Samanta Piano

Additively manufactured (AM) workpieces often undergo secondary machining operations to meet functional and geometric requirements, which can affect the optical properties of the surface, and thereby the performance of optical measurement systems. This study investigates which surface texture parameters most significantly influence the accuracy and precision of form error measurements obtained using a fringe projection (FP) system. Four AM workpieces, two as-built and two with secondary milling operations, were measured under five different exposure time settings ranging from 50 ms to 250 ms. Measurement accuracy was assessed by calculating form error bias relative to a reference surface acquired via contact measurements on a coordinate measuring machine (CMM). On the other hand, measurement precision was assessed by evaluating the uncertainty of the form error using Monte Carlo simulation. This uncertainty was propagated from the reference ground-truth surface acquired with a CMM, incorporating the standard uncertainty component of the FP measurement procedure through a regional Gaussian Random Field (rGRF) model. Results show that height (i.e. S _z , S _q , S _p , S _pk ) and volume surface texture parameters (i.e. V _mp , V _vc ) are strongly correlated with bias, while functional, hybrid and spatial parameters (i.e. S _mr , S _dq , S _dr , S _al ) impact the measurement uncertainty. Additionally, the proposed methodology demonstrated robustness across evaluated exposure time settings, as bias and expanded uncertainty variations remained below 1.3% of the mean form error value and 8.3% of the mean flatness value, respectively. This suggests that, for the surface conditions and optical setup considered in this study, exposure time does not need to be manually tuned. These findings support the integration of surface texture analysis into optical form error measurement workflows, improving the reliability and automation of FP-based inspection in industrial AM applications.

Surface normal estimation is a fundamental step in many applications, including robotics, manufacturing inspection and quality control. Reliable surface normal information is essential for accurate surface reconstruction, defect detection, and geometric analysis. In this paper, different approaches for estimating surface normal vectors from point cloud data are investigated, with particular focus on their suitability for generating ground-truth surface normals. Such ground-truth measurements are required to evaluate and validate surface normal estimation techniques used in practical metrology and 3D sensing systems in accordance with established surface texture standards such as ISO 25178. The analysis focuses on methods based on neighbourhood clustering followed by a surface normal fitting procedure. In addition, the influence of point cloud noise on the accuracy and stability of the estimated normals is systematically studied. By comparing the performance of different estimation strategies under different noise conditions, their suitability for generating reliable reference surface normals is investigated. The results demonstrate how point cloud characteristics and noise levels affect the robustness of surface normal estimation and highlight the advantages and limitations of commonly used approaches. The proposed analysis provides practical guidance for selecting appropriate methods when generating ground-truth surface normals for the validation of optical and geometric measurement systems. To show that the studied approaches can be used for surface normal estimation independent of metrology equipment, they are applied to the point clouds acquired from laser scanners, confocal optical measurement equipment, coherence scanning interferometers, and fringe projection systems with a variety of test objects. The results show that the studied approaches can estimate the surface normals. Highly accurate surface normal estimation may ease surface texture studies. The findings contribute to improving the reliability of point cloud analysis and surface normal estimation in manufacturing metrology and related applications.

Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optics. By adopting quantum parameter estimation methods, we determine the ultimate precision limits for estimating spatial moments of a general three-dimensional distribution of incoherent point sources in the sub-diffraction regime. Specializing this result to the axial profile, we show that the information on the first moment (mean height) and standard deviation (roughness) is bounded by a constant. While classical imaging techniques fail to achieve this bound, a quantum inspired imaging technique based on spatial mode demultiplexing is proven to be optimal for estimating the axial standard deviation. This provides a powerful and experimentally accessible route to measuring roughness of nearly smooth surface patches beyond the diffraction limit.

In 2025, Metrology (ISSN 2673-8244) received its first Impact Factor of 1

Coherence scanning interferometry (CSI) is widely used for high-precision surface topography measurement, where accurate height reconstruction from interferometric correlograms remains a key issue. The Hilbert transform (HT) and frequency domain analysis (FDA) are well-established methods for surface reconstruction from CSI signals. This paper investigates and compares envelope- and phase-based implementations of HT and FDA using simulated CSI interferograms. Two representative surface profiles are considered: a trapezoidal profile and a smooth sinusoidal profile, allowing the effects of abrupt height discontinuities and low-signal-to-noise-ratio conditions to be examined separately. Reconstruction performance is evaluated as a function of the light-source bandwidth and the spatial frequency content of the interferometric signal. The results show that reconstruction accuracy strongly depends on local fringe-frequency behaviour, noise level and fringe-order determination, with phase-based methods generally offering higher precision and FDA providing increased robustness under noisy conditions. The findings provide insight into the limitations and applicability of HT- and FDA-based reconstruction strategies and offer guidance for selecting suitable approaches for CSI measurements involving complex surface features and degraded signal quality.

Driven by the growing demand for high-speed 3D measurement in advanced manufacturing, optical metrology algorithms must deliver high accuracy and robustness under dynamic conditions. Fringe projection profilometry (FPP) offers high precision, yet the 2pi ambiguity of the wrapped phase means that conventional absolute phase recovery typically relies on multiple coded patterns, sacrificing temporal resolution. Deep learning-based composite FPP (CFPP) shows promise for single-shot phase recovery from a composite fringe, but limited interpretability makes it difficult to assess reconstruction reliability or trace error sources in the absence of ground truth. To address this, we propose HSURE-CFPP (Heteroscedastic Snapshot-ensemble Uncertainty-aware Ratio Estimation for CFPP). HSURE-CFPP predicts the numerator-denominator ratio used for wrapped-phase computation with a heteroscedastic snapshot-ensemble network, enabling ultra-fast 3D imaging from a single composite fringe and producing pixel-wise uncertainty maps for confidence assessment and unreliable-region identification. Specifically, a heteroscedastic likelihood jointly estimates pixel-wise noise variance to capture data uncertainty, while a snapshot ensemble quantifies model uncertainty via dispersion across snapshots, yielding total predictive uncertainty as an interpretable reliability measure. Experiments on static and dynamic scenes demonstrate that HSURE-CFPP achieves high-accuracy reconstruction at high speed and that the predicted uncertainty correlates well with reconstruction errors, providing a deployable quality-assessment mechanism for deep-learning-based FPP.

Precision component displacement, processing, and manipulation in an industrial environment require the high-precision positioning and orientation of industrial robots. However, industrial robots’ positioning includes uncertainties due to assembly and manufacturing tolerances. It is therefore required to use calibration techniques for industrial robot parameters. One of the major sources of uncertainty is the one associated with industrial robot geometrical parameter values. In this paper, using multi-objective meta-heuristic optimization approaches and optical metrology measurements, more accurate Denavit–Hartenberg (DH) geometrical parameters of an industrial robot are estimated. The sensor data used to perform this calibration are the absolute 3D position readings using a highly accurate laser tracker (LT) and industrial robot joint angle readings. Other than position accuracy, the mean absolute deviation of the DH parameters from the manufacturer’s given parameters is considered as the second objective function. Therefore, the optimization problem investigated in this paper is a multi-objective one. The solution to the multi-objective optimization problem is obtained using different evolutionary and swarm optimization approaches. The evolutionary optimization approaches are nondominated sorting genetic algorithms and a multi-objective evolutionary algorithm based on decomposition. The swarm optimization approach considered in this paper is multi-objective particle swarm optimization. It is observed that NSGAII outperforms the other two optimization algorithms in terms of a more diverse Pareto front and the function corresponding to the positional accuracy. It is further observed that through using NSGAII for calibration purposes, the root mean squared for positional error has been improved significantly compared with nominal values.

In recent years, the growth of optical techniques has introduced the possibility of allowing several alternative methods for non-contact gear measurement to be utilised. Optical methods can offer many advantages over tactile, such as the potential to evaluate delicate surfaces quickly and measure the whole area of the gear tooth flank at the sub-micron level. However, to maximise their potential, the magnitude of error and characterisation of the sources of error and uncertainty need to be understood. By utilising a series of designed experiments with known size gear artefacts, the effects caused by the change of specific key instrument parameters can be evaluated. These measurement trials demonstrate how the results from experimental methodologies can be used to determine the statistical significance of any predetermined instrument variables under study. When correctly planned, designed experiments allow the identification of the sources of error. By applying statistical methods, we can determine if these sources are significant or not. This will allow determination of which parameters need to be defined when optimising the conditions for measurement by comparing the results with those from the UK National Gear Metrology Laboratory. This comparison can also provide guidance on developing measurement uncertainty.