Introduction Remote sensing has been defined in many ways. It can be thought of as including traditional aerial photography, geophysical measurements such as surveys of the Earth's gravity and magnetic fields, and even seismic and sonar surveys. However, in a modern context, the term remote sensing usually implies digital measurements of electromagnetic energy often for wavelengths that are not visible to the human eye. A big advantage in remote sensing is that the final product is usually an image ("picture") of the Earth's surface which we can visualize and interpret as if it were as picture. Thus, many of the terms and concepts (e.g., brightness, contrast, color, intensity) are familiar, and we have a physical intuition for their meaning. Very often the ultimate goal of a remote sensing study is simply to be able to "see" some feature or changes in it well. Thus, the definition of a good result can be as subjective as deciding which of a series of photographs is best. However, one must be careful to remember that remote sensing images are more than just digital pictures, and we need to have a good understanding of their physical meaning. Remote sensing techniques measure the interaction of the Earth's surface (or at most the upper few meters) with electromagnetic energy from the sun and therefore are inherently a form of geographic information. Thus, the use of geographic information systems (GIS) to store and display remote sensing information is so common that the terms remote sensing and GIS are almost synonymous. The use and generation of digital elevation models is an example of how these two fields are merging. When properly geographically referenced (ie., the location of each measurement is carefully determined), images ("pictures") created from remote sensing measurements become maps of the Earth's response to various wavelengths of electromagnetic energy.

Aerial Photograph of Downtown District, El Paso, Tx Closeup view of downtown El Paso, Texas taken from an airplane. Note building shadows and clear resolution of image. Rectified USGS Digital Orthophoto Quarter Quadrangle El Paso SW January 28, 1996. Image by John Seeley, PACES.

Basic Principals of Electromagnetic Wave Propagation Most of the key physical principals we need to formulate a basic understanding of electromagnetic energy are familiar to us. In remote sensing, we classify electromagnetic energy by its wavelength. Visible light is the type of electromagnetic energy with which we are most familiar, but there is much to be learned from waves whose wavelengths are longer or shorter that those of visible light. The basic theory needed to understand electromagnetic energy well enough to use remote sensing techniques intelligently is surprisingly simple. The mathematics needed is not difficult, and the physical principles are straightforward. The trick is to link your training in mathematics and physics with your practical knowledge of physical phenomena (like light, x-rays, radar, and radio waves) to develop an intuitive understanding of the propagation of electromagnetic waves through the atmosphere and their interaction with the Earth's surface. One advantage is that many terms used in remote sensing are familiar and have the same meaning as in every day life (i.e., bright, dark, high and low contrast, and intensity). In physics, one learns that light (and electromagnetic energy of similar wavelengths) can be thought of as either a propagating wave or a stream of particles. In remote sensing, we usually think in terms of waves, and sensors are designed to detect waves whose wavelengths lie in specific bands (ranges of wavelengths).

Landsat Thematic Mappter (TM) Image West-central El Paso, Texas Image by John Seeley

Basic Concepts, Equations and Terms

There are a number of basic equations (and the terms involved in them) which form the basis for an understanding of electromagnetic waves and how to use them in practical applications.

1. Electromagnetic energy has been classified by wavelength and arranged to form the electromagnetic spectrum.
   

   This spectrum shows that visible light occupies only a very narrow band of wavelengths. Gamma rays, x-rays, and most ultra-violet energy do not penetrate the atmosphere so they are not used in remote sensing. However, infrared and microwave (radar) energy is measured regularly and is very useful in addition to energy at visible wavelengths. Thus, we must remember that almost images made from remote sensing data are false color in nature and are not pictures in the sense that humans would never see the Earth in this particular fashion. The images in fact detect objects and phenomena which could never be "seen" by the human eye. Primarily as the result of ozone (O3), CO2, and water vapor, the atmosphere absorbs energy in several discrete bands so sensors are designed to avoid these bands since little energy survives transmission through the atmosphere. Most remote sensing devices are passive in that they merely measure the intensity of the Sun's electromagnetic energy which is reflected off the surface of the Earth or is emitted (radiated) as heat. However, some systems (radar in particular) are active in that the energy that is measured is generated by the measuring system not the Sun.

2. As electromagnetic energy interacts with the atmosphere and the surface of the Earth, the most important concept to remember is the conservation of energy (i.e., the total energy is constant).

   Our main concern is the fate of the energy that makes it through the atmosphere to hit the surface of the Earth. The three main processes are reflection (scattering is a form of reflection), absorption (this energy is converted to heat and some is emitted with a change in wavelength and a time delay) , and transmission.

   Each of these phenomena are a function of wavelength (l), and conservation of energy leads to the following equation: Ei(l) = Er(l) + Ea(l) + Et(l), where, Ei(l) = the incident energy, Er(l) = the reflected energy , Ea(l) = the absorbed energy, and Et(l) = the transmitted energy.

   In the case of a lens, almost all of the energy is transmitted. However, the case of the Earth's surface most energy is reflected or absorbed. At a particular location, the ratio of the reflected energy to the incident energy as a function of wavelength (expressed as a %) is called the reflectance spectra, and is expressed as: R( l) = Er(l) / Ei(l)

   The interaction of the incident energy with the atomic structure of soil, rocks, plants, bodies of water, man-made objects, etc. governs how much energy is absorbed and thus how much is reflected. Materials such as minerals and leaves have a (at least somewhat) distinctive reflectance spectra which can be measured by a laboratory or field-portable spectrometer. These values can then be compared to remote sensing data in order to identify which materials are present in the area of an image.

   

3. As electromagnetic waves travel , they encounter objects (discontinuities in velocity) that reflect some energy like a mirror and transmit some energy after changing the travel path (refract - like a lens).

   A basic principle of optics that applies here is: Snell's law: sin i / C1 = sin r/ C2 The ratio of the velocities is called the index of refraction - n.

   This type of reflection (technically called specular reflection) is what we usually think of when we consider physical processes in optics, seismology, or billiards. However, it only occurs when the surface is smooth (irregularities are very small relative to the wavelength of the incident electromagnetic energy); examples are the reflection of objects in a mirror or a body of quiet water. However, in the case of the Sun's energy reflecting off the Earth, this only partly describes the processes that occur. Specular reflection is a function of wavelength, the size of the reflecting particle, and the index of refraction of the particle. In addition, some energy usually is transmitted through a few particles very near the surface and is thus effected by their absorptive properties (which are function of wavelength) as well as adjacent particles that are encountered (see below). The end result is that reflected energy leaves the surface at all angles (diffuse reflection) after interacting with particles near the surface. The resulting variations in reflectance with wavelength are the process which gives us color as we see it visually and the energy that we study in remote sensing. Thus, reflectance is basically a simple concept, but we must remember that it is a function of the wavelength of the incident energy (and to some extent the angle of incidence), the index of refraction and absorption of the materials which make up the reflecting surface, and the size of the particles which make of the surface.

   This is what really happens as light interacts with a surface.

4. The distance (d) a electromagnetic wave travels in a certain time (t) depends on the velocity of the material (v) through which the wave is traveling; d = v t.

   Since all electromagnetic energy travels at the speed of light (usually denoted by c) this is equation is very simple to apply. For example, we can generate radar waves and time their return after reflection from the Earth's surface. The distance to the reflecting object can be obtained from this simple equation.

5. The velocity (c), frequency (f), and wavelength(l) of a electromagnetic wave are related by the equation: c = f l.

   Strictly speaking, this equation applies to simple harmonic motion in which we are dealing with a wave that consists of motion with a single frequency (i.e. a sine wave), but in remote sensing, one usually treats measurements that are made for a narrow band of frequencies as representing a single frequency at the middle of the band.

   In the picture to the right, the wave is depicted as what happens to a particular point as the wave passes so the horizontal axis in this diagram is in units of time and the distance between two peaks is the period. We can also think of depicting the wave as if we could take a snapshot of it at one instant of time. In this case, we are looking at a spatial picture in which the horizontal axis is in units of distance and the distance between two peaks on the wave form is the wavelength.

   We usually think of electromagnetic waves as a constant stream of energy from the Sun for a particular frequency. Thus, the depictions in the figure of an EM Wave apply. In radar applications, we generate our own energy, and in this case, it is appropriate to think of these waves as a pulse (wavelet) of energy that is as short as possible in time. Strictly speaking, it is no longer simple to think of the wavelength or frequency of this wave although such terms are still commonly used in radar studies. One reason for this usage is the utility of wavelength as a measure of the spatial dimension of a electromagnetic wave relative to some object whose interaction with the wave is of interest.

6. We can draw on the analogy of a rock dropped into a pond to define wavefront.

   The circular ripples on which the wave motion is the same (a particular peak or trough) are wavefronts. In the case of most remote sensing applications, these fronts are spherical and spread out in three dimensions from the source (the Sun). Because of our great distance from the Sun, we think of the incoming wavefront as being planar, and in radar, we go to great lengths to generate a planar wavefront (we call this synthetic aperture radar and almost all modern data is of this type). In this way, one can think of the propagating electromagnetic energy as being very organized. When a wavefront encounters discontinuities that are large relative to a wavelength, the energy is reflected (and refracted for example through a lens) also in an organized fashion (Snell's law above). Thus, light whose wavelength is such that it is red looks red to us when it is reflected.

7. It is quite appropriate to look at the amplitude of a electromagnetic wave and think of it as a measure of the energy in that wave.

   Obviously, the larger the amplitude the more energetic the wave. However, technically we must remember that introductory physical treatments of simple harmonic motion show that energy is proportional to the square of the amplitude.

8. Electromagnetic waves lose energy (amplitude) as they travel because of several phenomena:
   • Spherical spreading
     This phenomena is simply the fact that the amplitude dies off with distance traveled ( i.e., the further you are from the source, the weaker the signal). This obvious physical effect is no different than observing that as one gets farther and farther from a source of sound, a weaker and weaker sound is heard. Technically, as the wave travels, the wavefront is a sphere whose radius gets larger and larger. Since the area of a sphere is 4piR2, at some radius (distance traveled), the energy per unit area on the wavefront is equal to the original energy divided by 4piR2. Since the energy is proportional to the square of the amplitude, the amplitude is proportional to 1/R. Strictly speaking, the energy is not diminished by this effect, it is just spread over the surface of larger and larger spheres.

   • Absorption
     It is appropriate to think of absorption as the tendency for materials to simply soak up electromagnetic energy and convert it to heat. We can measure some of this energy as radiated (emitted) heat that is at a longer wavelength than the original energy.

   • Scattering
     The interaction of electromagnetic waves with objects that are small relative to a wavelength (i.e., molecules in the atmosphere) leads to energy being reflected (scattered) in an unorganized fashion. This term is very intuitive, and we can just think of the energy being randomly dispersed in three dimensions. The primary scattering process at work is called Rayleigh scattering which proportional to 1 over the wavelength to the 4th power. Thus in the atmosphere, short wavelengths are subject to selective scattering which is basically due to the fact that many particles and molecules are too small to effect the longer wavelengths significantly. Short wavelength energy like UV and blue light are in fact scattered about twice as strongly as red light. For wavelengths in the visible light range, selective scattering causes us to see that color. Blue sky, which is the effect of selective scattering of blue light, is the classic example of this effect. This effect (along with absorption) is a fundamental restriction in remote sensing and limits the range of wavelengths that can be employed. When large particles like water droplets are encountered, the scattering effects a broad range of wavelengths (non-selective), and then we simply see unorganized white light. Classic examples of this effect are clouds and fog.

9. Resolution

   A question which constantly arises in electromagnetic studies is whether the target of a remote sensing study can actually be "seen" (resolved) in the data. When one looks at a printed copy of a particular image or picture, resolution can be quantified to some extent but is really no more complex than determining if the interpreter can see the object, pattern, signature, texture, etc. that is of interest. In the case of digital images, resolution is a technical issue in two ways. First of all by its very nature, a digital image is composed of pixels (ground resolution cells) of finite size. The measurement for each cell is the intensity of the reflected energy for a particular band of wavelengths, and the size of the pixel is a measure of spatial resolution. The simple fact is the smaller the pixels, the better the resolution.

   Good resolution is of course desirable, and as new satellites and airborne systems become available, the tendency is for the pixel size to decrease (30 m for Landsat Thematic Mapper, 10 m for SPOT, 5 m for IRS). There is also the question of spectral resolution. In this case, the question is how well have we determined the variation of reflectance with wavelength (the reflectance spectra). As a practical matter, this simply a question of how many bands a particular device is capable of measuring and what is their width (i.e., what is the range of wavelengths). A large number of narrow bands is desirable and again technology is providing data with better resolution. For example, Landsat Thematic Mapper makes measurements for 7 bands while the AVIRIS airborne system makes measurements for 224 bands. Thus in digital terms, the denser the measurement, the better the resolution. However, the data volume also increases greatly as the sampling rate (spatially or in wavelength) increases, and this will affect the speed and ease of the data processing.

   SPOT Panchromatic: Southern Tip of Franklin Mountains El Paso, Texas

   References

   Lilles and Thomas M., and R. W. Kiefer, 1987, Remote Sensing and Image Interpretation: John Wiley and Sons, New York, 721pp.

   Sabins, Floyd F., 1997, Remote Sensing: Principals and Interpretation: W. H. Freeman and Company, New York, 494pp.

   Vincent, Robert K., 1997, Fundamentals of Geological and Environmental Remote Sensing: Prentice Hall, Upper Saddle River, New Jersey, 366pp.