Bases of optical radiometry
The design and the performance of an electro-optical sensor rest upon a correct evaluation of the electrical output of its detector, and hence it is right here, at the detector outset, that the designer must validate the operating principle of the sensor to be. That is why this part is dedicated to some bases of radiometry, which will be used in part C for computing the optical signal incident upon the sensitive area of the detector, because this optical signal is at the origin of the electrical signal, object of part D.
Most electro-optical sensors respond to optical radiations of wavelengths typically comprised between 10-7 and 10-5 m (or photons of energies between 10-18 to 10–20 J), , by converting them into electrical signals, by means of its detector. At each instant, the detector output is proportional to the radiation instantaneous rate, or flux Φ, that is incident upon its sensitive area. Consequently, the flux arriving at the detector is the primary parameter to be optimized by the designer of the sensor.
In optics, there exists two types of detectors : quantum and thermal. Quantum detectors are sensitive to the photon rate of arrival of the incoming radiation, and thermal detectors to its energy rate, or power. For that reason, one may express a flux either in terms of either the photonic flux Φp ) (number of photons per second) or the optical power (or radiant flux, or energetic flux) Φe .
An ensemble of radiometric parameters have been defined in order to characterize optical radiations from the following points of view : geometry (size and position of sources, angular distribution), spectrum (radiant flux distribution with respect to wavelength), and variation with respect to time. These parameters are rapidly described below, starting with the ones applicable to non monochromatic radiations, i.e. spectrally extended.
In order to define a spectrally extended radiation at a given point, direction and wavelength, the recommended quantity is its spectral radiance dL/dλ, also called radiance spectral density.
At the point of interest, spectral radiance is the density of flux that is being radiated towards the said direction, per unit area (centered on the point and normal to that direction), per unit solid angle, and per unit spectral bandwidth. Depending upon the fact that one may be interested either in radiant flux (W) or in photonic flux (s-1), spectral radiance will be expressed in W m-2 sr-1 µm-1 or in s-1 m-2 sr-1 µm-1.
It is not always possible to define the spectral radiance of a source, nor is it necessary to know it in all cases : for example, each time the area of a radiating source is not known, it is impossible to evaluate the radiance of that source. In many applications, it may be sufficient to know the angular diagram of the emitter : if so, one will specify its spectral intensity dI/dλ :
For each direction in space starting from the emitter, the flux density per unit solid angle and per unit wavelength which is radiated along that direction. Units are W sr-1 µm-1 for spectral radiant intensity and s-1 sr-1 µm-1 for spectral photonic intensity.
To summarize, one will specify spectrally wide radiations by their spectral radiance whenever they are originating from an extended source (and if their emitting area is known), and by their spectral intensity whenever they come from a « quasi-point source », or from a source of unknown emitting area.
If it is desired to characterize a spectrally wide radiation at a given planar surface (surface of an object or of a detector), without taking into account its angular properties (angular properties are included in radiance as well as in intensity), one will have to use another parameter: it is the spectral irradiance dE/dλ, of that plane, which is the spectral flux density per unit area, in W m-2 µm-1 or in s-1 m-2 µm-1.
Now, if the incident radiation is quasi-monochromatic, i.e. if it occupies a very narrow spectral domain (typically less than a few percent of its central wavelength), it may be useless to specify its spectral properties : in many cases of quasi monochromatic sources (particularly in laser sensors where the spectral domain is the narrowest), one will specify the values of the previous parameters integrated inside the bandwidth of interest. The radiation will be then characterized either by its radiant flux or by its photonic flux (in W or s-1), by its radiance or by its photonic radiance (in W m-2 sr-1 or s-1 m-2 sr-1), by its radiant intensity or photonic intensity (W sr-1 or s-1sr-1), or by its irradiance or photonic irradiance (W m-2, ou s-1 m-2), at the wavelength of interest, without any more details about its exact spectral distribution.
In order to convert radiant quantities into photonic quantities, or vice versa, one will notice that, for a given wavelength, or inside a narrow spectral domain, any radiant quantity (either spectral or integrated) is the product of the corresponding photonic quantity by the photon energy at that wavelength (since it is the same for all photons). For example, radiant and photonic fluxes at a given wavelength λ are related to each other by the following equations :
and
It is recalled that all the above mentionned quantities are instantaneous ones, i.e. they express the spatial, angular and spectral properties of a radiation at each instant. The rate of change of these parameters with respect to time must also be taken into consideration, because it impacts upon the design of the electronic part of the sensor (bandpass, noise) : that will be the subject of part D.
In some applications, such as the detection of pulsed signals (laser pulses) or in the case of CCD image forming systems, the detected radiation is integrated during some integration time. Then it may be simpler to specify these time-integrated quantities, if one does not need any information about instantaneous values (it may be neccessary to care about instantaneous values whenever there is some risk of component saturation or degradation by high level signals as may be true with lasers). In case integrated quantities are sufficient, integrated radiant flux will lead to optical energy (in J), and a photonic flux being integrated over some time will result in a number of photons ; time integrated irradiance is called fluence (in Jm-2 , or in number of photons per m²).