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

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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., θ 1= θ 2= θ ), then

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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.

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.

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/m 3
Radiant flux	Φ		watt
Radiant flux density	E (irradiance) M (emittance)		watt/m 2
Radiant intensity	I		watt/steradian
Radiance	L		watt/steradian m 2
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.

Any wave can be considered as being composed of a number of sinusoidal component waves or spectral components, each carrying a part of the radiant flux of the total wave form. The spectral band over which these different components extend is called the spectral width or bandwidth of the wave. The manner with which the radiation quantities are distributed among the components of different wavelengths or frequencies is called the spectral distribution. All radiance quantities have equivalent spectral quantities that correspond to the density as a function of the wavelength or frequency. For instance, the spectral radiant flux Φ( λ ) is the flux in a narrow spectral width around λ divided by the spectra width:

To get the total flux from a wave form covering the spectral band from λ 1to λ 2, the spectral radiant flux must be integrated over that band:

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Figure 2.11 Spectral luminous efficiency V ( λ ).