Convolution and Fourier optics

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Difference between Convolution and Fourier optics

Convolution vs. Fourier optics

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated. Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the wave is regarded as a superposition of plane waves that are not related to any identifiable sources; instead they are the natural modes of the propagation medium itself.

Convolution theorem

In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution is the pointwise product of Fourier transforms.

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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.

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Digital image processing

In computer science, Digital image processing is the use of computer algorithms to perform image processing on digital images.

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Dirac delta function

In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.

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Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.

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Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

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Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Signal processing

Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.

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