Publication

High resolution displacement detection by speckle pattern analysis : accuracy limits in linear displacement speckle metrology

2010
Journal Articles

Abstract

We propose a simple reflection measurement setup and a motion evaluation procedure based on a two dimensional recording of subsequent speckle images. The averaging of cross correlation functions is used to measure displacements. We demonstrate experimentally a 10 nm precision on a 50 μm measurement range limited by systematical errors. An image library is proposed to extend the measurement range. Limitations are given and documented improvements predicted an accuracy better than 5 nm over a range of 150 μm.

Official source

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2010
Journal Articles

Abstract

Official source

Related concepts (28)

Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.

Observational error

Observational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not necessarily a "mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: random and systematic. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken.

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.