Integral quantities (like
radiant flux) describe the total effect of radiation of all
wavelengths or
frequencies, while
spectral quantities (like
spectral power) describe the effect of radiation of a single wavelength or frequency . To each
integral quantity there are corresponding
spectral quantities, defined as the quotient of the integrated quantity by the range of frequency or wavelength considered. For example, the radiant flux Φe corresponds to the spectral power Φe, and Φe,. Getting an integral quantity's spectral counterpart requires a
limit transition. This comes from the idea that the precisely requested wavelength
photon existence probability is zero. Let us show the relation between them using the radiant flux as an example: Integral flux, whose unit is
W: \Phi_\mathrm{e}. Spectral flux by wavelength, whose unit is : \Phi_{\mathrm{e},\lambda} = {d\Phi_\mathrm{e} \over d\lambda}, where d\Phi_\mathrm{e} is the radiant flux of the radiation in a small wavelength interval [\lambda - {d\lambda \over 2}, \lambda + {d\lambda \over 2}]. The area under a plot with wavelength horizontal axis equals to the total radiant flux. Spectral flux by frequency, whose unit is : \Phi_{\mathrm{e},\nu} = {d\Phi_\mathrm{e} \over d\nu}, where d\Phi_\mathrm{e} is the radiant flux of the radiation in a small frequency interval [\nu - {d\nu \over 2}, \nu + {d\nu \over 2}]. The area under a plot with frequency horizontal axis equals to the total radiant flux. The spectral quantities by wavelength and frequency are related to each other, since the product of the two variables is the
speed of light (\lambda \cdot \nu = c): :\Phi_{\mathrm{e},\lambda} = {c \over \lambda^2} \Phi_{\mathrm{e},\nu}, or \Phi_{\mathrm{e},\nu} = {c \over \nu^2} \Phi_{\mathrm{e},\lambda}, or \lambda \Phi_{\mathrm{e},\lambda} = \nu \Phi_{\mathrm{e},\nu}. The integral quantity can be obtained by the spectral quantity's integration: \Phi_\mathrm{e} = \int_0^\infty \Phi_{\mathrm{e},\lambda}\, d\lambda = \int_0^\infty \Phi_{\mathrm{e},\nu}\, d\nu = \int_0^\infty \lambda \Phi_{\mathrm{e},\lambda}\, d \ln \lambda = \int_0^\infty \nu \Phi_{\mathrm{e},\nu}\, d \ln \nu. == See also ==