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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.
It is an extension of Huygens–Fresnel principle, which describes each point on a wavefront as a spherical wave source. The equivalence of the imaginary surface currents are enforced by the uniqueness theorem in electromagnetism , which dictates that a unique solution can be determined by fixing a boundary condition on a system.
The restoration is based on different deconvolution algorithms, that permit the recovery of objects from images that are degraded by blurring and noise. In microscopy the blurring is largely due to diffraction limited imaging by the instrument; the noise is usually photon noise .
The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was named after William Richardson and Leon B. Lucy , who described it independently.
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 ...
The Hamilton optico-mechanical analogy is closely related to Fermat's principle and thus to the Huygens–Fresnel principle. [10] Fermat's principle states that the rays between wavefronts will take the path least time; the concept of successive wavefronts derives from Huygens principle.