Radiation can be observed either as a wave motion, or as single discrete packets of energy, photons. The two descriptions are not really contradictory. The energy is emitted as photons, but its statistical distribution over time is described by a wave.
Normally, one is dealing with a large number of photons arriving in a short time, and the radiation can be treated physically as a wave motion. However, in the visible and ultraviolet regions, very weak sources are typified by the detection of single photons.
The wave theory of radiation has been developed extensively. It impacts on remote sensing in the way that radiation is reflected at a surface and transmitted, absorbed and scattered in a medium. There is not time to go into the theory of wave motion except only in outline, giving some of the basic laws and results.
An electromagnetic wave propagates as shown in Figure 1, where the electric and magnetic components (vectors) oscillate at right angles to each other and to the direction of propagation. The energy of the wave is carried in the electric vector, and the wave shown in Figure l is polarised along the y-direction, and the radiation is described, in this case, as plane polarised. Naturally emitted radiation (eg. light sources, the sun) is usually unpolarised, as the light consists of many packets with the polarisation in random directions about x. Radiation from active radars or lidars is often plane polarised when emitted.
Figure 1: An electromagnetic wave propagating along the x-direction.
This wave theory shows that a ray of radiation will be reflected and refracted according to well known laws. Referring to Figure 2,
Reflected wave: i2 = i1 (3)
Refracted wave: n sin i1 = n' sin i'3 (4)
where n and n' are the refractive indices of the first and second media. As will be seen later, the relative intensity of the reflected and refracted rays are very dependent on the polarisation.
Figure 2: Reflection and refraction at a plane
surface.
Consider a ray of original intensity I traversing an absorbing medium.
Referring to Figure 3, let the reduction in intensity of the ray be dI for a path length
dx. Lamberts Law states that the fractional absorption dI/I is the same for all lengths
dx.
Thus,
which determines how the intensity of light is reduced, for instance, through the atmosphere when one of the gases is absorbing.
Often, particularly in gases, the absorption varies with wavelength. This is called selective absorption, and in the case of many gases, causes line absorption, which is absorption across a narrow band of wavelengths. If there are many absorption lines close together, then we have band absorption. In either case, a particular value of K is valid only for one narrow wavelength interval dA . Then,
To get the total absorption of a band of wavelengths, the absorption has to be integrated over the wavelengths.
A medium can either reflect, absorb, or transmit radiation. In terms of the total radiation flux,
where a is the absorptance, R the reflectance, and T the transmittance. According to Kirchhoff's Law, the absorptance a of a body is equal to emittance E. Now if a medium is strongly absorbing, so that there is no transmittance, then, from (9) above,
This states that if a body has a high emittance, then it has a low reflectance. The properties of actual surfaces are discussed later and it is shown that the above interpretation is not always so straight forward. Sometimes the absorption is so strong and radiation is absorbed so close to the surface, that reflection occurs rather than absorption. This occurs in a metal which is very opaque to radiation, but also very reflective. However, as T is zero, Equation (10) still holds.
As radiation can be described in terms of waves, then these waves can interfere or reinforce each other when waves are superimposed on top of each other. For instance, for a parallel-sided transparent plate of glass, say, which is an equal number of half wavelengths thick, multiple reflections from the two surfaces will reinforce each other to give strong transmission, whereas at other wavelengths they will not. This is the basis of the interference filter, used in radiometers to isolate a narrow band of wavelengths for detection.
Similarly, radiation will diffract through a lens aperture and the wave properties will cause parallel radiation to come to a focus in a finite spot of light rather than a point. This restricts the minimum distance between objects which can be resolved, especially at microwave wavelengths, where the receiver diameter/wavelength ratio is much smaller than in the visible or infrared.
