Dimensional Metrology Research Articles

Self-traceable angle standards with simplified traceability chain for dimensional metrology

Abstract Traceability is a fundamental issue for ensuring accuracy of nanometrology. A shortened traceability chain is advantageous for reducing calibration steps, thus reducing errors and raising application efficiency. A novel kind of two-dimensional grating is manufactured by atom lithography, whose pitch and (orthogonal) angle values are directly determined by natural constants, offering a feasible approach for effectively shortening the traceability chain. The PTB’s calibration results show that the two-dimensional grating has excellent orthogonality with a deviation of only 0.001°. Application of the two-dimensional grating is demonstrated for the characterization of the angular distortion of a SEM, showing its great application potential.

A research on improving the precision of laser tracker in alignment based on Pareto improvement principle.

The accuracy of laser trackers in large-scale dimensional metrology is subject to various influencing factors, with instrument positioning being a primary source of error. To address this, a multi-objective optimization algorithm, grounded in the Pareto improvement principle, is proposed. This algorithm is designed to optimize instrument placement, thereby minimizing measurement errors and enhancing the algorithm's efficacy in error reduction. Thereby, this article proved that positioning the laser tracker consistently on one side of the measurement area and aligning its height with the measuring points can effectively reduce the uncertainty of control point errors by up to 50%.

Computational vibration mitigation using phase interpolation in digital holographic microscopy for overlay metrology

Digital holographic microscopy retrieves amplitude and phase information of an image which allows us to computationally correct for imperfections in the imaging optics. However, digital holographic microscopy is an interferometric technique that is inherently sensitive to undesired phase variations between object and reference beam. These phase variations lower the fringe contrast if they are integrated over a finite exposure time which leads to a reduced amplitude of the retrieved image. This results in significant errors in applications that rely on a stable and accurate amplitude measurement, such as optical overlay metrology in the semiconductor industry. We present experimental results on a computational vibration mitigation method for the application of overlay metrology using phase interpolation between a sequence of measured holograms and demonstrate its capability to improve metrology precision in an overlay metrology application that uses digital holographic microscopy.

Shortened and simplified traceability chain for dimensional metrology based on self-traceable standards

Abstract Nanoscale measurement is an essential task of nanomanufacturing, and measurement traceability is a fundamental aspect of nanoscale measurement. High-precision nanoscale measurement instruments (e.g. atomic force microscopes (AFM) and scanning electron microscopes (SEM)) need to be calibrated by traceable standards to ensure their accuracy and reliability. However, due to the suboptimal accuracy, uniformity, and consistency of existing standards, they need to be calibrated by metrological instruments traceable to primary length standards (e.g. physical wavelength standards) before use. This results in a long traceability chain that leads to error accumulation and significantly reduces calibration efficiency. This paper proposes a novel shortened and simplified traceability chain, where the physical wavelength standard corresponding to the 7S3 → 7P4° transition frequency of chromium atoms is materialized into self-traceable gratings using the atom lithography technology. The self-traceable gratings can then be directly applied for calibrating measurement instruments. To verify this approach, the self-traceable gratings are calibrated using a metrological AFM of the Physikalisch-Technische Bundesanstalt. Measurement results confirmed the feasibility of the approach. Particularly, our results show that the self-traceable gratings have excellent uniformity over different measurement areas and consistency over different samples, both at 0.001 nm level. Finally, the application of the self-traceable gratings for the calibrations of a commercial AFM and SEM is demonstrated. The new traceability chain significantly simplifies the calibration process, providing a more reliable and higher efficient calibration approach for advanced nanomanufacturing than that of the state-of-the-art.

A novel semi-supervised robust learning framework for dynamic generative latent variable models and its application to industrial virtual metrology

Among a variety of virtual metrology models, dynamic generative latent variable models (DGLVMs) have proven to be an effective tool, owing to outstanding advantages in dealing with complicated data characteristics including temporal correlations, variable colinearities, high dimensionality, and process and measurement uncertainties. Presently, the vast majority of DGLVMs are developed upon the assumption that data are Gaussian-distributed, which is however, non-robust against outlying data and leads the DGLVMs to compromised performance, as the Gaussian distribution is susceptible to outliers that would skew the estimated parameters of DGLVMs. In view of this, this paper proposes a semi-supervised robust learning (SsRL) framework for the DGLVMs by designing an ad-hoc fully robust model structure that handles the outlying data by means of the heavy-tail properties of Student’s t distribution. In addition, the SsRL-DGLVM framework is initiated as a concrete model using probabilistic slow feature analysis (denoted RoSsPSFA) for which a rigorous training algorithm without resorting to any approximations is developed. The performance of the RoSsPSFA is thoroughly evaluated by both numerical and real-world industrial cases, showing the RoSsPSFA’s better immunity against outlying data and higher generalization accuracy.

Raman spectroscopy capabilities for advanced semiconductor technology devices

In semiconductor processing and metrology, Raman spectroscopy is a valuable characterization tool because of its nondestructive nature, high throughput, and versatility in terms of parameter sensitivity. However, with the miniaturization of semiconductor devices, the inherent diffraction limit of the optical technique becomes a roadblock. In order to re-enable the strengths of Raman spectroscopy at the nanometer scale, we exploit polarization-induced enhancement effects that focus the excitation light into the region of interest, without the need for external probes or particles. This allows the detection of structures with dimensions far smaller than the excitation wavelength, unlocking the strengths of Raman spectroscopy at the nanoscale for, e.g., stress and composition measurements. Moreover, under these conditions the experiment probes the totality of the materials stack and we show how this transforms the technique into a volumetric and geometric measurement. The result is a completely new application domain for Raman spectroscopy as a critical dimensional metrology toolkit for a wide variety of semiconducting and metallic materials.

Step height measurement of monoatomic silicon crystal lattice steps with a commercial atomic force microscope

Abstract Precise control of advanced materials relies on accurate dimensional metrology at the sub-nanometre scale. At this scale, the accuracy of scanning probe microscopy (SPM) has been limited by the lack of traceable transfer standard artefacts with calibration structures of suitable dimensions. With the adoption in 2019 of the silicon crystal lattice spacing as a secondary realization of the metre in the International System of Units (SI), SPM users have direct access to a realization of the SI metre at the sub-nanometre level by means of the step height of self-assembled monatomic lattice steps that can form on the surface of silicon crystals. A key challenge of successfully adopting this pathway is establishing the need for established protocols to minimize measurement errors and artifacts in routine laboratory use.
In this study, step height measurements of monoatomic lattice steps in an ordinal/staircase structure on a Si(111) crystal surface have been derived from images acquired with a commercially available, research-level atomic force microscope (AFM). Measurement results derived from AFM images using three different SPM image processing and analysis software packages are compared. Significant sources of measurement uncertainty are identified; principally the contribution from the dependence on scan direction. The calibration of the
AFM derived from this measurment was used to traceably measure the sub-nanometre lattice steps on a silicon carbide crystal surface to demonstrate the viability of this calibration pathway.

A Performance Comparison of 3D Survey Instruments for Their Application in the Cultural Heritage Field.

Thanks to the recent development of innovative instruments and software with high accuracy and resolution, 3D modelling provides useful insights in several sectors (from industrial metrology to cultural heritage). Moreover, the 3D reconstruction of objects of artistic interest is becoming mandatory, not only because of the risks to which works of art are increasingly exposed (e.g., wars and climatic disasters) but also because of the leading role that the virtual fruition of art is taking. In this work, we compared the performance of four 3D instruments based on different working principles and techniques (laser micro-profilometry, structured-light topography and the phase-shifting method) by measuring four samples of different sizes, dimensions and surface characteristics. We aimed to assess the capabilities and limitations of these instruments to verify their accuracy and the technical specifications given in the suppliers' data sheets. To this end, we calculated the point densities and extracted several profiles from the models to evaluate both their lateral (XY) and axial (Z) resolution. A comparison between the nominal resolution values and those calculated on samples representative of cultural artefacts was used to predict the performance of the instruments in real case studies. Overall, the purpose of this comparison is to provide a quantitative assessment of the performance of the instruments that allows for their correct application to works of art according to their specific characteristics.

Lensless single-shot dual-wavelength digital holography for industrial metrology

We demonstrate lensless single-shot dual-wavelength digital holography for high-speed 3D imaging in industrial inspection. Single-shot measurement is realized by combining off-axis digital holography and spatial frequency multiplexing of the two wavelengths on the detector. The system has 9.1 µm lateral resolution and a 50 µm unambiguous depth range. We determine the theoretical accuracy of off-axis dual-wavelength phase reconstruction for the case of shot-noise-limited detection. Experimental results show good agreement with the proposed model. The system is applied to industrial metrology of calibrated test samples and chip manufacturing.

Curved Linear Diode Array Imaging of a Historic Anchor Recovered from East Anglia ONE Offshore Wind Farm

The Industrial Metrology Business Unit of Nikon Corporation, on behalf of ScottishPower Renewables and Maritime Archaeology (MA), Southampton, UK, has employed X-ray CT (computed tomography) to visualise the internal structure of an anchor found in the North Sea. The non-destructive method of internal inspection and measurement has helped to determine approximately when it was made. The results indicate that the artefact, initially thought to be potentially Roman, is probably more recent, likely dating to between the late 16th and early 17th centuries CE. This paper presents the discovery, recovery, analysis and interpretation of a significant find from a UK offshore wind farm and underscores the valuable role that non-destructive X-ray CT played in the investigation.

Measuring the permittivity of fused silica with planar on-wafer structures up to 325 GHz

Fused silica has become an interesting alternative to silicon for millimeter-wave (mmWave) applications. Unfortunately, there are a few reports on the measurement of fused silica's permittivity above 110 GHz that use electrical rather than optical methods. Given that mmWave applications use electrical circuits, additional electrical data would be useful to industry. To test the feasibility of electrical methods, we applied on-wafer techniques based on coplanar waveguide transmission lines to measure the complex permittivity of fused silica to 325 GHz. Our approach used the multiline thru-reflect-line algorithm on the scattering parameter measurements of transmission lines. Our method combined these results with dc measurements of the resistivity of the metals, simulations of the coplanar waveguide cross section, and dimensional metrology. In short, our measurements do not show significant dielectric dispersion for fused silica up to 325 GHz. The resulting complex permittivity was ϵr=3.87±0.03 and a loss tangent tanδ< 0.005 from 320 MHz to 325 GHz. To support our conclusions, we performed an uncertainty analysis considering relevant sources of uncertainty. In the broader context, these results show that fused silica is a suitable substrate for mmWave electronics where the loss tangent must be less than 0.005 up to 325 GHz.

Low-power laser image enhancement via deep feature recovery for HDR 3D measurement.

Laser 3D measurement has gained widespread applications in industrial metrology . Still, it is usually limited by surfaces with high dynamic range (HDR) or the colorful surface texture of measured surfaces, such as metal and black industrial parts. Currently, conventional methods generally work with relatively strong-power laser intensities, which could potentially damage the sample or induce eye-safety concerns. For deep-learning-based methods, due to the different reflectivity of the measured surfaces, the HDR problem may require cumbersome adjustment of laser intensity in order to acquire enough training data. Even so, the problem of inaccurate ground truth may occur. To address these issues, this paper proposes the deep feature recovery (DFR) strategy to enhance low-light laser stripe images for achieving HDR 3D reconstruction with low cost, high robustness, and eye safety. To the best of our knowledge, this is the first attempt to tackle the challenge of high measurement costs associated with measuring HDR surfaces in laser 3D measurement. In learning the features of low-power laser images, the proposed strategy has a superior generalization ability and is insensitive to different low laser powers and variant surface reflectivity. To verify this point, we specially design the experiments by training the network merely using the diffusely reflective masks (DRM951) and testing the performance using diffusely reflective masks, metal surfaces, black industrial parts (contained in the constructed datasets DRO690, MO191, and BO107) and their hybrid scenes. Experimental results demonstrate that the proposed DFR strategy has good performances on robustness by testing different measurement scenes. For variously reflective surfaces, such as diffusely reflective surfaces, metal surfaces, and black parts surfaces, the reconstructed 3D shapes all have a similar quality to the reference method.

Efficient automated high dynamic range 3D measurement via deep reinforcement learning.

High dynamic range 3D measurement technology, utilizing multiple exposures, is pivotal in industrial metrology. However, selecting the optimal exposure sequence to balance measurement efficiency and quality remains challenging. This study reinterprets this challenge as a Markov decision problem and presents an innovative exposure selection method rooted in deep reinforcement learning. Our approach's foundation is the exposure image prediction network (EIPN), designed to predict images under specific exposures, thereby simulating a virtual environment. Concurrently, we establish a reward function that amalgamates considerations of exposure number, exposure time, coverage, and accuracy, providing a comprehensive task definition and precise feedback. Building upon these foundational elements, the exposure selection network (ESN) emerges as the centerpiece of our strategy, acting decisively as an agent to derive the optimal exposure sequence selection. Experiments prove that the proposed method can obtain similar coverage (0.997 vs. 1) and precision (0.0263 mm vs. 0.0230 mm) with fewer exposures (generally 4) compared to the results of 20 exposures.

Research on the Planning and Construction of National Industrial Metrology Center Park

Metrology refers to the activity of achieving unified physical and chemical units and ensuring accurate and reliable measurement values.In the field of metrology, we have always adhered to the principle that “Only accurate measurement can make perfect measurement”, and have clearly defined the important role of metrology in the manufacturing industry, then take “Only to create a fine, can be accurately measured” as the standard, the dialectical unity between the two. Different from the general sense of industrial architecture, the core task of industrial metrology park is “To build houses for precision equipment, to build laboratories for metrologists”, this has put forward many new requirements to the capital construction work from the planning, the design to the construction. With the successful acceptance of the park and put into use, this paper reviews and combs the construction process from the point of view of the pre-planning and design of the park, and puts forward a Shandong model for reference for the construction of similar projects.

Mathematical Camera Array Optimization for Face 3D Modeling Application.

Camera network design is a challenging task for many applications in photogrammetry, biomedical engineering, robotics, and industrial metrology, among other fields. Many driving factors are found in the camera network design including the camera specifications, object of interest, and type of application. One of the interesting applications is 3D face modeling and recognition which involves recognizing an individual based on facial attributes derived from the constructed 3D model. Developers and researchers still face difficulty in reaching the required high level of accuracy and reliability needed for image-based 3D face models. This is caused among many factors by the hardware limitations and imperfection of the cameras and the lack of proficiency in designing the ideal camera-system configuration. Accordingly, for precise measurements, we still need engineering-based techniques to ascertain the specific level of deliverables quality. In this paper, an optimal geometric design methodology of the camera network is presented by investigating different multi-camera system configurations composed of four up to eight cameras. A mathematical nonlinear constrained optimization technique is applied to solve the problem and each camera system configuration is tested for a facial 3D model where a quality assessment is applied to conclude the best configuration. The optimal configuration is found to be a 7-camera array, comprising a pentagon shape enclosing two additional cameras, offering high accuracy. For those who prioritize point density, a 9-camera array with a pentagon and quadrilateral arrangement in the X-Z plane is a viable choice. However, a 5-camera array offers a balance between accuracy and the number of cameras.

Enhancing particle size characterization performance through proficiency testing program: result and insights from inter-laboratory comparison

The proficiency testing (PT) for particle size characterization by inter-laboratory comparison was organized by the dimensional metrology department of the National Institute of Metrology Thailand (NIMT). This program aims to enhance and to expand the efficiency and capability of testing laboratories in the field of particle size characterization using various techniques, including atomic force microscope (AFM), transmission electron microscope (TEM), scanning electron microscope (SEM), and dynamic light scattering (DLS). The measurement range covers nanometer to micrometer scale. These instruments are importance for research and development especially to nanotechnology related industries. The PT program was conducted in 2022 where five artifacts were used: monodispersed gold nanoparticle (diameter 20 nm), monodispersed polystyrene particle (diameter 100 nm, 500 nm, and 1500 nm) and monodispersed silica oxide particle (diameter 100 nm). The monodispersed polystyrene particles, diameter 100 nm and 1500 nm are certified reference materials (CRMs). These two artefacts were used as the reference to evaluate accuracy of participant laboratories. The other 3 artefacts are reference material under development. Hence, the assigned values were calculated from consensus among all participants. To evaluate the performance of participant laboratories, En values and z-scores were calculated for each artefact and each measuring technique. The assessment of participant performance through performance scores allows the participant to determine how accurate and how appropriate the measurement results and measurement uncertainties evaluation are. From the results, unsatisfied results can be categorized into three scenarios. First, the measurement uncertainties were not appropriately evaluated. Secondly, measurands obtained from all measuring techniques are not the same. Lastly, the magnification used in microscopy techniques plays a crucial role to resolution and accuracy of size determination.

Two different experimental approaches for the uncertainty determination of X-ray computed tomography dimensional measurements on lattice structures

X-ray computed tomography (CT) is increasingly used in industrial dimensional metrology. However, the establishment of metrological traceability can be challenging for CT dimensional measurements, as the evaluation of their uncertainty is generally non-trivial. Moreover, uncertainty determination becomes even more difficult when dealing with complex measurement tasks, such as in the case of lattice structures produced by additive manufacturing, characterized by features not accessible from the outside and/or by complex surface topographies, which are problematic to be calibrated using other measuring principles to ensure sufficiently low calibration uncertainty. This paper presents a critical investigation of two different experimental approaches for the uncertainty determination of CT dimensional measurements performed on components with inaccessible and/or complex geometries, as well as complex surface topography. The first approach, the “substitution method”, is applied in this work using a newly developed reference object as the basis for the uncertainty assessment procedure through substitution measurements. The second one, the “multiple measurements approach”, is based on repeated measurements both on the uncalibrated workpiece in multiple orientations and on simple calibrated standards. This second approach, initially introduced some years ago for tactile coordinate measuring machines, is now investigated in this work for its application to CT metrology. The two approaches are discussed and compared through an industrial case study: the dimensional verification of lattice structures fabricated by metal additive manufacturing. For the selected case, both approaches yielded comparable measurement results and uncertainties. Finally, the multiple measurements approach was further investigated by applying it to the CT measurement of the calibrated object. The paper also discusses the open issues of both methods and outlines directions for future investigations.

Computed Tomography Artifact Reduction Employing a Convolutional Neural Network Within the Context of Dimensional Metrology

Abstract Utilizing accurate, nondestructive testing methods to improve quality control and reduce manufacturing errors has gained prominence in light of industry development in various fields. Industrial computed tomography (CT) scanning carries considerable weight among all conventional methods because of their unique features, such as providing a three-dimensional specimen model. Due to the prevalence of metals with high linear attenuation coefficients in industrial applications, beam hardening and scatter artifacts are two of the most prevalent artifacts in any reconstructed volume. Other notable artifacts include those with a nonideal focal spot and conical beam radiation. These artifacts may manifest as a distortion of gray value peaks, systematic discrepancies, blurring-like cupping, and streaking in reconstructed images, degrading volume reconstruction quality. In this paper, the effect of these artifacts is illustrated and mitigated by adopting our proposed method, a combination of conventional and contemporary techniques, including the use of a pretrained convolutional neural network (CNN). Five tests are replicated in different geometric parameters to perform a geometric configuration analysis, indicating how effective the proposed approach is at encountering different geometric situations. The results demonstrate that the proposed method has substantially achieved its goal of improving the accuracy of dimensional metrology performed on our phantom.

Dimensional metrology of image fusion: a computer vision approach

Many digital image processing works have emerged in recent decades in various fields. In industry and laboratories, we can highlight the application in the metrological area, where many equipments have the image of a specimen as an essential element to carry out any type of analysis or measurement. In this work, we present some results of dimensional measurement by image fusion. A methodology that quantitatively estimates a characteristic of interest of an image obtained by an optical coordinate measuring machine is presented.

CT-Based Dimensional Metrology for Quality Assessment of the Internal Structure of Additive Manufactured Aluminum Parts

Two common types of internal defects of additively manufactured (AM) samples are lack-of-fusion and gas-entrapped porosities. These internal defects can have different physical origins and particular local characteristics (e.g., different shape, size). Thus, the use of reliable non-destructive inspection techniques is essential for the accurate assessment of integrity, allowing the applicable AM processing parameters correction. To overcome this challenge, this work aims to evaluate the accuracy of volumetric characteristics measured by computed tomography for porosity evaluations in AM samples, including assessment of measurement uncertainty. The effect of different cumulative thickness on the evaluated measurements accuracy is also assessed. The results show that deviations of defect size measurements can be below 2% if the proposed procedure is followed. In addition, the expanded uncertainty can be up to 10% of the measured magnitude when the cumulative thickness is increased to 70 mm. The physical relationships obtained between the cumulative thickness and the individual measurements are also presented.