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The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. [1] The sum of these spherical wavelets forms a new wavefront.
Deconvolution maps to division in the Fourier co-domain. This allows deconvolution to be easily applied with experimental data that are subject to a Fourier transform. An example is NMR spectroscopy where the data are recorded in the time domain, but analyzed in the frequency domain. Division of the time-domain data by an exponential function ...
An example of an experimentally derived point spread function from a confocal microscope using a 63x 1.4NA oil objective. It was generated using Huygens Professional deconvolution software. Shown are views in xz, xy, yz and a 3D representation. In microscopy, experimental determination of PSF requires sub-resolution (point-like) radiating sources.
The principle yields an equivalent problem for a radiation problem by introducing an imaginary closed surface and fictitious surface current densities. It is an extension of Huygens–Fresnel principle, which describes each point on a wavefront as a spherical wave source.
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).
The Huygens–Fresnel principle is one such model; it states that each point on a wavefront generates a secondary wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point.
Cellular deconvolution algorithms have been applied to a variety of samples collected from saliva, [5] buccal, [5] cervical, [5] PBMC, [6] brain, [2] kidney, [1] and pancreatic cells, [1] and many studies have shown that estimating and incorporating the proportions of cell types into various analyses improves the interpretability of high ...
Treating a point on the path as a source is the minimum requirement of Huygens' principle, and is part of the explanation of Fermat's principle. But it can also be shown that the geometric construction by which Huygens tried to apply his own principle (as distinct from the principle itself) is simply an invocation of Fermat's principle. [4]