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.

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.

Social constructionism and the effects of media's portrayal of Nigeria's economic recession on foreign direct investment

Although Nigeria has the largest economy in Africa, it has been bedeviled by various issues in recent times, which has led to its experience of an economic recession. Its over-dependence on foreign products, the activities of militants and pipeline vandals in the Niger-Delta, poor economic planning and the delayed budget signing are some of the issues that have being credited to the fall into recession. However, some economists have suggested that Nigeria’s economy has the potential to rise from the recession and have identified the inflow of foreign direct investments as one of the key factors that will contribute to the rise. On the other hand, the media’s reporting of Nigeria’s recession seems to have caused mixed reactions from among the public who worry about their daily bread. Potential investors, both local and foreign, are also not left out in the expression of uncertainty. Since they rely on the media to provide information on the situation of the Nigerian economy, the power of the media in the making or marring of the government’s encouragement of FDI to boost the economy cannot be underestimated. The power of the media, which appears to be able to determine or construct the position and perception of individuals/organisation follow it can be relat-ed to the theory of social constructionism. So-cial constructionism suggests that the media’s have the capacity to selectively reproduce and construct the reality of any situation – in this case, Nigeria’s recession. However, it also acknowledges that the meanings offered by the media can be negotiated or rejected by those to whom it is directed. This study explores the capacity of the media’s construction of Nigeria’s economic recession to influence the inflow of foreign direct investments.

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).

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.

H2O Collisional Broadening Coefficients at 1.37 µm and Their Temperature Dependence: A Metrology Approach

We report self- and air collisional broadening coefficients for the H2O line at 7299.43 cm−1 and corresponding temperature coefficients for a temperature range spanning 293–573 K. New laser spectroscopic setups specifically designed for this purpose have been developed and are described. The line parameters reported here are in good agreement with those values reported in the HITRAN 2020 database, but the uncertainties have been reduced by factors of about 4, 1.3 and 4.4 for the self-broadening coefficient, air broadening coefficient and the temperature exponent of air broadening, respectively. Further, we combined our measurement approach with metrological data quality objectives, addressing the traceability of the results to the international system of units (SI) and evaluated the uncertainties following the guide to the expression of uncertainty in measurement (GUM).

Evaluating Risk in an Abnormal World: How Arbitrary Probability Distributions Affect False Accept and Reject Evaluation

Risk mitigation strategies commonly use the test uncertainty ratio (TUR) and end-of-period reliability (EOPR) to ensure a measurement is adequate for making acceptance decisions. Unfortunately, the common guidance of maintaining a TUR of at least 4:1 was developed to simplify the underlying calculus in an era predating modern computing and assumes that the probability distributions describing the product and the measurement uncertainty are unbiased and normally distributed. The Guide to the Expression of Uncertainty in Measurement and its supplements describe several situations where uncertainty in the measurement will not follow a normal distribution. Despite the evidence of non-normal behavior in measurements and products, risk evaluations typically assume normality in both distributions. While evaluating the probability of false accept (PFA) and the probability of false reject (PFR) is more challenging when the probability distributions are non-normal, the calculus is straightforward using either numerical integration or Monte Carlo techniques. This work considers several case studies of risk evaluation, including both global and specific risk, when the product or the test measurement uncertainty do not follow normal distributions. Neglecting non-normal behavior might greatly affect PFA and PFR by either over- or underestimating the probabilities depending on the parameters of the distributions.

Interpretation and use of standard atomic weights (IUPAC Technical Report)

Many calculations for science or trade require the evaluation and propagation of measurement uncertainty. Although relative atomic masses (standard atomic weights) of elements in normal terrestrial materials and chemicals are widely used in science, the uncertainties associated with these values are not well understood. In this technical report, guidelines for the use of standard atomic weights are given. This use involves the derivation of a value and a standard uncertainty from a standard atomic weight, which is explained in accordance with the requirements of the Guide to the Expression of Uncertainty in Measurement. Both the use of standard atomic weights with the law of propagation of uncertainty and the Monte Carlo method are described. Furthermore, methods are provided for calculating uncertainties of relative molecular masses of substances and their mixtures. Methods are also outlined to compute material-specific atomic weights whose associated uncertainty may be smaller than the uncertainty associated with the standard atomic weights.

Coverage Intervals

Since coverage intervals are widely used expressions of measurement uncertainty, this contribution reviews coverage intervals as defned in the Guide to the Expression of Uncertainty in Measurement (GUM), and compares them against the principal types of probabilistic intervals that are commonly used in applied statistics and in measurement science. Although formally identical to conventional confdence intervals for means, the GUM interprets coverage intervals more as if they were Bayesian credible intervals, or tolerance intervals. We focus, in particular, on a common misunderstanding about the intervals derived from the results of the Monte Carlo method of the GUM Supplement 1 (GUM-S1), and offer a novel interpretation for these intervals that we believe will foster realistic expectations about what they can deliver, and how and when they can be useful in practice

Messunsicherheitsbetrachtungen an einem fünfachsigen Nano-Koordinatenmessgerät NMM-5D nach einem vektoriellen Ansatz

Zusammenfassung Dieser Beitrag zeigt ein Konzept für eine fünfachsige Nano-Koordinatenmessmaschine zur Messung auf stark gekrümmten asphärischen und frei geformten optischen Oberflächen in einem Messvolumen von 25 mm × 25 mm × 5 mm 25\hspace{0.1667em}\text{mm}\times 25\hspace{0.1667em}\text{mm}\times 5\hspace{0.1667em}\text{mm} mit einem maximal möglichen Neigungswinkel von bis zu 60° zur Hochachse und einer maximalen Rotation von 360° um die Hochachse. Dabei wird die Probe translatorisch bewegt und der Sensor in seiner Orientierung verändert. Unter Einhaltung des Abbe-Komparatorprinzips für alle Messachsen wird die Bewegungsabweichung des Sensors bei der Rotation durch ein in-situ-Referenzmesssystem erfasst. Dieses besteht aus drei kartesisch angeordneten Fabry-Pérot-Interferometern mit dem Ursprung im Antastpunktes des Sensors, die den Abstand zu einer hemisphärischen Referenzfläche messen. Die Messunsicherheitsbetrachtung des Gesamtsystems erfolgt nach dem guide to the expression of uncertainty in measurement in einem vektoriellen Ansatz und liefert unter konservativen Annahmen eine Unsicherheit des Antastpunktes von maximal 72 nm ( k = 1 k=1 ).