# L8 - OPTI 280: Computer Programming Workshop Houssine...

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OPTI 280 Spring 2010 Lecture 8 H. Makhlouf, 1 OPTI 280: Computer Programming Workshop Houssine Makhlouf College of Optical Sciences, University of Arizona [email protected]

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OPTI 280 Spring 2010 Lecture 8 H. Makhlouf, 2 Learning Objectives Propagation of errors Identify and quantify sources of uncertainty in physical (optical) systems Understand relative effects of uncertainties on overall physical quantity Curve fitting Manipulate a given dataset obtained experimentally in order to predict (interpolate, extrapolate) new outcomes for similar experiments
OPTI 280 Spring 2010 Lecture 8 H. Makhlouf, 3 Propagation of Error In statistics, propagation of error is the effect of variables’ uncertainty on the function. In experiments, effect of uncertainty in measured values on estimated results.

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OPTI 280 Spring 2010 Lecture 8 H. Makhlouf, 4 Propagation of Errors (1) Consider: y = Ae x 1% error in measuring A gives 1% error in y 1% error in x could give much larger error Suppose x = 10 ± 0.1 (1% error) Then error in y is 10%, (difference between e 10 and e 10.1 )
OPTI 280 Spring 2010 Lecture 8 H. Makhlouf, 5 Propagation of Errors (1) In general error in y depends on the slope of the y vs. x curve

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OPTI 280 Spring 2010 Lecture 8 H. Makhlouf, 6 Propagation of Errors (2) Consider general case: (1) y is a physical quantity obtained from functional form or equation f(x) x is a directly measurable value from instruments during an experiment with uncertainty Δx ) ( x f y
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## This note was uploaded on 05/23/2010 for the course OPTI 280 taught by Professor Pau during the Spring '10 term at Arizona.

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L8 - OPTI 280: Computer Programming Workshop Houssine...

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