-1- Electromagnetic radiation (EMR) basics for remote sensing HANDOUT’s OBJECTIVES: • familiarize student with basic EMR terminology & mathematics • overview of EMR polarization as related to remote sensing • introduce ray/wave/particle descriptions of EMR • introduce geometrical & spectral classification of EMR • some practical remote-sensing applications of EMR fundamentals What do we mean by EMR? propagation through space of a time-varying wave that has both electrical and magnetic components Consider a simple sine wave as our model, with: wavelength ≡ λ (“lambda”), frequency ≡ ν (“nu”), and speed V = νλ 1 The wave’s period T = ν . In a vacuum, the speed is denoted as c (c ≈ 3 x 108 m/sec). wavelength λ crest wave amplitude E 0 trough c The real index of refraction n is defined by n = V . Ν.Β.: the speed referred to here is that of the waveform, not of any object, so that values of n < 1 (and thus V > c) are possible. SO431 — EMR basics for remote sensing (8-21-09) -2- How do we describe this EMR wave? arrow = propagation direction x Light consists of oscillating electrical fields (denoted E above), and magnetic fields (denoted B). We’ll concentrate on E and ignore B, however, we could just as easily describe light using B. We don’t do it because the interaction of magnetic fields with charged particles is more complex than electric fields, but we could. SO431 — EMR basics for remote sensing (8-21-09) -3- Light whose electric field oscillates in a particular way is called polarized. If the oscillation lies in a plane, the light is called plane or linearly polarized (top right). Linearly polarized light can be polarized in different directions (e.g., vertical or horizontal above). Light can also be circularly polarized, with its electric field direction spiraling in a screw pattern or helix that has either a right- or left-handed sense (bottom). Seen along propagation axis x this helix has a circular cross-section. Light can also combine linear and circular polarization — its electric field then traces out a helix with an elliptical cross-section. Such light is called elliptically polarized. We often speak of unpolarized light, yet each individual EMR wave is itself completely polarized. Unpolarized light is actually the sum of light emitted by many different charges that accelerate in random directions. Real detectors like radiometers can only observe the space- and time-averaged intensities of the myriad oscillating charges. If this light has an observable dominant polarization, we call it polarized. Polarized light in remote-sensing applications 1 1 P(θ) ⊥-polarized radiance 0.8 | |-polarized radiance 0.8 P at θ = 53° max 0.6 0.6 θ) P( 0.4 polarization by reflection 0.4 by water (n = 4/3) reflected 0.2 0.2 0 0 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° incidence angle (θ) Most environmental light sources such as sunlight are unpolarized. Thus passive remote-sensing systems usually don’t benefit from the extra information that a polarized light source provides. Radar and other active remote-sensing systems usually emit SO431 — EMR basics for remote sensing (8-21-09) -4- polarized EMR, and so they can exploit the different signal patterns reflected when different polarizations illuminate the surface. Yet even reflected sunlight can be polarized, as the graph above indicates. It shows how polarization varies with incidence angle θ (incident EMR’s angle with the surface normal) for unpolarized light reflected by a smooth water surface. Degree of polarization P varies from 0 (completely unpolarized reflected light) to 1 (completely polarized reflection). In fact, the graph explains an entire industry — manufacture of polarizing sunglasses. observer’s eye u ) n lly po ia d la rt te r a ec iz (p fl ed re i d nc ze id ri en la t po smooth, non-metallic surface Like all linear polarizers, the plastic sheet polarizers used in some sunglasses have a particular direction along which linearly polarized light is absorbed least; polarized light is absorbed more strongly in other directions. This minimum-absorption direction is called the polarizer’s transmission axis. When linearly polarized light’s oscillation direction parallels the polarizer transmission axis, we get maximum transmission. Rotate the light source 90˚ about its propagation axis (or rotate the filter 90˚ about that axis), and we get minimum transmission. • At what θ is there maximum polarization for reflection by water? • How does the P(θ) graph help explain the changing effectiveness of polarizing sunglasses? • To be most effective in reducing reflected glare, should the sunglasses’ transmission axis be oriented horizontal, diagonal, or vertical to the water surface? (Hint: Examine the drawing above to see the oscillation direction of the reflected, partially polarized light.) Now return to our explanation of EMR’s wave nature. Mathematically, the wave amplitude E is given by, at any time t and position x (with x measured along the direction of propagation): t x π[ - (Eq. 1). E = Eo sin(2 T λ]) SO431 — EMR basics for remote sensing (8-21-09) -5- By setting t, x to fixed values in Eq. 1, we can determine the electromagnetic wave’s propagation direction. In addition, we can use Fourier analysis to reduce any waveform, no matter how complicated, to a sum of simple sine and cosine waves. This has mathematical advantages when we try to analyze the wave’s physical significance and sources. Note that Eq. 1 can be rewritten as: π 2 → E = Eo sin( λ [ct - x]) πν → E = Eo sin(2 [t - x/c]) (factor out c from the [ ], and note that c/λ = ν) ω − δ E = Eo sin( t ), where ω = 2πν = 2π/T and δ = 2πx/λ. Note that ω is described as the rotational angular frequency (in radians/second), and δ denotes a phase angle (where “phase” refers to angular separation). Remember that 1 radian (~ 57˚) is that portion of a circle equal to the circle’s radius, so converting to radian notation above scales the x-propagation in “natural” rotational (or wave) terms. s θ R radius R = arc length s if θ = 1 radian (= 57.3°) What is the source of EMR? Fundamentally, EMR’s source is the acceleration of electrical charges. A convenient example of such a charge is an electron. If one electron approaches another, their paired negative charges will result in mutual repulsion. The closer they approach one another, the stronger this repulsive force (and the associated charge accelerations) will be. SO431 — EMR basics for remote sensing (8-21-09) -6- Remember that Coulomb’s law describes this force F between a pair of charges q1 and q2 by: k q1 q2 F = . R2 So the repulsive force varies inversely with the square of the charge separation R. The electric field strength vector (E) indicates the force per unit charge so that F E = q. Physically, the electric field lines are defined by the force lines. If we insert an electron into a previously vacant region of space, the charge’s presence is communicated at speed c along the electric field lines. By accelerating the electron to a new position, we have altered the field lines, producing bends or kinks in them. Because the kinks in the electric field lines propagate at the finite speed c (in a vacuum), we say that the radiation propagates at speed c. Back and forth acceleration of the electron produces oscillating field lines or waves. Note, however, that along the line of oscillation, there is no detectable displacement (and hence no electromagnetic wave). z-axis Instantaneous E pattern electron acceleration coincides with z-axis 1 kinked E-field line (x-y plane) y-axis x-axis Kinks in E-field caused by electron accelerations along z-axis radiate outward as EM waves ⊥ the x-y plane. SO431 — EMR basics for remote sensing (8-21-09) -7- The time-averaged magnitude (or amplitude) E of the electric field strength E varies as: E = qa sin(θ), R where θ is the angle between the direction of the oscillation and the direction of our detector, a is the magnitude of the electron acceleration, and R is the distance over which the acceleration occurs. In the diagram above, the z-axis corresponds to θ = 0˚, while the x-axis and y-axis (in fact, the whole x-y plane) corresponds to θ = 90˚. Now the intensity (denoted I, a measurable electromagnetic quantity) of this EM wave varies as the square of the electrical field’s magnitude. Thus I ∝ E2 sin2(θ). θ I along z-axis = 0 I( = 45°) (θ = 0°) = 0.5*E2 Time-averaged I from I in x-y plane = one accelerated 1*E2(θ = 90°) 2 electron ∝ sin (θ) We’ve just described a transmitter/emitter, in which we somehow accelerated the electrons. Conversely, if an oscillating wave “washes by” a charge that is initially at rest, the charge will accelerate in response. In this case, the electromagnetic wave does work on the charge. Now we have a receiver in which the originally stationary charge is accelerated by the presence of EMR. For convenience sake, thus far we have described EMR using wave terminology. This is appropriate because EMR often displays wavelike characteristics; e.g., interference. However, later it will be more convenient to discuss EMR using particle (or photon) terminology, as when we discuss scattering. Photons’ (massless) kinetic energies E are described by: E = h ν = h c/λ, where h = 6.626 x 10-34 J sec, Planck’s constant. How does E depend on both frequency and wavelength? SO431 — EMR basics for remote sensing (8-21-09) -8- How do we describe naturally occurring EMR? There are two main classes of descriptions that we need: 1) geometric, and 2) spectral.