Describing Radiation

If we stand in a field on a clear day and look around the sky we’ll notice that lots of light comes from the sun and little from the other directions. It is brighter in the open field than in the shadow of a tree, and darker at night than at noon. The amount of radiation, then, depends on space, time, direction, and wavelength. Because light travels so fast we usually ignore the time dependence.

The fundamental measure of radiation is the amount of energy traveling in a given direction at a certain wavelength. This measure is called spectral intensity I_l, and has dimensions of power per unit area per solid angle per spectral interval, or units of W m^-2 str^-1 µm^-1. Spectral intensity is assumed to be monochromatic, or consisting of exactly one wavelength, and depends on position.

If we want to know the total amount of energy traveling in a given direction (say, the amount of energy entering a camera lens or a satellite detector) we must integrate I_l across some portion of the spectrum to compute intensity (or broadband intensity) I:

3. 


The limits of integration in (3) depend on the application. If the film in our camera is sensitive only to visible light, for example, the integration is over the visible portion of the spectrum, while if the lens is behind a colored filter we include only those wavelengths the filter passes. Intensity has units of W m^-2 str^-1; we use the term broadband intensity when the integration is over a large part of the spectrum (all the infrared or all the visible, for example). Unless the radiation interacts with the medium neither I_l nor I change with distance.

Imagine next a sheet of black plastic placed on the ground in the sunlight. How much energy does the sheet absorb? If we start with just one wavelength, we see that the sheet absorbs energy at a rate F_l

4. 


Weighting by µ accounts for geometry: a ray encountering the surface at an angle is spread over a wider area than a beam coming straight at the surface. F_l is called the spectral flux, and has units of W m^-2 µm^-1. Flux is traditionally divided into upward- and downward-going components:

5. 
6. 


The black sheet absorbs at all wavelengths, so the total amount of energy absorbed F is computed by integrating over both solid angle and spectral interval:

7. 


Flux (or broadband flux) has units of W m^-2.

The terms radiance and irradiance are also used in textbooks and the technical literature; these correspond to our terms intensity and flux.

Why are so many different quantities used to describe radiation? Because the two main applications of radiation, remote sensing and energy budget computations, require fundamentally different kinds of information. Remote sensing instruments, for example, usually have a finite field of view and a finite spectral sensitivity; interpreting measurements from these sensors therefore requires calculations of intensity, which may be broadband, narrowband, or essentially monochromatic, depending on the detector.

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