EE/Ae 157a Introduction to the Physics and Techniques of Remote Sensing Week 2: Nature and Properties of Electromagnetic Waves 2-1 TOPICS TO BE COVERED • Fundamental Properties of Electromagnetic Waves – Electromagnetic Spectrum, Maxwell’s Equations, Wave Equation, Quantum Properties of EM Radiation, Polarization, Coherency, Group and Phase Velocity, Doppler Effect • Nomenclature and Definition of Radiation Quantities – Radiation Quantities, Spectral Quantities, Luminous Quantities • Generation of Electromagnetic Radiation • Detection of Electromagnetic Radiation • Overview of Interaction of EM Waves with Matter • Interaction Mechanisms Throughout the Electromagnetic Spectrum 2-2 ELECTROMAGNETIC SPECTRUM 2-3 MAXWELL’S EQUATIONS B E t D H J t B 0r H D 0 rE E 0 B 0 2-4 WAVE EQUATION From Maxwell’s Equations, we find: E H 0 r t 2E 0 r 0 r t 2 E E 2E 2E 2E 0 0 r 0 r t2 This is the free-space wave equation 2-5 SOLUTION TO THE WAVE EQUATION For a sinusoidal field, the wave equation reduces to 2 2 E 2 E 0 cr The solution to this equation is of the form E Aei kr t The speed of light is given by 1 c0 cr 0 r 0r r r 2-6 QUANTUM PROPERTIES OF EM RADIATION • Maxwell’s equations describe mathematically smooth motion of fields. • For very short wavelengths, it fails to describe certain significant phenomena when the wave interacts with matter. • In those cases, a quantum description is more appropriate. • In this description, the EM radiation is presented by a quantized burst with energy Q proportional to the frequency of the wave: Q h; h Planck' s constant 6.626 10 34 Joules/second • The energy in the wave train is delivered to a receiver on a probabilistic basis • Only when a large number of wave trains are present, will the overall average effect be described by Maxwell’s equations 2-7 WAVE POLARIZATION From the solution to the wave equation, we can write E A coskzt ih iv x x h A Ahe eh Ave ev Ey Ay coskzt v This can be written as 2 2 E E E E h v h v 2 2 cosh v sin h v Ah Av Ah Av This is the expression of an ellipse, and the wave is said to be elliptically polarized 2-8 POLARIZATION ELLIPSE v POLARIZATION av ELLIPSE ah h MAJOR AXIS MINOR AXIS 2-9 SPECIAL POLARIZATIONS When m; m 0,1, 2, the wave is said to be linearly polarized. In this case, the ellipse collapses to form a line. When Ax Ay and m 2, m 1,2, the wave is said to be circularly polarized. 2-10 SPECIAL POLARIZATIONS HORIZONTAL (LINEAR) VERTICAL (LINEAR) RIGHT-HAND CIRCULAR LEFT-HAND CIRCULAR 2-11 Stokes Parameters Another way to describe the polarization of a wave, particularly appropriate for the case of partially polarized waves, is through the use of the Stokes parameters of the wave. For a monochromatic wave, these four parameters are defined as 22 S0 ahv a 22 , S1 ahv a S2 2 ah a v cos h v S3 2 ah a v sin h v 2 2 2 2 Note that for such a fully polarized wave, only three of the Stokes parameters are independent, since SSSS0 1 2 3 Using the relations between the ellipse orientation and ellipticity angles and the wave amplitudes and relative phases, it can be shown that the Stokes parameters can also be written as SS10 cos 2 cos 2 SS20 cos 2 sin 2 SS30 sin 2 These relations lead to a simple geometric interpretation of polarization states. The Stokes parameters can be regarded as the Cartesian coordinates of a point on a sphere, known as the Poincaré sphere, of radius S0 2-12 Poincare Sphere S Left-Hand 3 Circular Linear Polarization (Vertical) 2 S2 Linear 2 Polarization (Horizontal) S1 S0 Right-Hand Circular 2-13 COHERENCY • The coherence time of two waves of frequency n and nDn is the time after which the waves are out of phase by exactly one cycle 1 nDt 1 n DnDt DnDt 1 Dt Dn • The coherence length is defined as: c Dl cDt Dn • If two waves are coherent, there is a systematic relationship between their instantaneous amplitudes. 2-14 COHERENCY • Assume the total electric field is the sum of two component fields: Et E1t E2t • The average power is 2 2 2 P ~ E t E1 t E2 t 2 E1tE2 t • If the two waves are incoherent, then E1tE2t 0 P P1 P2 • If the waves are coherent, then E1tE2 t 0 P P1 P2 or P P1 P2 2-15 Example of Coherence 2-16 PHASE VELOCITY • The phase velocity of a wave is the velocity at which a constant phase front progresses z vpDt Dz D kDz Dt 0 v Dt p k 2-17 GROUP VELOCITY • The group velocity is the velocity at which a plane of constant amplitude progresses Ez,t Ae ik Dkz D t Ae ikDkz D t 2 Ae ikz wt cosDkz Dt Dz D DkDz DDt 0 v Dt g Dk • In the limit, this becomes vgDt z v g k 2-18 PHASE vs GROUP VELOCITY • Group velocity represents the velocity at which energy is transported by a wave • As such, the group velocity must be less than or equal to the speed of light • For certain media, the phase velocity can be greater than the speed of light • For non-dispersive media, the group and phase velocity are the same and equal to the speed of light v p c k ck vg c k 2-19 DOPPLER EFFECT • If the relative difference between a source radiating a wave with a fixed frequency n and an observer changes with time, the frequency of the signal observed will be different than n • This difference in frequency is known as the Doppler shift • If the distance between the source and the observer is decreasing, the Doppler shift is positive, i.e. the observed frequency is higher than the transmitted one • If the distance is increasing, the Doppler shift is negative • The Doppler shift is used in remote sensing to measure target motion • It is also the effect used in Synthetic Aperture Radar to achieve high resolution in the along-track direction 2-20 DOPPLER EFFECT l cT vT cosq l c v c cosq n n n v v n n n cosq c q v Observer nd n cosq c c For radars: v n 2n cosq Constant Amplitudes d c 2-21 RADIANT ENERGY • Radiant energy is the energy carried by the electromagnetic wave • The amount of energy per unit volume is called radiant energy density • Radiant energy Q is measured in joule • Radiant energy density W is measured in joule m3 dQ W dV 2-22 RADIANT FLUX • Radiant flux is the time rate at which radiant energy passes a certain location dQ watt dt • Radiant flux density is the radiant flux intercepted by a unit area of a plane surface • The flux density incident upon a surface is called irradiance, M • The flux density leaving a surface is called emittance, E d E, M watt m2 dA 2-23 SOLID ANGLE • The solid angle W subtended by an area A on a spherical surface is that area divided by the radius of the sphere squared A W Area of Sphere R 4R2 A W R2 2-24 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 d I watt steradian dW 2-25 RADIANCE • Radiance is the radiant flux per unit solid angle leaving an extended source in a given direction per unit projected area in that direction Surface Normal Flux, W dI q L watt steradianm 2 dA cosq Projected Source Area Source Area Acosq A • If the radiance does not change as a function of direction of emission, the source is called Lambertian 2-26 REFLECTANCE, TRANSMITTANCE and ABSORPTANCE • Reflectance r is the ratio of the reflected exitance from a plane of material to the irradiance on that plane • Transmittance t is the ratio of the transmitted exitance, leaving the opposite side of the plane, to the irradiance • Absorptance a is the flux density that is absorped over the irradiance r t a 1 2-27 SPECTRAL QUANTITIES • Electromagnetic waves are usually made up of a collection of sinusiods of slightly different frequencies, each carrying a part of the radiant flux of the total wave • The spectral band over which these components extend is called the bandwidth of the signal • All radiance quantities have equivalent spectral quantities that correspond to the density as a function of frequency Flux in waves in band l Dl to l Dl Spectral flux l 2Dl l Total flux in Bandwidth = l to l 2 l dl 1 2 l 1 2-28 LUMINOUS QUANTITIES • Luminous quantities are related to the characteristic of the human eye to perceive radiative quantities • The relative effectiveness of the eye in converting radiant flux to visual response is called the spectral luminous efficiency Vl • This function is used as a weighting function in relating radiant quantities to luminous quantities 680 l V l dl n e 0 2-29 SPECTRAL LUMINOUS EFFICIENCY 2-30 COMPONENTS OF A REMOTE SENSING SYSTEM Source Detector Waves Emitted Scattering Object Collecting Aperture 2-31 GENERATION OF EM RADIATION • A variety of techniques are used to generate electromagnetic radiation in the different parts of the EM spectrum • At radio frequencies, waves are generated by alternating currents in wires, electron beams, or on the surfaces of antennas • At microwave frequencies, electron tubes (e.g.