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Chapter 4:
Spectrometer Specifications
In the very general sense of the word, every spectrometer is a filter and every filter is a spectrometer. Each is a device for isolating a relatively small portion of the entire spectrum. Thus, in this section discussing the descriptors, we use the terms filter and spectrometer interchangeably. The important concepts include wavelength, wave number, spectral resolution, line width, resolving power, and closely related concepts. 4.1 Spectral Variables There exist many ways to represent the spectral variable of a radiometric quantity. Perhaps the most familiar is the wavelength. It is the distance between two points of equal phase on a sinusoidal wave. It is usually given the symbol λ, and is measured in micrometers, μm, nanometers, nm, and angstroms, Å. The wave number may be the next most frequently used spectral variable. It is designated by either σ or v; I will use σ. It is defined as the number of waves in a centimeter, sometimes called a kayser, and usually is expressed in cm −1 . Therefore the relationship between wavelength (λ in μm) and σ wave numbers (σ in reciprocal centimeters) is σ[cm −1 ]=10000 λ[μm] =1 λ[cm] . The wave number in kaysers is simply the reciprocal of the wavelength in centimeters, but it is 10,000 times this if the wavelength is in micrometers. These are the two most frequently used variables, but k, v, f, and x are also used. The radian wave number k is 2π∕λ or 2 πσ; it is also the magnitude of the wave vector. When people use the term frequency, they often mean v, which has the units of Hertz or cycles per second. This is sometimes cited as f but I will save that symbol for focal length. The nondimensional frequency x is useful in radiometric work. It is defined as c 2 ∕λT , where c 2 is the second radiation constant and T is absolute temperature. 4.2 Resolution A spectral line usually has some predetermined shape, like Gauss, Lorentz, or Doppler. Lines are narrow maxima in the spectrum.
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