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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 ...
The pseudocode below performs the GS algorithm to obtain a phase distribution for the plane "Source", such that its Fourier transform would have the amplitude distribution of the plane "Target". The Gerchberg-Saxton algorithm is one of the most prevalent methods used to create computer-generated holograms. [2]
Jean-Baptiste Joseph Fourier (/ ˈ f ʊr i eɪ,-i ər /; [1] French: [ʒɑ̃ batist ʒozɛf fuʁje]; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre, Burgundy and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and ...
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.
Huygens' principle when applied to an aperture simply says that the far-field diffraction pattern is the spatial Fourier transform of the aperture shape, and this is a direct by-product of using the parallel-rays approximation, which is identical to doing a plane wave decomposition of the aperture plane fields (see Fourier optics).
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 ...