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Lecture #2 The Fundamentals of Electromagnetic Radiation Principles Contribution from R. Pu and M. D. King Outline 1. Electromagnetic energy interactions 2. Electromagnetic radiation models (wave/particle) 3. Atmospheric refraction 4. Atmospheric scattering 5. Atmospheric absorption (“atmospheric windows”) 6. Radiometric quantities and reflectance 7. Radiance and atmospheric transfer/correction 8. Summary 1. Electromagnetic Energy Interactions 1. Electromagnetic Energy Interactions • When the energy being remotely sensed comes from the Sun, the energy: – Propagates through the vacuum of space – Interacts with the Earth's atmosphere, surface, and atmosphere – Reaches the remote sensor (interacts with various optical systems, filters, emulsions, or detectors) Energy-matter interactions in the atmosphere, at the study area, and at the remote sensor detector Pictorial Explanation 2. Electromagnetic Radiation Models Fundamental Properties of Electromagnetic Radiation • The three basic ways in which energy can be transferred include, conduction, convection, and radiation • Energy may be conducted directly from one object to another as when a pan is in direct physical contact with a hot burner • The Sun bathes the Earth’s surface with radiant energy causing the air near the ground to increase in temperature – The less dense air rises, creating convectional currents in the atmosphere • The transfer of energy by electromagnetic radiation is of primary interest to remote sensing because it is the only form of energy transfer that can take place in a vacuum such as the region between the Sun and the Earth Fundamental Properties of Electromagnetic Radiation • The energy can be transferred in the three basic ways: conduction, convection, and radiation Electromagnetic Radiation Models To understand how electromagnetic radiation is created, how it propagates through space, and how it interacts with other matter, it is useful to describe the processes using two different models: • the wave model, and • the particle model Wave Model of EM Energy An electromagnetic wave is composed of electric and magnetic vectors that are orthogonal to one another and travel from the source at the speed of light (3 x 108 m s-1) The Wave Model of Electromagnetic Energy • Frequency: the number of wavelengths that pass a point per unit time • Wavelength: the mean distance between maximums (or minimums) • Common units: micrometers (m) or nanometers (nm) • One cycle per second is termed one hertz (1 Hz) Wave Model of Electromagnetic Energy The relationship between the wavelength, , and frequency, , of electromagnetic radiation is based on the following formula, where c is the speed of light: c v v c v c Note that frequency, is inversely proportional to wavelength, The longer the wavelength, the lower the frequency, and vice-versa Wave Model of Electromagnetic Energy Sources of Electromagnetic Energy • The Sun yields a continuous spectrum of EM energy • This process produces a large amount of short wavelength energy (from 0.4 - 0.7 m; blue, green, and red light) • Interacts with the atmosphere and surface materials (reflect, absorb) • Absorption: absorb the short wavelength energy and then re-emit it at a longer wavelength Electromagnetic (EM) Spectrum The Sun produces a continuous spectrum of energy from gamma rays to radio waves that continually bathe the Earth in energy The visible portion of the spectrum may be measured using wavelength (measured in m or nm) or electron volts (eV) – All units are interchangeable Stefan-Boltzmann Law • The total emitted radiation (M) from a blackbody is proportional to the fourth power of its absolute temperature – This is known as the Stefan-Boltzmann law and is expressed as: M = sT 4 where s is the Stefan-Boltzmann constant = 5.6697 x 10-8 W m-2 K-4 – T = absolute temperature (in Kelvin) • The greater the T, the greater the amount of radiant energy exiting the object – The temperature 0°C (in the common Celsius scale) corresponds to 273 K Wien’s Displacement Law • To compute its dominant wavelength (max) as: max = k / T where k is a constant equaling 2898 m K, and T is temperature in degrees Kelvin • The Sun approximates a 6,000 K blackbody, therefore its dominant wavelength is: 0.483 m = 2898 m K / 6000 K – T determines the wavelength Blackbody Radiation Curves • Blackbody radiation curves for the Sun: temperature approximate 6,000 K • For Earth: 300 K • As the temperature of the object increases, its dominant wavelength shifts toward the short wavelength portion of the spectrum Radiant Intensity of the Sun • The Sun (6,000 K blackbody) dominant: 0.5 µm • Earth (300 K blackbody) • Dominant: 9.7 µm • Sun: 41%: visible region from 0.4 - 0.7 µm • The other 59% (<0.4 µm) and (>0.7 µm) • Eyes are only sensitive to light from the 0.4 to 0.7 µm • Remote sensor detectors can be made sensitive to energy in the non-visible regions of the spectrum Particle Model of EM Energy • Quantum theory of electromagnetic radiation: energy is transferred in discrete packets called quanta or photons • The relationship between the frequency of radiation and the quantum is: Q=h • where Q is the energy of a quantum measured in Joules (J), h is the Planck constant (6.626 x 10-34 J s-1), and is the frequency of the radiation 3. Atmospheric Refraction Atmospheric Refraction The Speed of Light in a Vacuum and in the Atmosphere • The speed of light c is 3 x 108 m s-1 (same as Electromagnetic Radiation EMR) • When encounters substances of different density (air and water), refraction may take place • Refraction: bending of light when it passes from one medium to another – Refraction occurs because the media are of differing densities and the speed of EMR is different in each • The index of refraction, n: measure of the optical density of a substance – This index is the ratio of c, to the speed of light in the substance, cn: c n = __ cn Index of Refraction and Snell’s Law Atmospheric Refraction Incident radiant energy Normal to the surface n1 = index of refraction for this layer of 1 the atmosphere Optically less dense atmosphere n2 Optically more dense atmosphere n 3 Optically less dense atmosphere Path o f energy in ho mo gen eou s atmo sph ere 2 Snell’s law – for a given frequency of light, the product of the index of refraction and the sine of the angle between the ray and a line normal to the interface is constant n1 sin 1 = n2 sin 2 3 Path of radiant energy affected by atmospheric refraction 4. Atmospheric Scattering Atmospheric Scattering Electromagnetic radiation is propagated through the earth's atmosphere almost at the speed of light in a vacuum • Unlike a vacuum in which nothing happens, however, the atmosphere may affect speed of radiation intensity spectral distribution direction Atmospheric Scattering The type of scattering is a function of: • The wavelength of the incident radiant energy • The size of the gas molecule, dust particle, or water droplet encountered Atmospheric Layers and Constituents Major subdivisions of the atmosphere and the types of molecules and aerosols found in each layer Atmospheric Scattering Reflection: the direction predictable Scattering: direction unpredictable Water Droplets Based on wavelength of incident radiant energy, the size of the gas molecule, dust particle, or water vapor droplet essentially three types of scattering: • Rayleigh • Mie • non-selective scattering Rayleigh Scattering • Rayleigh scattering occurs when the diameter of the matter (usually air molecules) are many times smaller than the wavelength of the incident electromagnetic radiation • Rayleigh named after the English physicist Intensity of Rayleigh Scattering -4 Varies Inversely with 3 2.75 2.5 2.25 100 2 1.75 Energy in electron volts (eV) Intensity of Scattered Light 80 60 40 20 0 V 0.4 B G 0.5 YO 0.6 R 0.7 Wavelength in Micrometers Rayleigh Scattering • The amount of scattering is inversely related to the fourth power of the radiation's wavelength (-4) • For example, blue light (0.4 m) is scattered 16 times more than nearinfrared light (0.8 m) Mie Scattering • Mie scattering: when essentially spherical particles present in the atmosphere with diameters approximately equal to the wavelength of radiation • For visible light, water droplets, dust, and other particles ranging from a few tenths of a micrometer to several micrometers in diameter are the main scattering agents – The amount of scatter is greater than Rayleigh scatter and the wavelengths scattered are longer • Pollution also contributes to beautiful sunsets and sunrises – The greater the amount of smoke and dust particles in the atmospheric column, the more violet and blue light will be scattered away and only the longer orange and red wavelength light will reach our eyes Non-selective Scattering • Non-selective scattering: when particles in the atmosphere are several times (>10) greater than the wavelength of the radiation – All wavelengths of light are scattered, not just blue, green, or red Thus, water droplets scatter all wavelengths of visible light equally well, causing the cloud to appear white (a mixture of all colors of light in approximately equal quantities produces white) – Scattering can severely reduce the information content of remotely sensed data to make it difficult to differentiate one object from another Color of the Sky Two questions: • Why is the sky blue? • Why is the sunset orange? Color of the Sky • Why is the sky blue? – A clear cloudless day-time sky is blue because molecules in the air scatter blue light from the sun more than they scatter red light • Why is the sunset orange ? – When we look towards the sun at sunset, we see red and orange colors because the blue light has been scattered out and away from the line of sight • http://math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.html Angular Scattering Coefficient [(Q)] – Fractional amount of energy scattered into the direction Q per unit solid angle per unit length of transit [m-1 sr-1] Q dW Unit length Propagating beam f Scattering center Solid Angle Representation of Spherical Coordinates dW = sinddf Z rsindf rsin rd df dW d x f df y Volume Scattering and Extinction Coefficient • Volume scattering coefficient [ssca] – Fractional amount of energy scattered in all directions per unit length of transit [m-1] ssca = (Q)dW 2 = (Q)sinQdQdf 0 0 • Volume absorption coefficient [sabs] – Fractional amount of energy absorbed per unit length of transit [m-1] • Volume extinction coefficient [sext] – Fractional amount of energy attenuated per unit length of transit [m-1] sext = ssca + sabs • Single scattering albedo [0] – Fraction of energy scattered to that attenuated 0 = ssca/(ssca + sabs) Optical Thickness • Optical depth [t] – Total attenuation along a path length, generally a function of wavelength [dimensionless] X t() = sextdx 0 • Total optical thickness of the atmosphere [tt] – Total attenuation in a vertical path from the top of the atmosphere down to the surface tt() = sextdz 0 • Transmission of the direct solar beam t = exp[-tt()/µ0] t = exp[-tt()] 0 µ0 = cos0 Scattering Phase Function • Scattering phase function is defined as the ratio of the energy scattering per unit solid angle into a particular direction to the average energy scattered per unit solid angle into all directions F(cosQ) = (Q) (Q)dW = 4(Q) ssca 4 with this definition, the phase function obeys the following normalization 4 1 F(cosQ)dW 1 = 4 0 1 1 = F(cosQ)dcosQ 2 -1 • Rayleigh (molecular) scattering phase function F(cosQ) = 3 (1 + cos2Q) 4 Shapes of Scattering Phase Function Rayleigh (molecular) 90° 135° Composite 45° dW 180° 0° 225° 315° 270° Shapes of Scattering Phase Function Rayleigh (molecular) 90° 90° 135° 135° Composite Nonselective scattering 45° 45° Mie scattering dW 180° 0° 0° 180° 225° 315° 270° 225° 315° 270° 5. Atmospheric Absorption Atmospheric Absorption • Absorption is the process by which radiant energy is absorbed and converted into other forms of energy – An absorption band is a range of wavelengths (or frequencies) in the electromagnetic spectrum within which radiant energy is absorbed by substances such as water (H2O), carbon dioxide (CO2), oxygen (O2), ozone (O3), and nitrous oxide (N2O) • The cumulative effect of the absorption by the various constituents can cause the atmosphere to close down in certain regions of the spectrum – This is bad for remote sensing because no energy is available to be sensed Absorption • In certain parts of the spectrum such as the visible region (0.4 - 0.7 m), the atmosphere does not absorb much of the incident energy but transmits it effectively • Parts of the spectrum that transmit energy effectively are called “atmospheric windows” • The combined effects of atmospheric absorption, scattering, and reflectance reduce the amount of solar irradiance reaching the Earth’s surface at sea level Rotational and Vibrational Modes of Molecules 6. Radiometric Quantities and Reflectance Definition of Solar Zenith, View Zenith, and Relative Azimuth Angle z dW = sinddf 0 rsin W rd df dW f0 f rsind f d Df S y N E Definition of Reflection Function The reflection function is usually a function of at least 5 variables R(tt, 0; µ, µ0, f) where tt 0 µ µ0 f = = = = = total optical thickness the single scattering albedo (ratio of scattering to total extinction) absolute value of the cosine of the zenith angle |cos| cosine of the solar zenith angle cos0 relative azimuth angle between the direction of propagation of the emerging radiation and the incident solar direction Note: R, tt, 0 are all functions of wavelength Radiometric Quantities • Radiometric quantities: recording the incident and exiting radiant flux • The simple radiation budget equation: – the total amount of radiant flux incident to the ground (I) in specific wavelengths – the amount of energy reflected from the surface (r) – the amount of energy absorbed by the surface () – the amount of radiant energy transmitted through the surface (t); therefore, the radiation budget equation: I r+ + t Flux (Irradiance) on a Horizontal Surface at the Surface of the Earth The transmitted flux (irradiance) at the Earth’s surface can be calculated as: 2 E(tt , 0; µ0, µ, f) = I(tt, 0; µ, µ0, f)µdµdf + µ0F0exp(-tt/µ0) 0 0 2 1 = µ0F0 [ T(tt, 0; µ, µ0, f)µdµdf + exp(-tt/µ0)] 0 0 where the transmission function is defined in an analogous manner to reflection function T(tt, 0; µ, µ0, f) = I(tt, µ, f) µ0F0 Radiometric Quantities • The radiometric quantities are based on the amount of radiant incident to a surface from any angle in a hemisphere (i.e. a half of a sphere) Hemispherical reflectance (rl) or albedo is defined as the dimensionless ratio of the radiant flux reflected from a surface to the radiant flux incident to it Freflected r Radiometric Quantities Hemispherical transmittance (t) is defined as the dimensionless ratio of the radiant flux transmitted through a surface to the radiant flux incident to it Freflected r Radiometric Quantities • Hemispherical absorption () is defined by the dimensionless relationship rt • Radiant energy must be conserved • The net effect of absorption of radiation is that the energy is converted into heat, causing a subsequent rise in the substance's temperature Concept of Radiant Flux Density Radiant flux, F Irradiance F E = Area, A Radiant flux, F Exitance F M = Area, A • The concept of radiant flux density for an area on the surface of the earth • Irradiance is a measure of the amount of incoming energy in Watts m-2 • Exitance is a measure of the amount of energy leaving in Watts m-2 7. Radiance and Atmospheric Transfer/Correction Radiance The concept of radiance (L) leaving a specific projected source area (A) on the ground, in a specific direction (), and within a specific solid angle (W) The L is measured in watts per meter squared per steradian (W m-2 sr -1 ) – We are only interested in the radiant flux in certain wavelengths (F) leaving the projected source area (A) within a certain direction () and solid angle (W) Reflectance • Specular reflection (a): smooth (i.e., the average surface profile is several times smaller than the wavelength of radiation) • Diffuse reflection (b): rough, the reflected rays go in many directions • Lambertian surface (d) the radiant flux leaving the surface is constant for any angle of reflectance to the surface normal Path 1 contains spectral solar irradiance (E0) that was attenuated very little before illuminating the terrain within the IFOV – Notice in this case that we are interested in the solar irradiance from a specific solar zenith angle (0) and that the amount of irradiance reaching the surface is a function of the atmospheric transmittance at this angle (T0) – If all of the irradiance makes it to the ground, then the atmospheric transmittance (T0) equals one – If none of the irradiance makes it to the ground, then the atmospheric transmittance is zero Path 2 contains spectral diffuse sky irradiance (Ed) that never even reaches the Earth’s surface (the target study area) because of scattering in the atmosphere – The energy is often scattered directly into the IFOV of the sensor system in the form of Rayleigh scattering of diffuse sky irradiance – It contains much unwanted diffuse sky irradiance that was inadvertently scattered into the IFOV of the sensor system – Therefore, if possible, we want to minimize its Ed effects Path 3 contains energy from the Sun that has undergone some Rayleigh, Mie, and/or nonselective scattering and perhaps some absorption and reemission before illuminating the study area – Thus, its spectral composition and polarization may be somewhat different from the energy that reaches the ground from path 1 – It is referred to as the downward reflectance of the atmosphere (Edd) Path 4 contains radiation that was reflected or scattered by nearby terrain (rn) covered by snow, concrete, soil, water, and/or vegetation into the IFOV of the sensor system – The energy does not actually illuminate the study area of interest – Therefore, if possible, we would like to minimize its effects Path 2 and Path 4 combine to produce what is commonly referred to as Path Radiance, Lp Path 5 is energy that was also reflected from nearby terrain into the atmosphere, but then scattered or reflected onto the study area • Adjacency effect Atmospheric Correction Using ATCOR a) Image containing substantial haze prior to atmospheric correction. b) Image after atmospheric correction using ATCOR (Courtesy Leica Geosystems and DLR, the German Aerospace Centre) Atmospheric Correction • Atmospheric correction of ALI imagery (Beijing, China, May 3, 2001) Before After Before After SL Liang, University of Maryland, College Park Atmospheric Correction • MODIS imagery of Chinese northeastern coast, (False color composite, May 7, 2000) (Before AC) (After AC) SL Liang, University of Maryland, College Park Atmospheric Correction • MODIS imagery of Chinese northeastern coast, (False color composite, May 7, 2000) (Before AC) (After AC) SL Liang, University of Maryland, College Park 8. Summary 1. Electromagnetic energy interactions: interaction with atmosphere, earth, atmosphere, sensor system components (camera, film, emulsion, etc.) 2. Electromagnetic radiation models (wave/particle): three energy transfer ways (conduction, convection & radiation), two EM models (wave (c=v.), particle (Q=h.v), Q~), S. B. law (total emitted radiance) & Wien’s law (peak-wavelength), 3. Atmospheric refraction: n1.sine1= n2.sine2= n3.sine3 4. Atmospheric scattering: Rayleigh (d<<), Mie (d~), non-selective (d>>), blue sky phenomenon at noon, yellow/radish phenomenon at sunrise/set 5. Atmospheric absorption (“atmospheric windows”): ‘close down’ regions, ‘atmospheric windows’ 6. Radiometric quantities and reflectance:1=refectance+absorption+transmittance, three type reflectances (specular, diffuse & lambertian) 7. Radiance and atmospheric transfer/correction: irradiance, exitance and radiance, atmospheric transfer (path radiance, total radiance, etc.) • Reference Book: Graeme L. Stephens, Remote Sensing of the Lower Atmosphere, An Introduction, Oxford University Press, 1994 Ch. 2: 2.1, 2.2, Ch. 3: 3.1, 3.2, 3.4, 3.5 Ch. 4: 4.4