Method for determining uncertainty and error in the process of ophthalmic lens calibration

In the present investigation, a scientific procedure was developed, and a mathematical model was proposed, with the objective of determining, under standard conditions, the uncertainty, and the measurement of dioptric power in ophthalmic lenses. The methodology of the scientific procedure is based on the fundamentals of geometric optics, this process guarantees and establishes a standardized uncertainty measure in repeatable and reproducible processes. The methodology is complemented with a proposed mathematical model based on the guide for the expression of uncertainty in measurement - GUM. This model can be applied to lenses used for calibrating eye care equipment (such as lensometers, which are used to diagnose myopia and farsightedness) by evaluating the lenses without having direct contact with patients. When the proposed mathematical model was applied, its experimental result was a maximum expanded uncertainty of ± 0.0079 diopters in a 0.5-diopter lens. This is optimal compared to the result of other authors this article, who reported a maximum expanded uncertainty of ± 0.0086 diopters. In conclusion, the application of this scientific procedure provides manufacturers and users of this type of lenses with a reliable measurement thanks to a calibration process based on geometrical optics and centered on patient safety.

Uncertainty Assessment for Very High Temperature Thermal Diffusivity Measurements on Molybdenum, Tungsten and Isotropic Graphite

The French National Metrology Institute LNE has improved its homemade laser flash apparatus in order to perform accurate and reliable measurements of thermal diffusivity of homogeneous solid materials at very high temperature. The inductive furnace and the associated infrared (IR) detection systems have been modified and a specific procedure for the in situ calibration of the used radiation thermometers has been developed. This new configuration of the LNE’s diffusivimeter has been then applied for measuring the thermal diffusivity of molybdenum up to 2200 °C, tungsten up to 2400 °C and isotropic graphite up to 3000 °C. Uncertainties associated with these high temperature thermal diffusivity measurements have been assessed for the first time according to the principles of the “Guide to the Expression of Uncertainty in Measurement” (GUM). Detailed uncertainty budgets are here presented in the case of the isotropic graphite for measurements performed at 1000 °C, 2000 °C and 3000 °C. The relative expanded uncertainty (coverage factor k = 2) of the thermal diffusivity measurement is estimated to be between 3 % and 5 % in the whole temperature range for the three investigated refractory materials.

Development of a methodical approach for uncertainty quantification and meta-modeling of surface hardness in white layers of longitudinal turned AISI4140 surfaces

The formation of thermally and mechanically induced near-surface microstructures in the form of white layers leads to different hardness properties in these areas. Therefore, this paper conducts systematic surface hardness measurements and uncertainty quantification utilizing the Monte Carlo Method (MCM) in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM). Furthermore, several meta-models describing the hardness course in relationship to the material depth are used to model this nonlinear relationship via machine learning. The evaluation and selection of the optimal model considers the trade-off between measurement uncertainty and prediction quality in terms of mean squared error (MSE). The resulting measurement uncertainty is to be used for the calibration of a non-destructive micromagnetic material sensor. This will then be implemented for in-process monitoring in the outer diameter longitudinal turning process. This should make it possible to detect white layers during machining and to avoid them accordingly by controlling the machine parameters. By means of a soft sensor, the corresponding target value is to be derived from the micromagnetic material sensor measurement.

A General Mathematical Approach Based on the Possibility Theory for Handling Measurement Results and All Uncertainties

The concept of measurement uncertainty was introduced in the 1990s by the “Guide to the expression of uncertainty in measurement”, known as GUM. The word uncertainty has a lexical meaning and reflects the lack of exact knowledge or lack of complete knowledge about the value of the measurand. Thanks to the suggestions in the GUM and following the mathematical probabilistic approaches therein proposed, an uncertainty value can be found and be associated to the measured value. In the last decades, however, other methods have been proposed in the literature, which try to encompass the definitions of the GUM, thus overcoming its limitations. Some of these methods are based on the possibility theory, such as the one known as the RFV method. The aim of this paper is to briefly recall the RFV method, starting from the very beginning and the initial motivations, and summarize in a unique paper the most relevant obtained results.

In-Situ Evaluation of the Pitch of a Reflective-Type Scale Grating by Using a Mode-Locked Femtosecond Laser

Major modifications are made to the setup and signal processing of the method of in-situ measurement of the pitch of a diffraction grating based on the angles of diffraction of the diffracted optical frequency comb laser emanated from the grating. In the method, the improvement of the uncertainty of in-situ pitch measurement can be expected since every mode in the diffracted optical frequency comb laser can be utilized. Instead of employing a Fabry-Pérot etalon for the separation of the neighboring modes in the group of the diffracted laser beams, the weight-of-mass method is introduced in the method to detect the light wavelength in the Littrow configuration. An attempt is also made to reduce the influence of the non-uniform spectrum of the optical comb laser employed in the setup through normalization operation. In addition, an optical alignment technique with the employment of a retroreflector is introduced for the precise alignment of optical components in the setup. Furthermore, a mathematical model of the pitch measurement by the proposed method is established, and theoretical analysis on the uncertainty of pitch measurement is carried out based on the guide to the expression of uncertainty in measurement (GUM).

Gauge repeatability and reproducibility study of airborne sound isolation measurements

A gauge repeatability and reproducibility study (GRR) uses analysis of variations (ANOVA) on an appropriately designed experiment to separate and quantify the components of the overall uncertainty. The authors have previously presented results of GRR studies of the measurement of airborne and impact insulation of floor-ceiling and demising wall assemblies in several apartment buildings, in which the uncertainty in the measurement method and the variability of the nominally-identical assemblies were compared. The results of two additional GRR studies on measurements of airborne noise isolation of wood stud demising walls are presented. The first study, like previous studies, evaluates the components of variance attributable to operator, repeatability, and part. The second study uses a fixed operator and part, and evaluates the variance due to loudspeaker type, position, and level on the measured noise reduction. The measurement standard (ASTM E336) gives limited guidance on the type and location of the loudspeaker used on the source side, and this study can inform whether changes in the standard with regards to the loudspeakers could reduce the uncertainty in measurement.

Truth and Uncertainty. A critical discussion of the error concept versus the uncertainty concept

Contrary to the claims put forward in “Evaluation of measurement data – Guide to the expression of uncertainty in measurement”, issued by the Joint Committee for Guides in Metrology, the error concept and the uncertainty concept are the same. Arguments in favour of the contrary have been analyzed and were found not compelling. Neither was any evidence presented in this document that “errors” and “uncertainties” define a different relation between the measured and the true value of the variable of interest, nor does this document refer to a Bayesian account of uncertainty beyond the mere endorsement of a degree-of-belief-type conception of probability.