost solution for the developed long-range stage prototype.

Homing Sensor System Design for a 2D Long Range Nanopositioning Moving Platform

The nanotechnology field has been developing strongly in recent years and ultra-precision measuring systems are nowadays required. A new two-dimensional moving platform with 50x50 mm range of travel, nanometer resolution and sub micrometer accuracy is being designed by the authors in order to be integrated with an Atomic Force Microscope (AFM). In this work the definition, design and experimental characterization of a homing sensor system for this 2D moving platform is presented. The homing sensor system will allow the generation of an absolute 2D reference for the platform (X-Y axis and θz rotation), defining an initial cero for the measuring system, which is based on laser encoders.