# Lecture 1. The nature of electromagnetic radiation.

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1 Lecture 1. The nature of electromagnetic radiation. 1. Basic introduction to the electromagnetic field: Dual nature of electromagnetic radiation Electromagnetic spectrum. Basic radiometric quantities: intensity and flux. Recommended reading: Petty: chapters -3 Basic introduction to electromagnetic field. Electromagnetic (EM) radiation is a form of energy propagated through free space or through a material medium in the form of electromagnetic waves. EM radiation is so-named because it has electric and magnetic fields that simultaneously oscillate in planes mutually perpendicular to each other and to the direction of propagation through space. Electromagnetic radiation has the dual nature: its exhibits wave properties and particulate (photon) properties. Wave nature of radiation: Radiation can be thought of as a traveling transverse wave. z Figure 1.1 A schematic view of an electromagnetic wave propagating along the z axis. The electric E and magnetic H fields oscillate in the x-y plane and perpendicular to the direction of propagation. 1

2 As a transverse wave, EM radiation can be polarized. Polarization is the distribution of the electric field in the plane normal to propagation direction. Figure 1. Electric field E orientation for polarized and non polarized electromagnetic waves. Poynting vector gives the flow of radiant energy and the direction of propagation as (in the cgs system of units) S = c 0 E H ε [1.1] here c is the speed of light in vacuum (c =.9979x10 8 m/s 3.00x10 8 m/s) and ε 0 is vacuum permittivity (or dielectric constant). S is in units of energy per unit time per unit area (e.g., W m - ) NOTE: E H means a vector product of two vectors. S is often called instantaneous Poynting vector. Because it oscillates at rapid rates, a detector measures its average value <S> over some tome interval that is a characteristic of the detector.

3 Waves are characterized by frequency, wavelength, speed and phase. Frequency is defined as the number of waves (cycles) per second that pass a given point in space (symbolized by ~ ν ). Wavelength is the distance between two consecutive peaks or troughs in a wave (symbolized by the ). Relation between and ν ~ : ν ~ = c [1.] Since all types of electromagnetic radiation travel at the speed of light, shortwavelength radiation must have a high frequency. Unlike speed of light and wavelength, which change as electromagnetic energy is propagated through media of different densities, frequency remains constant and is therefore a more fundamental property. Wavenumber is defined as a count of the number of wave crests (or troughs) in a given unit of length (symbolized by ν): UNITS: Wavelength units: length Angstrom (A) : 1 A = 1x10-10 m; Nanometer (nm): 1 nm=1x10-9 m; Micrometer (µm): 1 µm = 1x10-6 m; Wavenumber units: inverse length (often in cm -1 ) ν = ν ~ /c = 1/ [1.3] NOTE: Conversion from the wavelength to wavenumber: ,000cm µ m ν [ cm ] = [1.4] [ µ m] 3

4 Frequency units: unit cycles per second 1/s (or s -1 ) is called hertz (abbreviated Hz) Table 1.1 Frequency units Unit Hertz, Hz 1 Kilohertz, KHz 10 3 Megahertz, MHz 10 6 Gigahertz, GHz 10 9 Frequency, (cycles/sec) Particulate nature of radiation: Radiation can be also described in terms of particles of energy, called photons The energy of a photon is given as: ε photon = h ~ ν = h c/ = hcν [1.5] where h is Plank s constant (h = 6.656x10-34 J s). Eq. [1.5] relates energy of each photon of the radiation to the electromagnetic wave characteristics (ν ~ and ). Photon has energy but it has no mass and no charge. NOTE: The quantized nature of light is most important when considering absorption and emission of electromagnetic radiation. PROBLEM: A light bulb of 100 W emits at 0.5 µm. How many photons are emitted per second? Solution: Energy of one photon is ε photon = hc/, thus, using that 100 W = 100 J/s, the number of photons per second, N, is N 100 ( Js ) ( m) ( s ) = = = h( Js) c( ms ) NOTE: Large number of photons is required because Plank s constant h is very small!!! 4

5 Spectrum of electromagnetic radiation: The electromagnetic spectrum is the distribution of electromagnetic radiation according to energy or, equivalently, according to the wavelength or frequency. Figure 1.3 Schematic representation of the electromagnetic spectrum. Figure 1.4 Visible region of the electromagnetic spectrum. NOTE: In remote sensing, sensor s spectral bands in the visible are often called by their color (e.g., blue, green, and read channels) 5

6 Effects of atmospheric gases: Figure 1.5 A generalized diagram showing relative atmospheric radiation transmission at different wavelengths. Blue zones show low passage of incoming and/or outgoing radiation and white areas show atmospheric windows, in which the radiation doesn't interact much with air molecules and hence, isn't absorbed. Figure 1.6 Schematics showing the role of Earth s atmospheric composition in remote sensing. 6

7 Table 1. Common names and relationships between radiation components. Name of Wavelength Spectral equivalence spectral region region, µm Solar Ultraviolet + Visible + Near infrared = Shortwave Terrestrial Far infrared = Longwave Infrared Near infrared + Far infrared Ultraviolet Near ultraviolet + Far ultraviolet = UV-A + UV-B + UV-C + Far ultraviolet Shortwave Solar = Near infrared + Visible + Ultraviolet Longwave Terrestrial = Far infrared Visible Shortwave - Near infrared - Ultraviolet Near infrared Solar - Visible - Ultraviolet = Infrared - Far infrared Far infrared Terrestrial = Longwave = Infrared - Near infrared Thermal Terrestrial = Longwave = Far infrared (up to 1000) Microwave Microwave Radio > 10 6 Radio Table 1.3 Microwave frequency bands used in remote sensing Bands Frequency Old New [GHz] L D 1- S E, F -4 C G, H 4-8 X I, J 8-1 Ku J 1-18 K J 18-6 Ka K 6-40 Example: L-band is used onboard American SEASAT and Japanese JERS-1 satellites. 7

8 . Basic radiometric quantities: intensity and flux. Solid angle is the angle subtended at the center of a sphere by an area on its surface numerically equal to the square of the radius s Ω = r [1.6] UNITS: of a solid angle = steradian (sr) r A differential solid angle can be expressed as Ω ds s d Ω = = sin( θ ) d θdφ, r using that a differential area is ds = (r dθ) (r sin(θ) dφ) Example: Solid angle of a unit sphere = 4π PROBLEM: What is the solid angle of the Sun from the Earth if the distance from the Sun to the Earth is d=1.5x10 8 km? Sun s radius is R s = 6.96x10 5 km. SOLUTION: Ω = π d R s = 6.76 x10 5 sr Intensity (or radiance) is defined as radiative energy in a given direction per unit time per unit wavelength (or frequency) range per unit solid angle per unit area perpendicular to the given direction: I ε d = ds cos( θ ) dωdtd [1.7] I is referred to as the monochromatic intensity. Monochromatic does not mean at a single wavelengths, but in a very narrow (infinitesimal) range of wavelength centered at. NOTE: same name: intensity = specific intensity = radiance UNITS: from Eq.[1.7]: (J sec -1 sr -1 m - µm -1 ) = (W sr -1 m - µm -1 ) 8

9 Figure 1.7 Intensity is the flow of radiative energy carried by a beam within the solid angle d Ω. Properties of intensity: a) In general, intensity is a function of the coordinates ( r ), direction ( Ω ), wavelength (or frequency), and time. Thus, it depends on seven independent variables: three in space, two in angle, one in wavelength (or frequency) and one in time. b) In a transparent medium, the intensity is constant along a ray. If intensity does not depend on the direction, the electromagnetic field is said to be isotropic. If intensity does not depend on position the field is said to be homogeneous. 9

10 Flux (or irradiance) is defined as radiative energy in a given direction per unit time per unit wavelength (or frequency) range per unit area perpendicular to the given direction: UNITS: from Eq.[1.8]: (J sec -1 m - µm -1 ) = (W m - µm -1 ) ε d F = [1.8] dtdsd From Eqs. [1.7]-[1.8], the flux is integral of normal component of radiance over some solid angle Ω F = I cos(θ ) dω [1.9] NOTE: Many satellite sensors have a narrow viewing angle and hence measure the intensity (not flux). To measure the flux, a sensor needs to have a wide viewing angle. Depending on its spectral resolution, a detector measures electromagnetic radiation in a particular wavelength range,. The intensity I and flux F in this range are determined by integrating over the wavelength the monochromatic intensity and flux, respectively: I = I d F = F d [1.10] 1 1 NOTE: Lecture gives classification of the sensors with respect to their spectral resolution: broad-band, narrow-band, spectral and hyperspectral. Examples: Broad-band sensor: CERES (Clouds and the Earth's Radiant Energy System) Three bands (channels): Solar region: µm; IR window: 8-1 µm; and total: 0.3 to > 100 µm Narrow-band sensor: MODIS (Moderate Resolution Imaging Spectroradiometer) 10

11 Table 1.4 MODIS spectral bands Primary Use Band Bandwidth¹ Spectral Radiance² Required SNR³ Land/Cloud/Aerosols Boundaries Land/Cloud/Aerosols Properties Ocean Color Phytoplankton Biogeochemistry Atmospheric Water Vapor Surface/Cloud Temperature (300K) (335K) (300K) (300K) 0.07 Atmospheric Temperature (50K) (75K) 11

12 Cirrus Clouds Water Vapor (SNR) Cloud Properties Ozone (40K).18 (50K) 9.58 (300K) 3.69 (50K) 0.05 Surface/Cloud Temperature (300K) (300K) 0.05 Cloud Top Altitude (60K) (50K) (40K) (0K) 0.35 * Footnotes: 1 Bands 1 to 19 are in nm; Bands 0 to 36 are in µm Spectral Radiance values are (W/m² -µm-sr) 3 SNR = Signal-to-noise ratio 4 NE(delta)T = Noise-equivalent temperature difference 1

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### Intended Learning Outcomes

An Introduction to Thermal Radiation This problem provides an introduction to thermal and atmospheric physics. Intended Learning Outcomes By the end of this activity students should be able to: Use basic

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21 The Nature of Electromagnetic Waves When we left off talking about the following circuit: I E v = c B we had recently closed the switch and the wire was creating a magnetic field which was expanding