Metrology

Rapid advancements in surveying technology have necessitated the development of more accurate and efficient tools. Leica Geosystems AG (Heerbrugg, Switzerland), a leading provider of measurement and surveying solutions, has initiated a study to enhance the capabilities of its GNSS INS-based surveying systems. This research focuses on integrating the Leica GS18 I GNSS receiver and the AP20 AutoPole with a Time of Flight (ToF) camera through sensor fusion. The primary objective is to leverage the unique strengths of each device to improve accuracy, efficiency, and usability in challenging surveying environments. Results indicate that the fused AP20 configuration achieves decimetre-level accuracy (2.7–4.4 cm on signalized points; 5.2–20.0 cm on natural features). In contrast, the GS18 I fused configuration shows significantly higher errors (17.5–26.6 cm on signalized points; 16.1–69.4 cm on natural features), suggesting suboptimal spatio-temporal fusion. These findings confirm that the fused AP20 configuration demonstrates superior accuracy in challenging GNSS conditions compared to the GS18 I setup with deviations within acceptable limits for most practical applications, while highlighting the need for further refinement of the GS18 I configuration.

The calibration of levelling staff is a key prerequisite for achieving high-precision levelling. Traditionally, this process is carried out using laser interferometric systems, which provide the required accuracy but are demanding in terms of operation, maintenance, and measurement conditions. This paper focuses on verifying the applicability of the convergent photogrammetry method for levelling staff calibration with a target accuracy of 0.010 mm. An experimental prototype of a photogrammetric calibration system (without real scale) was developed and tested using three different lenses, two processing software packages (Photomodeler and Agisoft Metashape), and two different approaches to camera calibration (self-calibration and field calibration). The repeatability of measurements was evaluated based on mutual lengths between selected checkpoints and the accuracy of determining the 3D positions of these points. The results showed that the Nikon AF-S NIKKOR 35 mm f/1.8G ED lens achieved the best repeatability and met the target accuracy requirement, while Photomodeler yielded smaller standard deviations in the determination of control point positions compared to Agisoft Metashape. The findings indicate that convergent photogrammetry, when applied under optimal conditions, has the potential to achieve the accuracy required for high-precision measurements in metrology, and may even offer an alternative to laser interferometric calibration systems in certain applications.

The concept of dynamic symmetry in art and extensive measurements on Greek vases suggest that a vase and its parts can be inscribed into similar rectangles, with all rectangles having the same ratio of lengths of their side. Such an observation is often used in describing self-similarity and fractal geometry. This work proposes a hypothesis that a logarithmic spiral describes the equation of the cross-section of a Greek vase. From extensive measurements, the parameters of such spirals are computed, and explicit formulae are derived for volume based on a few size measurements. The exact formula is quite complex and cannot be easily used, certainly not in antiquity. Therefore, a simple approximation formula is proposed for amphorae, the most important type of vase. This formula expresses the volume of the vase in terms of its diameter and the height of the corresponding solid. The approximation is compared with some exact volume computation results reported for amphorae, and it is shown that the proposed approximation is fairly close to the exact value. The simplicity of the proposed formula suggests an efficient method of calculating volume that was probably known in antiquity.