Basic Principles of Electromagnetic Energy: Wave Definitions

Whether in the form of radio waves or visible light, all electromagnetic energy is inherently similar. The behaviour of electromagnetic energy is governed by basic wave theory, which is described by Maxwell's equations. These equations describe electromagnetic radiation as traveling at a velocity [c] equal to 3 x 108 m/s, in a sinusoidal, harmonic fashion. The electromagnetic wave is propogated in a direction perpendicular to the electric and magnetic fields. According to this, electromagnetic waves are characterized by amplitude, wavelength, period, frequency, and velocity.
 
Some Basic Definitions: 
  • Amplitude is the distance from a wave's midpoint to its crest or trough.
  • Wavelength (lambda)is the distance between crests
  • Period (T) is the time elapsed between two consecutive crests passing a given point
  • Frequency (f) is the number of crests passing a given point in one second. Frequency is the inverse of period (f=1/T). For example, if T = 0.1 seconds, f= 10 per second.
  • Velocity (v) is the distance traveled in a given period of time (v=distance/time). 
 

Remember that wavelength of an electromagnetic wave is the distance between crests and the period of an electromagnetic wave is the time between crests. The velocity of an electromagnetic wave is the wavelength (distance) divided by the period (time). This is not an especially useful description of velocity, however, because many applications of remote sensing make reference to wavelength and frequency, not wavelength and period. However, since the definitions above tell us frequency is the inverse of the period, it is not too difficult to express velocity in terms of freqency and wavelength:

A very important point to make at this time is that this relationship holds for all waves. Velocity always equals frequency times wavelength. Beyond this, electromagnetic waves are a special case, because the velocity of electromagnetic waves is essentially constant. Electromagnetic energy travels at the speed of light (indeed, light is electromagnetic energy), and that is always 3 x 108 meters/second (186,000 miles/second) in a vacuum.

Because the speed of light is constant, you can see a simple inverse relationship between the frequency and wavelength of electromagnetic waves. As the frequency increases, the wavelength decreases, and the opposite is true as well. Notice how the diagram on the left has a very short wavelength (but high frequency) compared with the diagram on the right.

This chart indicates the relationship between wavelength and frequency.
 

Although most of the characteristics of electromagnetic waves are described sufficiently by classical wave theory, at very short wavelengths electromagnetic radiation interacts with matter in ways that wave theory (and Maxwell's equations) cannot account for. In this case, a particle description of electromagnetic radiation is more appropriate than a wave description. In such a description, electromagnetic energy travels in discrete units, or quanta, of energy. The energy of a quantum is given as Q=hf, where h = Plank's constant (6.26 X 10-34 Jsec), f = frequency, and Q is the energy of a quantum is Joules. The basic difference between the wave description and quantum (particle) description is that the quantum description predicts energy will be delivered to a target on a probabilistic basis, not as if it is spread evenly over the wave. However, even though light has this "particle nature", the overall average effect in nature follows Maxwell's equations.

You can relate the wave and quantum models of electromagnetic radiation by:
 
1. solving for f yielding 
2. substituting into Q=hf  yielding 
You should be able to see from this equation that the shorter the wavelength, the higher its energy content (the inverse is also true). For this reason, shorter wavelengths are easier to sense than very long ones such as passive terrestrial microwave emissions.


Energy Sources

Electromagnetic waves are radiated through space from some source. When the energy encounters an object, even a very tiny one like a molecule of air, one of three reactions occurs. The radiation will be (1) reflected off the object, (2) absorbed by the object, or (3)transmitted through the object. The total amount of radiation that strikes an object is referred to as the incident radiation, and is equal to:

reflected radiation + absorbed radiation + transmitted radiation

In remote sensing, we are largely concerned with REFLECTED RADIATION. This is the radiation that causes our eyes to see colors, causes infrared film to record vegetation, and allows radar images of the earth to be created. The source of a vast majority of this reflected radiation is the sun.

While the sun is the most obvious source of the electromagnetic energy measured in terrestrial remote sensing, it is not the only energy source one might encounter. This is because all matter at temperatures greater than absolute zero (0 Kelvin) continuously emits electromagnetic radiation. Generally, the hotter an object is, the more it radiates, but all objects with even the slightest sub-molecular motion radiate some energy. More on this idea follows.

Remote Sensing uses electromagnetic energy from both natural and man-made sources. Those energy sources which occur naturally are often referred to as passive energy sources. Remote sensing based on electromagnetic energy deriving from man-made sources is usually referred to as active. Solar energy (including infrared, visible, and ultraviolet light, as well as x-rays and gamma rays) and radiant heat (detectable as the far-infrared) are examples of passive energy sources. Radar and laser profilers are examples of active energy sources.

Electromagnetic energy (radiation) is one of many forms of energy (such as chemical, electrical, kinetic, magnetic, nuclear, or thermal). There are a number of transformation mechanisms that convert the forms of energy listed above into electromagnetic radiation. Some of these are summarized in the following table:
 
Transformation Mechanisms for the Generation of Selected Bands of Electromagnetic Energy (after Elachi, 1987)
Wavelength
Method of Generation
radio Periodic currents of electric charges in wires, electron beams, or antennae
microwave Electron tubes use high-speed electrons to generate a variable electric/magnetic field, which is then guided into a radiating structure.
infrared/visible Molecular excitation (vibrational or orbital) followed by decay. The frequency emitted is directly related to the energy difference between the two energy levels of the molecules.



Blackbody Model

A blackbody is a perfect absorber and emitter of radiation. That is, in a perfect blackbody, all radiation incident on the object is re-emitted, and emittance is a function only of temperature. In nature, true blackbodies do not exist. However, many objects approximate blackbodies.

In the discussion that follows, a number of equations are given that describe the electromagnetic energy emitted by a blackbody. Before getting into the mathematics of perfect emitters, let's describe the blackbody curves in this figure. These curves show the amount of energy radiated at each wavelength for blackbodies of various temperatures. The red line is the blackbody curve for the earth, whose ambient temperature (the "average" temperature given off by the soil, water, vegetation, and built environment) is about 300 Kelvin. The area under this curve is the total energy emitted across all wavelengths by the earth. You can see on the figure that the area under the 1200 K curve is greater than the area under the 300 K curve. There is a direct relationship between the temperature of a blackbody and the amount of electromagnetic energy it emits. The hotter the object, the more energy it gives off. Even though a perfect blackbody is only a theoretical construct, most objects in nature behave like "imperfect" blackbodies, and you will find they obey this principle. For instance, consider this diagram which overlays the theoretical curve created by a perfect blackbody and the actual curve created by the Sun.The hotter an object is, the more electromagnetic energy it emits. This is the relationship the Stefan-Boltzmann Law (below) describes.

You should also notice on the "Blackbody Radiation" figure that the curves for hotter temperatures "peak" at lower wavelengths than do the curves for cooler temperature objects. Just as the total amount of energy emitted by an object depends on its temperature, the wavelength at which the largest portion of energy is emitted depends on temperature. Hotter objects emit more energy at lower wavelengths than do cooler objects. Think about this relationship. It takes more energy to make something hotter, and the quantum description of electromagnetic radiation (section 2.33) indicates that EM radiation with more energy has a shorter wavelength. Now, you are seeing an instance where hotter objects (more energy) emit more at shorter wavelengths than do cooler objects. Notice how, on the diagram, the peak of the 300 K line is at about 9 micrometers. Indeed, the earth continually emits radiation at 9.7 micrometers. It is extremely important to take this "background" radiation into account when collecting remote sensing data in the thermal infrared portion of the electromagnetic spectrum. Now look again at the figure in which the solar radiation curve and 6000 K blackbody curve are superimposed. Notice that the "peak" wavelengths are between 0.4 and 0.8 micrometers -- the wavelengths of visible light! The wavelength at which a blackbody has its peak emittance is given by Wien's Displacement Law (below).


Plank's Radiation Law for Blackbodies gives the spectral radiance of an object as a function of its temperature.

Wien's Displacement law

If we differentiate Plank's Radiation Law for blackbodies and set it equal to zero, we arrive at a formula which gives the wavelength of maximum radiance for a blackbody of a given temperature. This formula is referred to as Wien's Displacement Law.

Finally, if a blackbody is acting as a perfect emitter, the total emitted energy over the whole spectrum is given by the Stefan-Boltzmann law:

At this point you have a fairly good understanding of the properties of electromagnetic radiation as it travels through a vacuum. In the next module we will consider what effects the earth's atmosphere has on this energy as it moves from its source, through the atmosphere, and to our sensors.