Output signal from the detector

Two types of detectors may be used in electro-optical sensors : thermal and quantum. The first ones convert incident energy in temperature rise, and the second ones directly into electric charges. Whatever its type, the detector will generally be specified by its spectral sensitivity Ri(λ) in AW-1 , which is the ratio between its output current and the input flux, with respect to wavelength. In case a quantum detector is being used, one may also specify its spectral quantum efficiency η(λ), or ratio between the number of output electrons per input photons, with respect to wavelength. Spectral quantum efficiency η(λ) and sensitivity Ri(λ) are related by :

If the incident radiation is spectrally wide, every narrow spectral band, of elemental width dλ centered at wavelength  λ produces the following elemental output from the detector :

where dΦp and dΦe are the expressions, in photonic ( s-1) and radiant (W),units, of the incident flux inside that band, q the charge of an electron, and h Planck's constant.

As and ,there results that, in response to an incoming spectrally wide radiation, the output current from the detector is :

If the incident radiation is monochromatic, the output current of the detector is more simply written as :

Defining the pertinent output signal from the detector of an EO sensor is not always an easy task : in some cases, the detector may be permanently receiving a non negligible flux from the bakground, and hence delivering some permanent signal, even in the absence of the pertinent source. In the visible and in the very near infrared, this background current may be brought down to a minimum level, or dark current, simply by putting the sensor in total darkness, because thermal radiation at room temperature is negligible in that spectral band ; by doing so, one can say that the detector output is not far from being representative of the signal to detect. If the same sensor is being operated at high illumination levels (in presence of the sun or of some artificial lamps), then the detector may be exposed to stray light, but these perturbations may be easily be taken into account.

In the infrared, the situation is quite different, because thermal radiation at room temperature is present even if the sensor is operating in complete darkness. This permanent radiation gives rise to a non negligible signal and it is present in temperatures measurements applications such as thermography or thermal imaging. Although applications look very similar at first sight, their « useful or pertinent signals » are defined differently : on one hand, the useful signal in thermography is the value of the detector output, because it is the one that carries information about the temperature of an object, after calibration on standard sources such as blackbodies. In thermal imaging applications, the signal that matters is is not so much the previous output, as its changes from point to point on the object.

At the design stage of an EO sensor, it is very important for the designer to define the nature of the pertinent output signal. What applies to thermal imagery may be applied to a large number of domains, where the interesting information is not the total value of the detector output, but its variation in time or in space : this is true of optical telecommunications (difference between bits 0 and 1), imaging systems (differences in reflectance or in temperature), target detection (target presence or absence), laser pulse detection (rangefinding), surveillance (intrusion detection),...