Sources Of Measurement Uncertainty Research Articles

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.

On Bayesian inference of reliability parameter in Burr-type XII model based on imprecise data: a survey on fuzzy modelling

There are always two major sources of uncertainty in measurements related to lifetime surveys: variation among the observations and imprecision of individual observation called fuzziness. The typical statistical analysis is based on variation among the observations and does not consider the imprecision due to individual observation. However, ignoring the imprecision of individual observations may cause losing information and getting misleading results. It is mandatory to analyse such data, to extend the real numbers classically and Bayesian estimation methods to fuzzy numbers. Inference on the Burr-type (BT) XII model, based on precise measurements, is carried out by researchers, yet the problem of estimating parameters, in the presence of fuzzy data, remains unresolved. We are estimating the BT XII distribution parameters and their corresponding reliability when the available data are in the fuzzy numbers. The maximum likelihood estimation (MLE), the Bayesian method and the method of moments are used for estimating parameters. Finally, these estimators are compared via a Monte-Carlo simulation study.

X-ray spectroscopy station for sample characterization at ELI Beamlines

X-ray spectroscopy is a demanded tool across multiple user communities. Here we report on a new station for X-ray emission spectroscopy at the Extreme Light Infrastructure Beamlines Facility. The instrument utilizes the von Hamos geometry and works with a number of different sample types, notably including liquid systems. We demonstrate a simple and reliable method for source position control using two cameras. This approach addresses energy calibration dependence on sample position, which is a characteristic source of measurement uncertainty for wavelength dispersive spectrometers in XES arrangement. We also present a straightforward procedure for energy calibration of liquid and powder samples to a thin film reference. The developed instrumentation enabled us to perform the first experimental determination of the Kα lines of liquidized K3Fe(CN)6 as well as powdered and liquidized FeNH4(SO4)2. Finally, we report on proof-of-principle use of a colliding jet liquid sample delivery system in an XES experiment.

Effectiveness of vertical error budget model for portable multi-beam echo-sounder in shallow water bathymetric survey

With the increasing availability of portable survey equipment and platforms, hydrographic data acquisition now offers a diverse range of device options and installation methods. Tailoring the mounting and installation of hydrographic survey devices to fit the boat or platform dimensions has become common practice. The use of portable equipment is essential, given the wide selection of combined options available in the market. Consequently, sensor offsets and device performance differ for each survey conducted, necessitating the constant verification of accuracy performance.This paper examines the capabilities of portable multibeam echosounder (MBES) deployments on various types of survey boats. The investigation focuses on error budget modeling and field tests. A model is developed to estimate the propagated uncertainty resulting from different sources of measurement uncertainties. The model primarily considers vertical sources of error in MBES surveys, as they have the most significant impact on hydrographic data quality. To validate the model, field tests are conducted at two different locations using different boat and device configurations. The results demonstrate that the modeled uncertainties align with the measured standard deviations, particularly in the Pramuka area, where the standard deviation of data acquired at the widest beam angle of ±60° is 0.25m, close to the predicted value of 0.28m. However, in the Patimban area, the model overestimates the uncertainty, predicting 0.27m compared to the measured standard deviation of 0.17m.

A Bayesian hierarchical age model for optical dating of single grains of quartz

In optical dating, the last time that a sample of sediment was exposed to sunlight is determined by dividing its equivalent dose (De) by the dose rate. For single-grain dating, the sample De is based on the statistical analysis of the distribution of De values estimated for individual grains, whereas the dose rate is usually determined from measurements of the environmental radioactivity of the bulk sample, together with allowances for radiation sources internal to the grains and cosmic rays. Conventionally, the De and dose rate are measured and analysed separately to produce an estimate of the depositional age of a sample, but this approach may result in loss of information because distributions of single-grain De values are influenced by several factors. Existing statistical models do not incorporate all the key information contributing to age estimation, such as the pattern and scale of dispersion of single-grain De values and dose rates, the associated measurement uncertainties, the effect of natural variability among grains, and the outlier probabilities of De and dose rate estimates. Here we propose an empirical Bayesian hierarchical age model (BHAM) for optical dating of quartz samples that incorporates the above information to estimate their depositional ages. The BHAM is based on the implementation of standardised growth curve and LnTn methods to integrate information on the full distribution of single-grain De values, sources of measurement uncertainty, beta-dose heterogeneity (observed or modelled), and detection of outliers. We present the results of validation tests using data sets of optically stimulated luminescence measurements and dose rates obtained for quartz samples dated previously from Denisova Cave (Russia) and for simulated samples. We conclude that the BHAM represents a robust and flexible approach to dealing with data for single grains of quartz within a Bayesian hierarchical framework and is suitable for application to sediments deposited in a variety of depositional settings.

Possibilities of Diffuse Reflectance Spectroscopy in Determining and Operational Control of the Optical Properties of Finely Dispersed Scattering Media

The characteristics of modern portable spectrometers based on photodetector arrays make it possible to create on their basis a new class of devices for operational control of the optical properties of various media. The introduction into the practice of diffuse reflectance spectroscopy with spatial resolution is hampered by the lack of an analysis of the influence of the width of the spectral region used and other sources of measurement uncertainty on the unambiguous determination of the optical properties of finely dispersed scattering materials. This article describes a method of determining the coefficient of local diffuse reflection and calculating the spectral parameters of the reduced scattering and absorption of radiation based on the differences in their shape, which are clearly manifested in a wide range of the spectrum. This allows the reduction in the determination of the desired spectral dependencies to the formation of a residual function that requires varying the values of only two parameters. A method for normalising the recorded spectral dependencies is described, which makes it possible to minimise the influence of the spectral characteristics of the equipment used on the recorded spectral–spatial profiles. Approbation of the method was carried out on examples of processing spectral–spatial diffuse reflection profiles of four samples of finely dispersed scattering structural materials, as well as diffuse reflection profiles of living tissue in the palm thenar region. The sources of uncertainty that affect the uniqueness of the obtained solutions are found, and solutions are proposed to minimise their influence on the desired spectral dependencies. The results obtained indicate the prospects of using the described method for creating equipment for non-destructive control of the optical properties of finely dispersed materials and media, including living tissues and food products.

Noise estimation for head-mounted 3D binocular eye tracking using Pupil Core eye-tracking goggles.

Head-mounted, video-based eye tracking is becoming increasingly common and has promise in a range of applications. Here, we provide a practical and systematic assessment of the sources of measurement uncertainty for one such device - the Pupil Core - in three eye-tracking domains: (1) the 2D scene camera image; (2) the physical rotation of the eye relative to the scene camera 3D space; and (3) the external projection of the estimated gaze point location onto the target plane or in relation to world coordinates. We also assess eye camera motion during active tasks relative to the eye and the scene camera, an important consideration as the rigid arrangement of eye and scene camera is essential for proper alignment of the detected gaze. We find that eye camera motion, improper gaze point depth estimation, and erroneous eye models can all lead to added noise that must be considered in the experimental design. Further, while calibration accuracy and precision estimates can help assess data quality in the scene camera image, they may not be reflective of errors and variability in gaze point estimation. These findings support the importance of eye model constancy for comparisons across experimental conditions and suggest additional assessments of data reliability may be warranted for experiments that require the gaze point or measure eye movements relative to the external world.

A Novel Parallel-Plate Dielectric Resonator Method for Broadband Complex Permittivity Measurement in the Millimeter-Wave Bands

This article proposes a novel measurement method based on parallel-plate dielectric resonator (PPDR) for determining complex permittivity of low-loss dielectric materials over a wide frequency range. Two 1.0-mm coaxial probes are placed symmetrically as a coupling structure in the center of top and bottom of the PPDR, and only the TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathrm{0np}}$</tex-math> </inline-formula> resonant modes will be selectively excited. For each value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> , the resonator will operate over a specific frequency range, within which there are usually multiple frequency points available for testing. Based on this unique feature, dielectric constants of cylindrical or disk-shaped samples can be measured from less than 20 up to 110 GHz by utilizing TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathrm{0np}}$</tex-math> </inline-formula> high-order modes. Rigorous analysis of the PPDR based on the electromagnetic field matching method is carried out and verified numerically. Moreover, the PPDR method is further validated experimentally by measuring several specimens processed from well-known materials, the main sources of measurement uncertainty are also analyzed in detail, and some recommendations are made accordingly. The results show that the PPDR method can perform high-accuracy measurement of complex permittivity in the millimeter-wave bands, even when the sample thickness exceeds the maximum value limited by the current state of the art.

Evaluation of Matrix-Assisted Laser Desorption Ionization-Time of Flight Mass Spectrometry for Molecular Typing of Acinetobacter baumannii in Comparison with Orthogonal Methods.

Colonization and subsequent health care-associated infection (HCAI) with Acinetobacter baumannii are a concern for vulnerable patient groups within the hospital setting. Outbreaks involving multidrug-resistant strains are associated with increased patient morbidity and mortality and poorer overall outcomes. Reliable molecular typing methods can help to trace transmission routes and manage outbreaks. In addition to methods deployed by reference laboratories, matrix-assisted laser desorption ionization-time of flight mass spectrometry (MALDI-TOF MS) may assist by making initial in-house judgments on strain relatedness. However, limited studies on method reproducibility exist for this application. We applied MALDI-TOF MS typing to A. baumannii isolates associated with a nosocomial outbreak and evaluated different methods for data analysis. In addition, we compared MALDI-TOF MS with whole-genome sequencing (WGS) and Fourier transform infrared spectroscopy (FTIR) as orthogonal methods to further explore their resolution for bacterial strain typing. A related subgroup of isolates consistently clustered separately from the main outbreak group by all investigated methods. This finding, combined with epidemiological data from the outbreak, indicates that these methods identified a separate transmission event unrelated to the main outbreak. However, the MALDI-TOF MS upstream approach introduced measurement variability impacting method reproducibility and limiting its reliability as a standalone typing method. Availability of in-house typing methods with well-characterized sources of measurement uncertainty could assist with rapid and dependable confirmation (or denial) of suspected transmission events. This work highlights some of the steps to be improved before such tools can be fully integrated into routine diagnostic service workflows for strain typing. IMPORTANCE Managing the transmission of antimicrobial resistance necessitates reliable methods for tracking outbreaks. We compared the performance of MALDI-TOF MS with orthogonal approaches for strain typing, including WGS and FTIR, for Acinetobacter baumannii isolates correlated with a health care-associated infection (HCAI) event. Combined with epidemiological data, all methods investigated identified a group of isolates that were temporally and spatially linked to the outbreak, yet potentially attributed to a separate transmission event. This may have implications for guiding infection control strategies during an outbreak. However, the technical reproducibility of MALDI-TOF MS needs to be improved for it to be employed as a standalone typing method, as different stages of the experimental workflow introduced bias influencing interpretation of biomarker peak data. Availability of in-house methods for strain typing of bacteria could improve infection control practices following increased reports of outbreaks of antimicrobial-resistant organisms during the COVID-19 pandemic, related to sessional usage of personal protective equipment (PPE).

A diagnostic for quantifying secondary species emission from electrospray devices.

Measuring the polydisperse beam of charged species emitted by an electrospray device requires accurate measurements of current. Secondary species emission (SSE) caused by high-velocity nanodroplet or molecular ion impacts on surfaces contributes to substantial uncertainty in current measurements. SSE consists of both positive and negative species; hence, mitigating measurement uncertainty requires different considerations other than plasma diagnostic techniques. The probe and analysis methods described herein distinguish between current contributions from positive SSE, negative SSE, and primary species. Separating each contribution provides positive and negative SSE yield measurements and corrected current measurements that reflect the true primary current. Sources of measurement uncertainty in probe design are discussed, along with appropriate mitigation methods. The probe and analysis techniques are demonstrated on an ionic liquid electrospray operating in a droplet emission mode to obtain an angular distribution of positive and negative SSE yields for an ionic liquid electrospray.

Validation of an Uncertainty Propagation Method for Moving‐Boat Acoustic Doppler Current Profiler Discharge Measurements

AbstractThe moving‐boat Acoustic Doppler Current Profiler (ADCP) gauging method is extensively used to measure the discharge of rivers and canals. Informed decisions related to water management require reliable estimates of the uncertainty of such measurements. The evaluation of the uncertainty is however a difficult task because of the complexity of the ADCP data workflow and the lack of reference discharges in rivers and canals. This study presents an evolution of the OURSIN method, which follows the framework of the Guide to the expression of Uncertainty in Measurement. The method has been implemented in the QRevInt software which provides an ADCP data quality review prior to the uncertainty analysis. As a computationally efficient alternative to the Monte Carlo approach, the uncertainty propagation combines elemental measurement uncertainty sources, transect‐to‐transect discharge variability, and estimation of the uncertainty of discharges in unmeasured areas by sensitivity analysis. The OURSIN uncertainty results are validated using empirical uncertainty estimates from two large‐scale repeated measures experiments with variable site and flow conditions. The mean and the 95% quantiles of the uncertainty differences are −0.4% [−4.4%; +2.5%]. The OURSIN method provides a comprehensive uncertainty budget that is helpful for understanding the relative impacts of error sources and defining strategies to minimize them. The method should be further evaluated with experiments in different conditions, and additional uncertainty components and options such as GPS reference for boat velocity could be implemented.

Templates of expected measurement uncertainties for average prompt and total fission neutron multiplicities

In this paper, we provide templates of measurement uncertainty sources expected to appear for average prompt- and total-fission neutron multiplicities, $ \overline\nu_p $ and $ \overline\nu_t $ , for the following measurement types: absolute manganese-bath experiments for $ \overline\nu_t $ , absolute and ratio liquid-scintillator measurements for $ \overline\nu_p $ . These templates also suggest a typical range of these uncertainties and their correlations based on a survey of available experimental data, associated literature, and feedback from experimentalists. In addition, the information needed to faithfully include the associated experimental data into the nuclear-data evaluation process is provided.

Comparison and uncertainty quantification of roof pressure measurements using the NIST and TPU aerodynamic databases

The pressure coefficient of a low-rise building in the ASCE wind load design provision is usually obtained from boundary-layer wind-tunnel tests. Although these tests tend to be standardized, inconsistent results from different facilities have been acknowledged as a long-standing issue. This work compares roof pressure for a low-rise building model archived in the National Institute of Standards and Technology (NIST) aerodynamic database and the Tokyo Polytechnic University database, followed by quantifying the measurement and data reduction uncertainties of the NIST datasets. The Monte Carlo simulation propagates four elemental uncertainties to the mean Cp¯, standard deviation Cp′ and peak pressure coefficient Cp,peak. Results indicate that pronounced differences in the roof pressure from two datasets are attributed to different inflow characteristics (including the Jensen number variation) and the inherent measurement uncertainties. High measurement uncertainties of Cp¯ and Cp,peak are strongly correlated with vortical flow structures, either separated flow or conical vortices at the roof corner and windward edges. Two dominant measurement uncertainty sources are distinguished: the dynamic pressure ratio uncertainty and the surface pressure tap uncertainty. Alternative flow and pressure measurement techniques are noted to potentially reduce the two dominant uncertainty sources. This work is intended to clarify measurement uncertainty sources of obtaining pressure coefficients in wind-tunnel model tests and shed lights on why large differences exist from different tests.

Change detection from high-resolution airborne laser scans using penalized composite likelihood screening

The study of elevation change using pre- and post-event raster grids obtained by airborne laser scans is central to many scientific areas, including geomorphology, landscape science and environmental science. Separating real elevation change from noise is a nontrivial task due to complex sources of measurement uncertainty causing errors to be spatially variable. For high-resolution grids, an additional hurdle is the excessive computational effort required by common statistical models for the spatial error. This paper introduces a screening methodology for change detection in high-resolution elevation difference grids using a composite likelihood regularization framework. We propose to model the spatial error by a sparse spatial autoregressive conditional heteroscedasticity process and obtain simultaneous detection of change location and change size estimation by maximizing a penalized composite likelihood objective. The methodology is implemented through a fast coordinate-wise maximization algorithm with computational complexity growing linearly with the grid size. Numerical studies on simulated and real data show satisfactory accuracy for both change detection and parameter estimation.

Measurements as the basis for interpreting the content of emotionally coloured acoustic signals

Nowadays, there has come to life a growing demand of society for obtaining objective quantitative evaluations in psychology, biology, neurophysiology, and other fields that did not concern metrology before. Such evaluations should meet measurement requirements. The measurement of emotions associated with acoustic signals is a typical example. On the strength of emotion evolution, the authors, for the first time, propose the definition of emotions as measurable multidimensional quantities and a measurement scale that includes 8 basic emotions. A measurement model is justified. It enables identifying mammal basic emotions by the evaluation of the infrasound spectrum in the zone of 3 brain biorhythms after a non-linear conversion of the acoustic signals and by the determination of the frequency zone with the maximum signal energy. The sources of measurement uncertainty, experimental results related to various animals as well as prospects for further research and development are given and discussed.

Evaluation of performance and precision of a radiochemical procedure for quantification of low concentrations of 234U and 238U in water samples

ABSTRACT Uranium isotopes 238U, 234U, and 235U are alpha-particle emitters and can be directly measured by alpha spectrometry. To evaluate the accuracy of the determination of low concentration of U isotopes in water samples, six spiked water samples were analysed by extraction chromatography using uranium selective resin. The separated uranium isotopes were electrodeplated on a disc of stainless steel and were measured by an alpha spectrometer for the determination of radiochemical yield using 232U isotopic tracer. Three certified IAEA reference water samples (IAEA-Cu-2010-03, IAEA-420 and IAEA-421) have been analysed for method validation. The measurement uncertainty sources were identified, and the combined standard uncertainty of the measurement has been determined. Although the activity of uranium isotopes in the certified reference samples was very low, the obtained results were reliable and were within the certified range with 95% confidence level. The characteristic limits (the decision threshold and detection limit) were calculated. The combined uncertainty of the results was mostly attributed to the count rates in the region of interest of the analyte and the tracer in the blank as well as in the sample spectra. Based on the results of the acceptance criteria including Z-score, u-test, trueness and precision, the used radiochemical procedure was found accurate and precise as well.

International interlaboratory comparison of Raman spectroscopic analysis of CVD-grown graphene

There is a pressing need for reliable, reproducible and accurate measurements of graphene’s properties, through international standards, to facilitate industrial growth. However, trustworthy and verified standards require rigorous metrological studies, determining, quantifying and reducing the sources of measurement uncertainty. Towards this effort, we report the procedure and the results of an international interlaboratory comparison (ILC) study, conducted under Versailles Project on Advanced Materials and Standards. This ILC focusses on the comparability of Raman spectroscopy measurements of chemical vapour deposition (CVD) grown graphene using the same measurement protocol across different institutes and laboratories. With data gathered from 17 participants across academia, industry (including instrument manufacturers) and national metrology institutes, this study investigates the measurement uncertainty contributions from both Raman spectroscopy measurements and data analysis procedures, as well as provides solutions for improved accuracy and precision. While many of the reported Raman metrics were relatively consistent, significant and meaningful outliers occurred due to differences in the instruments and data analysis. These variations resulted in inconsistent reports of peak intensity ratios, peak widths and the coverage of graphene. Due to a lack of relative intensity calibration, the relative difference reported in the 2D- and G peak intensity ratios () was up to 200%. It was also shown that the standard deviation for values reported by different software packages, was 15× larger for Lorentzian fit functions than for pseudo-Voigt functions. This study has shown that by adopting a relative intensity calibration and consistent peak fitting and data analysis methodologies, these large, and previously unquantified, variations can be significantly reduced, allowing more reproducible and comparable measurements for the graphene community, supporting fundamental research through to the growing graphene industry worldwide. This project and its findings directly underpin the development of the ISO/IEC standard ‘DTS 21356-2—Nanotechnologies—Structural Characterisation of CVD-grown Graphene’.

Quantitative assessment of fitting errors associated with streak camera noise in Thomson scattering data analysis.

Thomson scattering measurements in high energy density experiments are often recorded using optical streak cameras. In the low-signal regime, noise introduced by the streak camera can become an important and sometimes the dominant source of measurement uncertainty. In this paper, we present a formal method of accounting for the presence of streak camera noise in our measurements. We present a phenomenological description of the noise generation mechanisms and present a statistical model that may be used to construct the covariance matrix associated with a given measurement. This model is benchmarked against simulations of streak camera images. We demonstrate how this covariance may then be used to weight fitting of the data and provide quantitative assessments of the uncertainty in the fitting parameters determined by the best fit to the data and build confidence in the ability to make statistically significant measurements in the low-signal regime, where spatial correlations in the noise become apparent. These methods will have general applicability to other measurements made using optical streak cameras.

Measurement uncertainty quantification for myocardial perfusion using cardiac positron emission tomography imaging

Perfusion, the flow of blood, and hence oxygen, is essential to the functioning of the heart. Reduced perfusion (or ischemia), is a reliable indicator of the presence of significant obstructive coronary artery disease (CAD), which is one of the biggest causes of death in Europe. Myocardial perfusion imaging is a non-invasive technique used in the diagnosis, management and prognosis of CAD and is a key component in the triage of patients into treatment and non-treatment groups. Cardiac positron emission tomography (PET) is an imaging technique with high sensitivity and specificity to CAD, however perfusion measurements are difficult to calibrate against a common reference standard, and confidence in them is generally not quantified in terms of measurement uncertainty. There are a number of steps involved in measuring perfusion using cardiac PET—from patient preparation to data analysis—each associated with potential sources of uncertainty. The absence of measurement uncertainty quantification can lead to inaccuracies in measurement results, a lack of comparability between devices or scanning facilities, and is likely to be detrimental to a decision-making process. In this paper, we identify some of the sources of measurement uncertainty in the cardiac PET perfusion measurement pipeline. We assess their relative contribution by performing a sensitivity analysis using experimental data of a flow phantom acquired on a PET scanner. The results of this analysis will inform users of how parameter choices in their imaging pipeline affect the output of their measurements, and serves as a starting point to develop an uncertainty quantification method.

Measurements of the Complex Anisotropic Permittivity of Laminates With TM₀ₙ₀ Cavity

Low-loss dielectric laminates that are routinely used in the manufacturing of printed circuit boards (PCBs) are known to be anisotropic. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-plane</i> and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out-of-plane</i> components of the dielectric permittivity have been so far typically determined using one of several available methods. In this article, we performed measurements of both components of complex permittivity of selected isotropic and anisotropic laminar materials employing a combination of a few split-post dielectric resonators (SPDRs) and one cylindrical cavity supporting several TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{0n0}$ </tex-math></inline-formula> modes in the microwave band. Based on obtained data a novel, more precise approach to measuring the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out-of-plane</i> component of complex permittivity of laminar samples has been proposed. Additionally, a detailed analysis of several sources of measurement uncertainty (e.g., due to finite tolerances of manufacturing of the sample) has been performed and some recommendations formulated.