Spectral Parameters Used in Illumination Engineering

[1.2] There are four spectral parameters that are widely used in different disciplines. The spectral parameter used in illuminating engineering is almost always wavelength, λ, in units of nanometer (nm = 10-9 m), micrometer (μm = 10-6 m) or Ångstromi (Å = 10-10 m). The name wavelength and symbol λ will be used as the spectral parameter in this publication except where otherwise specifically indicated. The other spectral parameters, their symbols, and equations for computing them from wavelengths in nanometers are as follows:

frequency,ii ν (s-1, or Hz) ν = c • 109/λ
wavenumber, σ (cm-1) σ = (λ)-1 • 10-7
photon energy, q (J) q = hν •109/λ

where:

c = the speed of light in vacuum, 299,792,458 (m • s-1)
h = the Planck constant of action 6.626176 • 10-34 (J • s)

When a parameter symbol, e.g., λ, is used as a subscript to a radiometric quantity symbol, it denotes the parameter concentration of that quantity; e.g., spectral radiant flux, Φλ = dΦ/dλ. To denote a distribution, it is also shown as a function of that parameter; e.g., the spectral distribution of radiant flux, Φλ(λ). Properties, such as reflectance or emissivity, also vary with, and may be shown as functions of, the radiation parameters; e.g., directional emissivity (θ,φ), or spectral transmittance τ(λ).

Since they are not distributions, but only weighting functions, the use of parameter subscripts to property symbols may be misleading and is accordingly deprecated. The value of a function (distribution or weighting function) at a particular parameter value is denoted by replacing the parameter symbol in the function notation by that value, e.g., spectral flux at 555 nanometers would be: Φλ (555 nm).

Note: In addition to the spectral parameter, the other radiation parameters that together fully characterize the distribution of radiant flux in the domain of ray optics are: the spatial parameters of position (x,y for a point on a surface or x,y,z for a point in space) and direction (θ,φ), where θ = the angle from a reference axis and φ = the azimuth angle from a reference direction perpendicular to that axis; time (t) or frequency (ƒ << ν) of fluctuation or modulation; and polarization (e.g., the Stokes parameters1).


i Deprecated unit.
ii Conventionally, ν is the symbol for spectral frequency, and ƒ is the symbol for time frequency.

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