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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.
In functional terms, it is the spatial domain version (i.e., the inverse Fourier transform) of the optical transfer function (OTF) of an imaging system. It is a useful concept in Fourier optics , astronomical imaging , medical imaging , electron microscopy and other imaging techniques such as 3D microscopy (like in confocal laser scanning ...
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]
During World War II Duffieux discovered Fourier optics, presenting his ideas at a meeting of the French Society of Physics in Paris in 1941, [5] and publishing several papers. [6] He completed a monograph on the subject in 1943–1944, which was privately published after the war in 1946. [ 7 ]
The van Cittert–Zernike theorem also places constraints on the sensitivity of an adaptive optics system. In an adaptive optics (AO) system, a distorted wavefront is provided and must be transformed to a distortion-free wavefront. An AO system must make a number of different corrections to remove the distortions from the wavefront.
Some of the earliest work on what would become known as Fresnel diffraction was carried out by Francesco Maria Grimaldi in Italy in the 17th century. In his monograph entitled "Light", [3] Richard C. MacLaurin explains Fresnel diffraction by asking what happens when light propagates, and how that process is affected when a barrier with a slit or hole in it is interposed in the beam produced by ...
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 ...