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The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum.It is usually denoted by , and is closely related to the resolving power of the spectrograph, defined as =, where is the smallest difference in wavelengths that can be distinguished at a wavelength of .
An expression for n as a function of photon energy, symbolically written as n(E), is then determined from the expression for k(E) in accordance to the Kramers–Kronig relations [4] which states that n(E) is the Hilbert transform of k(E). The Forouhi–Bloomer dispersion equations for n(E) and k(E) of amorphous materials are given as:
where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths. The coefficients are usually quoted for λ as the vacuum wavelength in micrometres. Usually, it is sufficient to use a two-term form of the ...
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write: =where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m 2 = kg·m −1 ·s −3); Φ is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m 2); and λ is the wavelength (SI unit: meter, m).
This holds for any trial φ since, by definition, the ground state wavefunction has the lowest energy, and any trial wavefunction will have energy greater than or equal to it. Proof: φ can be expanded as a linear combination of the actual eigenfunctions of the Hamiltonian (which we assume to be normalized and orthogonal): ϕ = ∑ n c n ψ n ...
In this case, [1] spectral flux density is the quantity that describes the rate at which energy transferred by electromagnetic radiation is received from that unresolved point source, per unit receiving area facing the source, per unit wavelength range. At any given wavelength λ, the spectral flux density, F λ, can be determined by the ...
In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule. [1] [2] For example, if an emissive state has a small oscillator strength, nonradiative decay will outpace radiative decay.
The photons will be shifted away from the line center, thus rendering the height of the emission line a poor measure of its overall strength. The equivalent width, on the other hand, "measures the fraction of energy removed from the spectrum by the line," regardless of the broadening intrinsic to the line or a detector with poor resolution. [3]