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Fourier optics begins with the homogeneous, scalar wave equation (valid in source-free regions): (,) = where is the speed of light and u(r,t) is a real-valued Cartesian component of an electromagnetic wave propagating through a free space (e.g., u(r, t) = E i (r, t) for i = x, y, or z where E i is the i-axis component of an electric field E in the Cartesian coordinate system).
Formally, the optical transfer function is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source). As a Fourier transform, the OTF is generally complex-valued; however, it is real-valued in the common case of a PSF that is symmetric about its center.
The work gained little attention outside France until Born and Wolf called attention to it in their text, Principles of Optics (1959). [8] A second edition of Duffieux's book was published in 1970 by Masson (Paris) and an English translation appeared in 1983. [9] After the war, Duffieux moved to Besançon and became the chair of optics at the ...
Since the (incoherent) point spread function is also related to the optical transfer function via a Fourier transform, a direct relationship exists between the pupil function and the optical transfer function. In the case of an incoherent optical imaging system, the optical transfer function is the auto correlation of the pupil function. [2] [5]
The Gerchberg-Saxton algorithm. FT is Fourier transform. The Gerchberg–Saxton (GS) algorithm is an iterative phase retrieval algorithm for retrieving the phase of a complex-valued wavefront from two intensity measurements acquired in two different planes. [1]
He is the author of approximately 220 technical publications, including the textbooks Introduction to Fourier Optics (1968, Second Edition 1996, Third Edition 2005, Fourth Edition 2017), Statistical Optics (1985, Second Edition 2015), Speckle Phenomena in Optics (2006, Second Edition 2020) and (with R.M. Gray) Fourier Transforms: An ...
Contrast transfer theory provides a quantitative method to translate the exit wavefunction to a final image. Part of the analysis is based on Fourier transforms of the electron beam wavefunction. When an electron wavefunction passes through a lens, the wavefunction goes through a Fourier transform. This is a concept from Fourier optics.
The adaptive-additive algorithm was originally created to reconstruct the spatial frequency phase of light intensity in the study of stellar interferometry.Since then, the AA algorithm has been adapted to work in the fields of Fourier Optics by Soifer and Dr. Hill, soft matter and optical tweezers by Dr. Grier, and sound synthesis by Röbel.