[Blog] Sensors and their Relationship to Weapons Range

The Boltzmann constant (kB or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas.

The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature.





For an ideal absorber/emitter or black body, the Stefan–Boltzmann law states that the total energy radiated per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the black body's temperature,

Bandwidth Factor, F



Thermal radiators emit their energy over a wide band of wavelengths. In general it is not possible to design a detector which will be equally sensitive over all the wavelengths in this range. Therefore, there will be some upper and lower bounds on the wavelengths that can be detected. Designate these bounds as (wavelength)upper and (wavelength)lower. For our purposes, we assume that the detector can pick up any energy that is within this range, and nothing that is outside of it. Since the spectrum of the radiation from a thermal emitter will not all be within the detection band, we define the bandwidth factor, F, to be the fraction of the radiation that is within the detector band.

The detector bandwidth factor, F, could be obtained by integrating the flux vs. wavelength curve for the source between the limits of wavelengths for the detector. This curve varies with target temperature, so it is useful to remove this dependence. The universal black-body curve represents the fraction of the total flux which is outside of the band from zero to the new variable (wavelength)T, in units of mm-K.