Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.1 W.D. Philpot, Cornell University, Fall 1 3. EM INTERACTIONS WITH MATERIALS In order for an object to be sensed, the object must reflect, emit or transmit radiation to the sensor. The interactions of electromagnetic radiation will be reviewed to develop a better understanding of how radiation from an object can be used to learn something about the object. 3.1 Reflected, absorbed and transmitted components Radiation that strikes an object will be reflected, absorbed or transmitted (Fig. 3.1). For conservation of energy, the total amount of incoming or incident radiation must equal the amounts that are reflected, absorbed or transmitted. This relationship must hold at every wavelength or spectral band. Consequently, any object can be characterized by the proportions of incident radiation that it reflects, absorbs or transmits, at each wavelength or band of wavelengths. These proportions will be peculiar to, though not necessarily unique, for any object. Fig. 3.1: Reflection, refraction, absorption and transmission in real media. An object's reflectivity or reflectance 1,, defines the proportion of incident radiation (e.g., from the sun) that will be reflected; its absorptivity or absorptance,, defines the proportion that will be absorbed; and its transmissivity or transmittance,, defines the proportion that will be transmitted. Because these are spectral quantities varying with wavelength, an object will be characterized by its spectral reflectance,, spectral absorptance,, or spectral transmittance,. In accordance with conservation of energy, these quantities are related by Kirchoff's Law: + + = 1 (3.1) 1 Formally, reflectivity is the property of a material and is characteristic of an optically thick sample of the material; reflectance is the property of a particular sample of that material or a particular surface and may vary with the thickness of the sample. Most of the materials on the earth surface can be considered optically thick ( =0), making the distinction moot. As with reflectivity, absorptivity is a property of the material while absorptance refers to a specific sample and, since it is a ratio of the radiation absorbed by a sample to the radiation incident on a sample, it depends directly on the thickness of the sample. In remote sensing we are dealing with optically deep targets (no transmission) and so are concerned with the change in the spectral change of the reflected light due to absorption. Again, the difference is moot. Yet another term, absorbance (without the t), also known as optical density, is defined as A =log 10 (I 0 /I) where I 0 is the light incident on the sample, and I is the light emerging from the sample.
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3. W.D. Philpot, Cornell University, Fall 1 In remote sensing of the earth, we are generally concerned with land or water for which light that is not reflected is assumed to be absorbed. Transmission can be an important factor to consider in some cases (e.g., when considering clouds or the light reaching the understory of a full canopy forest), but we will generally be concerned with opaque objects for which, = 0 and + = 1 (3.) Reflectance is another matter entirely. As is indicated in Fig. 3.1, there are several components of reflection that must be considered. We need to consider not only reflectance at the surface of the material, but within its volume. Absorption may occur at the surface or in the volume, but the absorption that is viewed with remote sensing systems is usually characterized as a property of the volume of the material. 3.1.1 Reflection from a flat surface Reflection occurs at a boundary between two materials with different indices of refraction. If the surface is smooth relative to the wavelength of incident radiation, then the angle of reflection will be equal to the angle of the incident radiation (relative to the normal to the surface), but in the opposite direction (Fig. 3.). The radiation that is not reflected (or absorbed) is transmitted into the second material, making an angle with the local normal that is given by Snell's Law: n 1 sin 1 = n sin (3.3) where 1 is the angle of incidence, is the angle of refraction, and n 1 and n are the indices of refraction of material 1 and respectively. 1 1 n 1 n Fig. 3.: Angles of reflection and refraction at an optically smooth boundary Specifying the proportion of the radiation that is reflected or refracted is complicated by the fact that it is sensitive to the polarization of the incident radiation. The plane of polarization is defined as parallel ( ) or perpendicular () relative to the plane defined by the incident, reflected and refracted rays. (In remote sensing, particularly for microwave systems where polarization is a major issue, parallel polarization is often called "vertical" polarization and perpendicular polarization is referred to as "horizontal" polarization.) With this in mind, we may write the Fresnel equations for reflectance and transmittance of radiation. We will assume that there is no absorption at the surface. In that case, Fresnel's equations for reflection may be written either in terms of the angles of incidence and refraction, or equivalently, in terms of the angle of incidence and the relative index of refraction, n = n /n 1, where n 1 is the refractive index in the medium on the side of the incident radiation:
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.3 W.D. Philpot, Cornell University, Fall 1 r 1 1 1 1 1 1 sin cos n sin sin cos n sin (3.4) r 1 n sin 1 n cos 1 1 1 1 tan ( ) tan ( ) n sin n cos (3.5) Similarly, Fresnel's equations for the transmission coefficients are: t t sin 1 cos cos 1 sin( 1/ 1 ) cos 1 n sin 1 sin 1 cos cos 1 1/ 1 1 n sin 1 n cos 1 sin( ) cos( ) (Note that if n 1 =1, then n=n. n 1 =1 for a vacuum but this is also a good approximation for air.) These coefficients describe the transmission and reflection of the amplitude of the radiation. To compute the transmission of the electric vector one would need to use the square root of these formulae. (3.6) (3.7) Fig. 3.3: Fresnel reflection coefficients for a reflection between two media for which n 1 < n and n 1 /n = 1.34. The reflection coefficients are shown in Fig. 3.3 as a function of the incidence angle for light in air striking a medium with an index of refraction of 1.34. Note that the value of r //, except for the extremes at 0 and 90, is always less than r, and that it drops to zero at one point. The angle at which r // = 0 is called Brewster's angle. (Brewster's angle may be calculated from the relationship tan B = n.) At Brewster's angle, the reflected light is linearly polarized in a plane perpendicular to the incident plane. This polarization by reflection is exploited in numerous optical devices. The difference in polarization of the reflected radiation is exploited with polarized sunglasses. Light reflected from a level surface (pavement, snow, water) is rich in polarized light and poor in
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.4 W.D. Philpot, Cornell University, Fall 1 polarized light over a wide range of angles. Thus looking through a lens that is (vertically) polarized will block most of the radiation reflected from the surface, thus reducing the glare. 3.1. Reflection (scattering) from a rough surface Most natural surfaces are not mirror-like and the reflection from that surface is not restricted to a well-defined angle of reflection. Rather, the incident light is reflected or scattered over a wide range of angles. Predicting both the distribution and intensity of reflected radiation is problematic, and we will limit our discussion to a phenomenological description of the problem. In general, the reflectivity of a surface is defined as the ratio of the radiant exitance, M, (upwelling irradiance, E u ) from a surface to the incident irradiance, E (downwelling irradiance, E d ). The reflectivity, or albedo, is actually an irradiance ratio, defined as: M Eu r E E (3.9) More generally, we must include a sense of the directionality of both the illumination and the reflected radiation. The types of reflection that we need to describe are illustrated in Fig. 3.4. d Fig. 3.4: Reflection from real surfaces may range from mirror-like specular reflection (a) to very general distributions (d). For remote sensing applications, the general description of reflection is the Bidirectional Reflectance Distribution Function (BRDF). This quantity is defined as: L( v, v) BRDF E (, ) d s s where E is the irradiance (flux density) measured in a plane perpendicular to the direction of propagation, incident on a surface from the source direction ( s, s ) and L v is the radiance scattered from the surface toward the viewer into the solid angle, d v, in the direction ( v, v ) (Fig. 3.5). (3.9)
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.5 W.D. Philpot, Cornell University, Fall 1 Fig. 3.5: Diagram describing the BRDF. For simplicity, s and v are omitted from this drawing. Note that the irradiance is assumed to be collimated radiation from direction ( s, s ). This is a reasonable assumption for solar radiation and for appropriate laboratory light sources. For a fixed area on the ground, the downwelling irradiance, E d = E cos s. The BRDF is quite adaptable and can be used to describe situations ranging from specular reflection to perfectly diffuse reflection. One of the more common representations is that of the perfectly diffuse, or Lambertian, surface. The concept of a Lambertian surface is that, regardless of the nature of the illumination, the scattered radiance will be equal in all directions (isotropic). If the surface has a reflectivity of ρ, then the BRDF of a Lambertian reflector is: BRDF Lambertian = ρ π (3.10) For a perfectly reflecting surface (ρ = 1.0) that is also Lambertian, we have the additional relationship: where E d is the upwelling (reflected) irradiance from the surface. 3.1.3 Volume reflectance (scatter) E u = π L (3.11) Radiation that penetrates the surface of a material has a much greater chance of being absorbed by that material and light that is scattered back from the interior bears a much stronger imprint of absorption by the material than that reflected from the surface. In most cases, volume reflectance is not separable from surface reflectance. Rather, volume reflectance simply contributes to the overall reflected radiance observed. However, one may optimize a measurement to emphasize surface or volume reflectance, and most laboratory spectra collected to characterize materials are designed to maximize the volume reflectance and minimize the specular reflectance.
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.6 W.D. Philpot, Cornell University, Fall 1 Fig. 3.6: Typical reflectance spectra for several different materials. Several typical reflectance spectra are illustrated in Fig. 3.6. The point of this figure is to emphasize that there is a substantial range of spectral and brightness detail in these spectra. 3. Field Radiometry In making radiometric measurements of reflectance in the field one must take into account several practical issues. Chief among these is the fact that the light source is the sun, which illuminates both directly and after scattering by the atmosphere. Natural light can be quite variable even on relatively clear days. This suggests that measurements intended to represent a single target must be made quickly, if not simultaneously. It follows that the measurements must be simple. In most cases this means that a full BRDF will not be feasible. This leads to the definition of the Remote Sensing Reflectance, Rrs, which is defined generally as the ratio of the radiance in the viewing direction to the total downwelling irradiance at the surface: L u v, v, 1 R rs v, v, (sr ) E d (3.1) where (θ v, φ v ) represents the viewing direction. Note that this reflectance has units of inverse steradians. Natural surfaces are generally assumed to be Lambertian reflectors unless noted otherwise. While this assumption is not precisely true, it suffices for many purposes and is often reasonable if the viewing direction is near nadir and far enough away from the specular point or the anti-solar point. Thus, the practical implication of this assumption is that one should avoid specular reflectance and retroreflectance and should also try to insure that the portion of the target viewed is reasonably uniform and, ideally, diffuse. Beyond the assumption of a Lambertian target, the main consideration is the stability of the illumination. Stability of the light field is always an issue in field measurements because sun and skylight can vary rapidly. Reflectance requires a pair of measurements (L u & E d ). If one has a single radiometer the usual case then it is necessary to make the measurements sequentially.
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.7 W.D. Philpot, Cornell University, Fall 1 If the light field changes between measurements, the computed value for reflectance will be unreliable. This means that the two measurements must be made quickly and that there should be some method to check that the light field has not varied significantly over the measurements period. If one has a pair of radiometers then it will be possible to measure L u and E d simultaneously. However, the radiometers must be carefully cross-calibrated to avoid introducing instrumental artifacts. (In the laboratory it is generally less of a problem to use one radiometer since the illumination can be controlled.) The ideal sensor for collecting field reflectance data would measure radiance from the object at the same instant that it is measuring irradiance on the object. Lacking such an instrument, investigators have adopted different approaches. The most common is to determine the object's reflectance relative to the reflectance of a standard, which is normally a flat, rigid, diffuse white surface (e.g., coated with barium sulfate or magnesium oxide). This approach involves measuring radiance from the object, L o, and radiance from the standard, L s, and dividing the two values (i.e., irradiance is not measured). The resulting measure of relative reflectance should be multiplied by the reflectance of the standard, R s, which is determined periodically in the laboratory. It is emphasized that all values of radiances, irradiance and reflectance are spectral, relating to one or more corresponding bands of wavelengths. Investigators who adopt this approach often use a single radiometer or spectroradiometer to make sequential measurements of radiance from the object and the standard (Figure 6.3). Unfortunately, substantial changes in irradiance can occur rapidly between the time of the two radiance measurements. This will produce error in the reflectance determination, and the amount of error is unpredictable. Target, L t Standard, L s (Lambertian) Fig. 3.7: Reflectance measurements using a single radiometer. Single Radiometer Procedure (Fig. 3.7): Using a single radiometer (or spectroradiometer), sequentially measure 1) the upwelling radiance from a target and ) the upwelling radiance from a reflectance standard.
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.8 W.D. Philpot, Cornell University, Fall 1 Measurements must be made close enough in time to ensure that the atmospheric conditions have not changed. The absolute radiance reflectance can be retrieved from the relative reflectance if the absolute reflectance (R s ) of the standard is known: L t ( ) R t(abs) ( ) R s( ) L s( ) Note that the standard is assumed to be both Lambertian level, and that the measurements are made perpendicular to the target and standard surfaces. If the standard can be assumed to be Lambertian, then E d = π L s, and the remote sensing reflectance is then given by: L t ( ) R rs( ) R s( ) L s( ) (3.13) (3.14) Once again, this procedure will produce consistent results ONLY if the downwelling irradiance has not changed in the time between the measurement of L t and L s. One remedy to the sequential measurement problem is to use two matching instruments. The measurements of radiance from the object and radiance from the standard can thus be made simultaneously with the different instruments (Fig. 3.8). This approach requires that the two instruments be inter-calibrated and that the two measurements be, in fact, made simultaneously, possibly by two observers or an electronic data logger. A B A target, L t standard, L s a) b) target, L t B Irradiance, E d Fig. 3.8: a) Reflectance measurements made using two equivalent radiometers making simultaneous measurements of radiance from the target and a reflectance standard. b) Reflectance measured using simultaneous measurements of the target and the downwelling cosine irradiance. With either the "two-instrument" or "sequential" measurement approach just described, the standard reflector must be taken into the field. This is undesirable; because the standard is usually awkward to handle in addition to being easily damaged or covered with dust or insects. A third approach eliminates both the need for transporting the standard into the field and the problem of sequential measurements. This approach also involves simultaneous measurements with two matching instruments; however, while one instrument measures radiance from the object, the second measures irradiance (Fig. 3.8a). The optical aperture or apertures of the second instrument are fitted with light-diffusing filters ("cosine receptors"), and the instrument is aimed vertically upward.
Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.9 W.D. Philpot, Cornell University, Fall 1 In order to determine how one instrument responds relative to the other for the third approach, the two instruments must be inter-calibrated. This is done by substituting the standard reflector for the field object (Fig. 3.8b) and making simultaneous measurements over a wide range of irradiance conditions (i.e., sun angles from morning until late afternoon). The instrument used for measuring radiance from field objects is thus aimed vertically downward to measure radiance from the standard (L s ) instead of from a field object, while the instrument measuring irradiance is aimed vertically upward to measure irradiance (E s ). If the calibration measurements are repeated over a sufficient range of irradiance conditions, a curve of "E s /L s " versus "E s " can be plotted or its best-fit equation determined. After calibration and field measurements are completed, the reflectance of any object is then computed as: R = (L o /E o ) x (E s /L s ) x R s (3.15) where: L o and E o are simultaneously measured values of radiance from, and irradiance on, the field object, respectively; E s and L s are irradiance and radiance values derived through calibration measurements with the standard reflector; and R s is the absolute reflectance of the standard (determined in the laboratory). Values of "E s /L s " are obtained from a pre-plotted curve or equation for values of E s equal to E o. In this way, the object's reflectance is determined from R = (L o /L s ) x R s, where L o and L s are radiance values which correspond to the same levels of irradiance. Two remaining items should be mentioned in this introduction to radiometry. The first is to reiterate that radiance and irradiance measurements are made with the radiometer or spectroradiometer aimed vertically downward or upward. Level bubbles should be used to ensure proper orientation. While other orientations might be considered for measuring radiance, vertical measurements of radiance are generally more repeatable and, if taken within about three hours of solar noon, they are not terribly sensitive to changes in sun angle. The second item relates to how the instruments are physically supported in the field or during calibration. Although hand-holding the instruments is, by far, the most expedient approach to field data collection, it can lead to unexpected and unpredictable amounts of error. These are caused primarily by possible changes in orientation from vertical at the instant of measurement as well as by light that may be reflected onto, or shielded from, the object by the observer. For maximum accuracy, both instruments should be mounted on tripods or equivalent platforms, away from possible interference.