Publication

Shannon entropy and degree of polarization of a speckle pattern

Abhijit Roy
2021
Journal Articles

Abstract

The dependence of the Shannon entropy (SE) of a speckle pattern on the degree of polarization (DoP) of the pattern is investigated both experimentally and numerically. The superposition of two uncorrelated speckle patterns with polarization diversity is utilized to control the DoP of the superposed speckle pattern, and the SE of the pattern is estimated from the determined probability density function of intensity of the pattern. The SE is observed to be increasing quadratically with the DoP of the speckle pattern. The experimental observations are supported by the numerical studies. As the change of the SE indicates a change in the randomness of the intensity distribution, the variation of the standard deviation of intensity with the DoP is also investigated. Moreover, a linear relation between the SE and the standard deviation of intensity of a speckle pattern is also established. (C) 2021 Optical Society of America

Official source

https://infoscience.epfl.ch/entities/publication/a26a3b18-0d45-4ab7-a455-37fe8dbc96a1

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Abhijit Roy
2021
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a26a3b18-0d45-4ab7-a455-37fe8dbc96a1

About this result

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (28)

Standard deviation

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Average absolute deviation

The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean, median, mode, or the result of any other measure of central tendency or any reference value related to the given data set. AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated as MAD). Several measures of statistical dispersion are defined in terms of the absolute deviation.

Median absolute deviation

In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample. For a univariate data set X1, X2, ..., Xn, the MAD is defined as the median of the absolute deviations from the data's median : that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values. Consider the data (1, 1, 2, 2, 4, 6, 9).

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