Fundamentals of Electromagnetic Radiation

1. Lecture #2The Fundamentals of Electromagnetic Radiation PrinciplesContribution from R. Pu and M. D. King

2. 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

3. 1. Electromagnetic EnergyInteractions

4. 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)

5. Energy-matter interactions in the atmosphere, at the study area, and at the remote sensor detector

6. Pictorial Explanation

7. 2. Electromagnetic Radiation Models

8. 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

9. Fundamental Properties of Electromagnetic Radiation The energy can be transferred in the three basic ways: conduction, convection, and radiation Fundamental Properties of Electromagnetic Radiation

10. 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

11. 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)

12. 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)

13. The relationship between the wavelength, , and frequency, , of electromagnetic radiation is based on the following formula, where c is the speed of light: Wave Model of Electromagnetic Energy Note that frequency,  is inversely proportional to wavelength,  The longer the wavelength, the lower the frequency, and vice-versa

14. Wave Model of Electromagnetic Energy

15. 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) Sources of Electromagnetic Energy Interacts with the atmosphere and surface materials (reflect, absorb) Absorption: absorb the short wavelength energy and then re-emit it at a longer wavelength

16. 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 mm or nm) or electron volts (eV) • All units are interchangeable Electromagnetic (EM) Spectrum

17. Stefan-Boltzmann Law • The total emitted radiation (Ml) 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: • Ml = 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

18. Wien’s Displacement Law • To compute its dominant wavelength(lmax) as: • lmax = 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: • 0.483mm = 2898 mmK/ 6000K • T determines the wavelength

19. 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

20. 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

21. 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

22. 3. Atmospheric Refraction

23. 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

24. Index of Refraction and Snell’s Law 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

25. 4. Atmospheric Scattering

26. 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

27. 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 Scattering

28. Atmospheric Layers and Constituents Major subdivisions of the atmosphere and the types of molecules and aerosols found in each layer

29. Reflection: the direction predictable • Scattering: direction unpredictable • Based on wavelength of incident radiant energy, the size of the gas molecule, dust particle, or water vapor dropletessentially three types of scattering: • • Rayleigh • • Mie • • non-selective scattering Atmospheric Scattering Water Droplets

30. 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 Rayleigh Scattering

31. 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 near-infrared light (0.8 m)

32. 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 Mie Scattering

33. 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 Non-selective Scattering

34. Two questions: • Why is the sky blue? • Why is the sunset orange? Color of the Sky

35. 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 Color of the Sky

36. Fractional amount of energy scattered into the direction Q per unit solid angle per unit length of transit [m-1 sr-1] Angular Scattering Coefficient [()] Q dW Unit length Propagating beam f Scattering center

37. Z dW= sinqdqdf Solid Angle Representation ofSpherical Coordinates rsinqdf rsinq rdq df q dW dq x f df y

38. Volume scattering coefficient [ssca] • Fractional amount of energy scattered in all directions per unit length of transit [m-1] • ssca = b(Q)dW • = b(Q)sinQdQdf • 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) Volume Scattering and Extinction Coefficient 2  0 0

39. Optical depth [t] • Total attenuation along a path length, generally a function of wavelength [dimensionless] t(l) = sextdx • Total optical thickness of the atmosphere [tt] • Total attenuation in a vertical path from the top of the atmosphere down to the surface tt(l) =sextdz • Transmission of the direct solar beam X Optical Thickness 0  0 t =exp[-tt(l)/µ0] t =exp[-tt(l)] q0 µ0 = cosq0

40. 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 with this definition, the phase function obeys the following normalization • 1 =F(cosQ)dW • = F(cosQ)dcosQ • Rayleigh (molecular) scattering phase function F(cosQ) = (1 + cos2Q) Scattering Phase Function 4p b(Q) b(Q) F(cosQ) = = • b(Q)dW • ssca 4p 4 1 4p 0 1 1 2 -1 3 4

41. Rayleigh (molecular) 90° Composite Shapes of Scattering Phase Function 135° 45° dW 180° 0° 225° 315° 270°

42. Rayleigh (molecular) 90° 90° Composite Nonselective scattering Shapes of Scattering Phase Function 135° 45° 135° 45° Mie scattering dW 180° 0° 0° 180° 225° 315° 225° 315° 270° 270°

43. 5. Atmospheric Absorption

44. 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 Atmospheric Absorption

45. 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”

46. The combined effects of atmospheric absorption, scattering, and reflectancereduce the amount of solar irradiance reaching the Earth’s surface at sea level

48. Rotational and Vibrational Modes of Molecules