Introduction to the Physics and Techniques of Remote Sensing. Jakob J. van Zyl

2.9). In this case, the Doppler shift is given by

      (2.32)

Figure 2.7 Doppler geometry for a moving source, fixed observer.

Figure 2.8 Geometry illustrating wave fronts passing by a moving observer.

Figure 2.9 Doppler geometry for a moving scatterer with fixed source and observer.

and if the source and observer are collocated (i.e., θ₁ = θ₂ = θ), then

      (2.33)

      The Doppler effect is used in remote sensing to measure target motion. It is also the basic physical effect used in synthetic aperture imaging radars to achieve very high resolution imaging.

2.2 Nomenclature and Definition of Radiation Quantities

A number of quantities are commonly used to characterize the electromagnetic radiation and its interaction with matter. These are briefly described here and summarized in Table 2.1.

      2.2.1 Radiation Quantities

      Radiant energy: The energy carried by an electromagnetic wave. It is a measure of the capacity of the wave to do work by moving an object by force, heating it, or changing its state. The amount of energy per unit volume is called radiant energy density.

      Radiant flux: The time rate at which radiant energy passes a certain location. It is closely related to the wave power, which refers to the time rate of doing work. The term flux is also used to describe the time rate of flow of quantized energy elements such as photons. Then the term photon flux is used.

      Radiant flux density: Corresponds to the radiant flux intercepted by a unit area of a plane surface. The density for flux incident upon a surface is called irradiance. The density for flux leaving a surface is called exitance or emittance.

      Solid angle: The solid angle Ω subtended by area A on a spherical surface is equal to the area A divided by the square of the radius of the sphere.

      Radiant intensity: The radiant intensity of a point source in a given direction is the radiant flux per unit solid angle leaving the source in that direction.

Table 2.1 Radiation quantities.

Quantity	Usual symbol	Defining equation	Units
Radiant energy	Q		joule
Radiant energy density	W		joule/m3
Radiant flux	Φ		watt
Radiant flux density	E (irradiance) M (emittance)		watt/m2
Radiant intensity	I		watt/steradian
Radiance	L		watt/steradian m2
Hemispherical reflectance	ρ
Hemispherical absorptance	α
Hemispherical transmittance	τ

Figure 2.10 Concept of radiance.

Radiance: The radiant flux per unit solid angle leaving an extended source in a given direction per unit projected area in that direction (see Fig. 2.10). If the radiance does not change as a function of the direction of emission, the source is called Lambertian.

      A piece of white matte paper, illuminated by diffuse skylight, is a good example of a Lambertian source.

      Hemispherical reflectance: The ratio of the reflected exitance (or emittance) from a plane of material to the irradiance on that plane.

      Hemispherical transmittance: The ratio of the transmitted exitance, leaving the opposite side of the plane, to the irradiance.

      Hemispherical absorptance: The flux density that is absorbed over the irradiance. The sum of the reflectance, transmittance, and absorptance is equal to one.

      2.2.2 Spectral Quantities

      Any wave can be considered