Electromagnetic Spectrum: Transmittance, Absorptance, and Reflectance

 Some objects are capable of transmitting the light through their bulk without significant diminution (note how the beam bends twice at the medium 1/medium 2 interface but emerges at the same angle as entry). Other materials cause the light energy to be absorbed (and in part emitted as longer wavelength radiation). Or, the light can be reflected at the same angle as it formed on approach. Commonly the nature of the object’s surface (owing to microscopic roughness) causes it to be scattered in all directions.

The primary source of energy that illuminates natural targets is the Sun. Solar irradiation (also called insolation) arrives at Earth at wavelengths which are determined by the photospheric temperature of the sun (peaking near 5600 °C). The main wavelength interval is between 200 and 3400 nm (0.2 and 3.4 µm), with the maximum power input close to 480 nm (0.48 µm), which is in the visible green region. As solar rays arrive at the Earth, the atmosphere absorbs or backscatters a fraction of them and transmits the remainder.

The diagram is a plot of the relative irradiance of sunlight as a function of wavelengths; note that the maximum irradiation is in the green region of the visible spectrum; the upper curve shows the relatively smooth curve for sunlight before entering the atmosphere whereas the lower curve shows the general reduction in incoming radiation by the atmosphere, with absorption bands or troughs associated with specific constituents; the shape of the curve is determined by the Planck Blackbody Law and the Wien Displacement Law discussed in Section 9.

Upon striking the land and ocean surface (and objects thereon), and atmospheric targets, such as air, moisture, and clouds, the incoming radiation (irradiance) partitions into three modes of energy-interaction response:

(1) Transmittance (τ) – some fraction (up to 100%) of the radiation penetrates into certain surface materials such as water and if the material is transparent and thin in one dimension, normally passes through, generally with some diminution.

(2) Absorptance (α) – some radiation is absorbed through electron or molecular reactions within the medium ; a portion of this energy is then re-emitted, usually at longer wavelengths, and some of it remains and heats the target;

(3) Reflectance (ρ) – some radiation (commonly 100%) reflects (moves away from the target) at specific angles and/or scatters away from the target at various angles, depending on the surface roughness and the angle of incidence of the rays.

Because they involve ratios (to irradiance), these three parameters are dimensionless numbers (between 0 and 1), but are commonly expressed as percentages. Following the Law of Conservation of Energy: τ + α + ρ = 1.

A fourth situation, when the emitted radiation results from internal atomic/molecular excitation, usually related to the heat state of a body, is a thermal process. The theory underlying thermal remote sensing is treated in Section 9.

When a remote sensing instrument has a line-of-sight with an object that is reflecting solar energy, then the instrument collects that reflected energy and records the observation. Most remote sensing systems are designed to collect reflected radiation.

There are two general types of reflecting surfaces that interact with EMR: specular (smooth) and diffuse (rough). These terms are defined geometrically, not physically. A surface may appear to be smooth in a physical sense, i.e., it appears and feels smooth, but at a scale on the order of wavelengths of light, many irregularities might occur throughout that surface. (A concrete roadway may appear smooth and flat from a distance but feels rough when a finger passes over it, owing to small grooves, pits, and protuberances.) Radiation impinging on a diffuse surface tends to be reflected in many directions (scattered). The Rayleigh criterion is used to determine surface roughness with respect to radiation:

h is less than or equal to wavelength λ/8cosθ

where h is the surface irregularity height (measured in Angstroms), λ is the wavelength (also in Angstroms) and θ is the angle of incidence (measured from the normal [perpendicular] to the surface). If λ is less than h, the surface acts as a diffuse reflector; if greater than h, the surface is specular.

A specular surface (for example, a glass mirror) reflects radiation according to Snell’s Law which states that the angle of incidence θi is equal to the angle of reflectance θr (where the light ray moves in the principal plane that passes normal to the surface). Actual values (e.g., radiances) of specular reflected radiation depend on the type of material making up the specular surface. Specular reflectances within the visible wavelength range vary from as high as 0.99 (%) for a very good mirror to as low as 0.02-0.04 (%) for a very smooth water surface.

In general, natural surfaces are almost always diffuse and depart significantly from specular at shorter wavelengths (into the infrared) and may still be somewhat diffuse in the microwave region.

The behavior of a perfectly diffuse, or Lambertian, surface is described with the help of this figure:

Effect of a Diffuse Surface on incoming radiation.

Consider a bundle of rays (making up the radiation flux) from a single distant source position at an incident angle θI (relative to the zenith direction) and an azimuth angle φ0 (relative to north). Imagine the (arbitrarily) horizontal plane of a target being irradiated to be enclosed in a hemisphere (this simplifies some calculations because it allows polar coordinates to be used [which we will ignore here]). For the wavelength conditions we set, the surface is considered rough or diffuse and has irregularities where the surface departs from horizontal, at varying slopes. A given ray RI located in the principal plane now strikes the surface at a point Q1. It will be reflected according to the position of the minute surface at Q depending on its slope. If that surface is horizontal (slope = 0°), the ray moves away along path RR in the principal plane as though this geometry is specular. But if the point surface Qs is non-horizontal, i.e., has varying slopes defining the shape of the irregularity, the ray (mathematically treatable as a vector) will now move out along some direction RD through its scattering plane whose position is defined by θD and φD. At other points (Qn) on the surface, the direction of the outgoing R will differ according to the orientation of the slope at the immediate irregularity. Thus, a large number of incoming rays meeting the surface at other irregularities (most probably with randomly oriented slopes) will be redirected (diverge) in all possible directions extending through the hemisphere of reference.

The radiance in any one direction is, on average, the same as any other; in other words, radiance is constant at any viewing position on the hemishpere and is therefore independent of θ0. However, the radiant intensity at any position will vary according to the relation Iθ = I0cosθ. This states that as the angle of incident radiation Iθ is varied, the intensity of outgoing radiation also changes. For normal incidence (from the zenith), θ is 0 and cosθ is 1, so Iθ = I0. For all other angles cosθ is less than 1 and I0 is reduced. Although a homogeneous, non-variant surface viewed from any position will seem to be uniformly illuminated (constant radiance), that surface will become less bright as the source is moved from a vertical (overhead) position towards the plane itself (horizon).

The term bidirectional reflectance describes the common observational condition in remote sensing in which the viewing angle φ differs from the angle θ of rays incident on a diffuse surface, and incoming/outgoing rays are not in the same principal plane (different azimuths). Thus, reflectances from the same target (type) change in value from various combinations of θ and φ: this is particularly important when the sensor operates off-nadir (looking sidewards) and the Sun angle and azimuth vary during the period of operation (as occurs when an aircraft moves back and forth along flight paths during an aerial photography mission). Consider this diagram (treating the two dimenionsal case; the behavior can be displayed in the third dimension using a hemisphere as reference):

Bidirectional Reflectance.

For an imperfectly diffuse reflector (having a specular component) and a viewer directly overhead (such as a sensor looking straight down normal to the Earth’s surface), scattering will produce three-dimensional envelopes (shown here as a two-dimensional slice) of reflectances deriving from rays A, B, and C. These radiances vary in intensity in an asymmetric way (except for A). Thus, for B and C rays, there is general diffuse reflectance in all directions plus a “spike” or differential increase in directions spread around the angle of the specular component. Since reflectances also vary with wavelength, envelopes of bidirectional reflectance must be calculated for each wavelength in the range of λs considered; this is commonly not done in routine image analysis but is often necessary when a quantitative study involving field measurements is undertaken.


About Rashid Faridi

I am Rashid Aziz Faridi ,Writer, Teacher and a Voracious Reader.
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