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Metrology

Metrology is an international, peer-reviewed, open access journal on the science and technology of measurement and metrology, published quarterly online by MDPI.

Quartile Ranking JCR - Q3 (Instruments and Instrumentation)

All Articles (188)

  • Technical Note
  • Open Access

Many fields or disciplines (e.g., uncertainty analysis in measurement science) require a combination of probability distributions. This technical note examines three methods for combining probability distributions: weighted linear pooling, geometric pooling, and the law of combination of distributions (LCD). Although these methods have been discussed in the literature, a systematic comparison of them appears insufficient. In particular, there is no discussion in the literature regarding the potential information loss that these methods may cause. This technical note aims to fill this gap. It provides insights into these three methods under the normality assumption. It shows that the weighted linear pooling method preserves all the variability (including heterogeneity) information in the original distributions; neither the geometric pooling method nor the LCD method preserves all the variability information, leading to information loss. We propose an index for measuring the information loss of a method with respect to the weighted linear pooling method. This technical note also shows that the weighted linear pooling method can be used as an alternative to the traditional random-effects meta-analysis. Three examples are presented: the combination of two normal distributions, the combination of three discrete distributions, and the determination of the Newtonian constant of gravitation.

4 January 2026

The weighted PDFs of the two original distributions with 
  
    
      
        μ
      
      
        1
      
    
    =
    10
  
, 
  
    
      
        σ
      
      
        1
      
    
    =
    2
  
 and 
  
    
      
        μ
      
      
        2
      
    
    =
    20
  
, 
  
    
      
        σ
      
      
        2
      
    
    =
    3
  
, and the combined PDFs based on the three methods.

Photoacoustic (PA) velocimetry offers a promising solution to the limitations of conventional techniques for measuring blood flow velocity. Given its moderate penetration depth and high spatial resolution, PA imaging is considered suitable for measuring low-velocity blood flow in capillaries located at moderate depths. High-resolution measurements based on PA signals from individual blood cells can be achieved using a high-frequency transducer. However, high-frequency signals attenuate rapidly within biological tissue, restricting the measurable depth. Consequently, low-frequency transducers are required for deeper measurements. To date, PA flow velocimetry employing low-frequency transducers remains insufficiently explored. In this study, we investigated the effect of the concentration of particles that mimic blood cells within vessels under low-concentration conditions. The performance of flow velocity measurement was evaluated using an ultrasonic transducer (UST) with a center frequency of 10 MHz. The volume fraction of particles in the solution was systematically varied, and the spatially averaged flow velocity was assessed using two different distinct analysis methods. One method employed a time-shift approach based on cross-correlation analysis. Flow velocity was estimated from PA signal redpairs generated by particles dispersed in the fluid, using consecutive pulsed laser irradiations at fixed time intervals. The other method employed a pulsed Doppler method in the frequency domain, widely applied in ultrasound Doppler measurements. In this method, flow velocity redwas estimated from the Doppler-shifted frequency between the transmitted and received signals of the UST. For the initial analysis, numerical simulations were performed, followed by experiments based on displacement measurements equivalent to velocity measurements. The target was a capillary tube filled with an aqueous solution containing particles at different concentration levels. The time–domain method tended to underestimate flow velocity as particle concentration increased, whereas the pulsed Doppler method yielded estimates consistent with theoretical values, demonstrating its potential for measurements at high concentrations.

18 December 2025

Theoretical diagram of Doppler frequency analysis using the PW Doppler method: (a) time signal with a phase shift of —
  
    π
    /
    8
  
, (b) time signal with a phase shift of —
  π
, (c) time signal with a phase shift of —
  
    3
    π
    /
    2
  
, and (d) variation of correlation values with a phase change.

Enhancing GNSS-INS-Based Surveying with Time of Flight Cameras

  • Amna Qayyum,
  • Joël Bachmann and
  • David Eugen Grimm

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.

16 December 2025

Leica GS18 I: (a) top view. (b) front view with the built-in camera. (c) side view showing the battery compartment and the services panel. (Source: [17]).

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.

14 December 2025

Showcase of the prototype photogrammetric calibration system.

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Metrology - ISSN 2673-8244