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Since a spectrum is an important diagnostic, having a spectrum for each pixel allows more science cases to be addressed. In astronomy, this technique is commonly referred to as integral field spectroscopy , and examples of this technique include FLAMES [ 50 ] and SINFONI [ 51 ] on the Very Large Telescope , but also the Advanced CCD Imaging ...
A spectral map f: X → Y between spectral spaces X and Y is a continuous map such that the preimage of every open and compact subset of Y under f is again compact. The category of spectral spaces, which has spectral maps as morphisms, is dually equivalent to the category of bounded distributive lattices (together with homomorphisms of such ...
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Spectral line shape or spectral line profile describes the form of an electromagnetic spectrum in the vicinity of a spectral line – a region of stronger or weaker intensity in the spectrum. Ideal line shapes include Lorentzian , Gaussian and Voigt functions, whose parameters are the line position, maximum height and half-width. [ 1 ]
The angular spectrum method is a technique for modeling the propagation of a wave field.This technique involves expanding a complex wave field into a summation of infinite number of plane waves of the same frequency and different directions.
The Fourier transform of a function of time, s(t), is a complex-valued function of frequency, S(f), often referred to as a frequency spectrum.Any linear time-invariant operation on s(t) produces a new spectrum of the form H(f)•S(f), which changes the relative magnitudes and/or angles of the non-zero values of S(f).
Modern analyzers have slits as narrow as 0.05 mm. The energy–angle–angle maps are usually further processed to give energy–k x –k y maps, and sliced in such a way to display constant energy surfaces in the band structure and, most importantly, the Fermi surface map when they are cut near the Fermi level.
That is, there is some element x in X and a neighborhood N of x such that (T − λ)(y) is never in N. In this case, the map (T − λ) −1 x → x may be bounded or unbounded, but in any case does not admit a unique extension to a bounded linear map on all of X. Then λ is said to be in the residual spectrum of T, σ r (T).