Publication

Fourier spectrum of curvilinear gratings of the second order

Isaac Amidror
1998
Journal Articles

Abstract

The class of second-order curvilinear gratings consists of all the curvilinear gratings that are obtained by second-order spatial transformations of periodic gratings. It includes, for example, circular, elliptic, and hyperbolic gratings as well as circular, elliptic, and hyperbolic zone plates. Such structures occur quite frequently in optics, and their Fourier transforms may arise, for instance, in connection with the Fraunhofer diffraction patterns generated by these structures. I present the two-dimensional Fourier spectra of the most important second-order curvilinear gratings for gratings having any desired intensity profile (cosinusoidal, sawtooth wave, square wave, etc.). These analytic results are also illustrated by figures showing the various gratings and their spectra as they are obtained on a computer by two-dimensional fast Fourier transform

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https://infoscience.epfl.ch/entities/publication/b2cdef90-ebfc-462e-a69a-79f95fcd0e1d

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Isaac Amidror
1998
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/b2cdef90-ebfc-462e-a69a-79f95fcd0e1d

About this result

Related concepts (32)

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Fast Fourier transform

A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical.

Related publications (32)

Fourier spectrum of curvilinear gratings of the second order

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