Linear Error Analysis
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propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When error propagation division the variables are the values of experimental measurements they have uncertainties error propagation calculator due to measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the function. error propagation physics The uncertainty u can be expressed in a number of ways. It may be defined by the absolute error Δx. Uncertainties can also be defined by the
Error Propagation Chemistry
relative error (Δx)/x, which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, σ, the positive square root of variance, σ2. The value of a quantity and its error are then expressed as an interval x ± u. If the statistical probability distribution of error propagation reciprocal the variable is known or can be assumed, it is possible to derive confidence limits to describe the region within which the true value of the variable may be found. For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are ± one standard deviation from the value, that is, there is approximately a 68% probability that the true value lies in the region x ± σ. If the uncertainties are correlated then covariance must be taken into account. Correlation can arise from two different sources. First, the measurement errors may be correlated. Second, when the underlying values are correlated across a population, the uncertainties in the group averages will be correlated.[1] Contents 1 Linear combinations 2 Non-linear combinations 2.1 Simplification 2.2 Example 2.3 Caveats and warnings 2.3.1 Reciprocal 2.3.2 Shifted reciprocal 3 Example formulas 4 Example calculations 4.1 Inverse tangent function 4.2 Resistance measurement 5 See also 6 References 7 Further reading 8 External links Linear combinations[edit] Let { f
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Error Propagation Inverse
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Propagated Error Calculus
password?Sign in via your institutionOpenAthens loginOther institution login Purchase Help Direct export Export file RIS(for EndNote, Reference Manager, ProCite) BibTeX Text RefWorks Direct Export Content https://en.wikipedia.org/wiki/Propagation_of_uncertainty Citation Only Citation and Abstract Advanced search JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page. JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page. This page uses JavaScript to progressively load the article content as a user scrolls. Click the View http://www.sciencedirect.com/science/article/pii/S0030402612000940 full text link to bypass dynamically loaded article content. View full text Optik - International Journal for Light and Electron OpticsVolume 124, Issue 8, April 2013, Pages 710–717 Linear error analysis of differential phase shifting algorithmsM. Miranda, , B.V. Dorrío , J. Blanco , J. Diz-Bugarin Applied Physics Department, University of Vigo, Campus Universitario 36310, Vigo, SpainReceived 9 September 2011, Accepted 11 January 2012, Available online 29 March 2012AbstractAn important process in optical metrology is the determination of the difference between test and reference states. Direct calculation of the optical phase difference encoded in two fringe patterns can be done by using differential phase shifting algorithms (DPSAs). If the phase difference does not reach a complete period, DPSAs provide directly its continuous values and the known limitations of the unwrapping stage are avoided. This work presents a generic design protocol of DPSAs obtained by a least squares fitting that combines phase shifting algorithms (PSAs) in a suitable non-linear way. Results are also provided that quantitatively characterize the effect on some representative DPSAs by the
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