Propagation of radiations

In vacuum, radiations are not attenuated at all : their basic properties, such as spectral radiance or intensity, keep constant all along the path of propagation. By the contrary, in matter (atmosphere, water, optical fiber,...), the spectral, spatial and time properties of radiations degrade along the propagation, because of two main interactions with the medium : scattering and absorption.

Scattering originates from collisions between photons and constituents of the medium : large particles for Mie scattering, small particles and molecules for Rayleigh scattering; because of these collisions, a fraction of the incident photons is being directed in space towards directions other than the initial one ; consequently, the number of photons that go on propagating along the original path is reduced. Absorption originates from the fact that inside matter, a fraction of the energy being radiated is transferred into the medium itself at some specific frequencies, corresponding to vibration, rotation natural frequencies of electrons, atoms and molecules of the medium.

There are two parameters that are well suited to characterize the influence of a given medium upon the propagation of light at each point along the light path (figure 11) : these are its spectral, linear scattering and absorption coefficients, and , and they represent the percentages of light being respectively scattered and absorbed per unit length of the propagating medium, at the wavelength of interest.

If the refractive index of the medium is not constant, i.e. if it varies from one point to another, and/or with respect to wavelength, the velocity of light is being modified and so are the time and space characteristics of a light beam propagating in such a medium.

On the other hand, chaotic fluctuations of refractive indices make light rays depart from the rules of geometrical optics, which modifies the geometric shapes of objects as seen through « turbulent media » (well known example of mirages, created by atmospheric turbulence). These phenomena are outside the scope of this course and are only mentionned here for the sake of information, without more detail.

The percentage of the flux that propagates along its original direction at some wavelength (figure 11), after traversing a distance D inside a given medium (figure 11) is the spectral transmittance of the medium at that wavelength and over that distance.

A medium is said to be « inhomogeneous », if its absorption and scattering coefficients,   and β vary from point to point. One must then write :

If the medium is homogeneous, that means that   and β sare constant along the path at each wavelength, and the spectral transmittance of the medium over some range D is equal to :

The global attenuation of a propagating medium results from both effects, scattering and absorption : it is specified by the spectral attenuation (or extinction) coefficient   of the medium, as :

The spectral transmittance of the medium over some given path length D is therefore :

The first negative effect of scattering and absorption by a medium upon the performance of an electro-optical sensor is the attenuation of radiations as they propagate along. The second one is that, besides attenuating the radiations of interest for the sensor, a scattering and absorbing medium radiates stray light (or undesirable light), either by thermal emission (which is the case of the atmosphere in the infrared) or by scattering of ambient light (that is the origin of the « blue sky » in the visible), or both.

Let us consider, for instance, the case of an image forming sensor observing an extended scenery over a large spectrum : the apparent spectral radiance of an object, i.e. the spectral radiance at the sensor, is the sum of its initial radiance, attenuated by the spectral transmittance Tm(λ,D) of the medium over the distance of observation, and of the stray light radiance Lapp,m(λ,D) of the medium over the observation distance: