Infrared thermography

Transcription

1 Infrared thermography In microwave radiometry hν << kt, then the Rayleigh-Jeans radiation law is valid. As a result, the power P, received by an antenna whose beam intercepts an emitting surface, is directly proportional to the temperature T of the surface, according to the Nyquist relation: P = ktδν (Δν is the receiver bandwidth). 1

2 Stefan-Boltzmann Law At infrared radiation wavelenghts, the condition hν << kt is not verified: it should therefore be used, in this band of the electromagnetic spectrum, an other law. Integrating the expression of the Planck radiation law at all frequencies, we obtain the total brightness L for a blackbody radiator: 2h L 2 c Solving the integral, we obtain the Stefan-Boltzmann law : 0 e ν hν kt L σ T shown in the figure above with the area under the curve of the Planck s 3 1 radiation law at the temperature T (green area plus red area). σ = 5, W m 2 K is the Stefan-Boltzmann constant, which includes c, h, k and a constant resulting from the calculation of the integral. dν 2

3 Emissivity If the radiator is not a perfect blackbody, it is necessary to insert, in the expression of the Stefan-Boltzmann law, a parameter ε, called emissivity, which is defined as the energy radiated (not reflected) by the surface of the considered material as compared with that emitted by a blackbody at the same temperature: material blackbody L σ T We observe that: - the relationship between temperature and radiance of the emitting surface is not linear; - as indicated in the figure above, devices that work at the infrared wavelenghts cover only a small sector (red zone) of the entire emission spectrum of a thermal radiator. The entire emission spectrum is considered in the deduction of the Stefan-Boltzmann law. W W So ε can vary between 0 (white body) and 1 (blackbody). The most general form of the Stefan-Boltzmann law becomes: 3

4 Thermal imager Equipment that displays the image, at the infrared wavelengths, of the object or of the environment to which is pointed out and measures their temperatures. The imager can have: - a single sensor and it scans the surface; - an array of sensors. The image obtained is called thermal image or thermography. It can be shown: - in black and white (the hottest parts of the emitting body are associated with brighter thermography areas); - in false colours (the temperature scale is associated with a colour scale, i. e. the parts at more elevated temperature are represented in yellow, zones at lower temperatures are red, the areas most cold are blue). Then in this case the colors of the thermography do not correspond, as in photography, at different wavelengths of the received radiation, but at different intensity of it. The previous considerations have shown that the sensor response to the temperature being measured cannot be linear. This nonlinearity must be compensated by the electronics of the camera.

5 Thermal imager The bodies pointed by the thermal imager have ε <1, because, in addition to radiate, they reflect radiation from surrounding objects. Then the equipment receives the sum of the energy emitted and reflected. So that the thermal imager outputs the true temperatures of the area at which it points out, you must subtract from the energy received the portion due to reflection. The thermal imager provides this operation but it is necessary to set the emissivity (which you should know) of the body you are pointing out. IR radiation Input optics Sensor matrix Amplification and A/D conversion Image construction and correction Display 5