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Black body radiation,planck's radiation, wien's law, stephen boltzmann law in remote sensing
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Black body radiation,planck's radiation, wien's law, stephen boltzmann law in remote sensing


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Black body radiation,planck's radiation, wien's law, stephen boltzmann law ,P K MANI

Black body radiation,planck's radiation, wien's law, stephen boltzmann law ,P K MANI

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  • Remote sensing is affected by how well the illuminating energy penetrates the atmosphere. This is especially important when the distance involved is great, such as from a satellite.
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    • 1. Remote Sensing and its Applications in Soil Resource Mapping(ACSS-754)(2+1) Dr. P. K. Mani Bidhan Chandra Krishi Viswavidyalaya E-mail: Website:
    • 2. B. Radiation & Atmosphere Remote sensing is affected by how well the illuminating energy penetrates the atmosphere. This is especially important when the distance involved is great, such as from a satellite.
    • 3. The Nature of Light • In the 1860s, the Scottish mathematician and physicist James Clerk Maxwell succeeded in describing all the basic properties of electricity and magnetism in four equations • This mathematical achievement demonstrated that electric and magnetic forces are really two aspects of the same phenomenon, which we now call electromagnetism
    • 4. Kirchhoff’s Laws
    • 5. Kirchoff’s First Spectral Law • Any hot body produces a continuous spectrum – if it’s hot enough it looks something like this – digitally like this Intensity Wavelength
    • 6. Kirchoff’s Second Spectral Law • Any gas to which energy is applied, either as heat or a high voltage, will produce an emission line spectrum like this – or digitally like this Intensity Wavelength
    • 7. Kirchoff’s Third Spectral Law • Any gas placed between a continuous spectrum source and the observer will produce a absorption line spectrum like this – or digitally like this Intensity Wavelength
    • 8. Astronomers’ Observations
    • 9. A perfect radiator, “one that radiates the maximum number of photons in a unit time from a unit area in a specified spectral interval into a hemisphere that any body at thermodynamic equilibrium at the same temperature can radiate.”
    • 10. Black Body Radiation: Blackbody radiation field is characterised as: Isotropic and nonpolarized; Independent of shape of cavity; Depends on only temperature (T). In a perfect blackbody emisivity is equal to unity due to thermodynamic equilibirium. WMO-RMTC-EUMETSAT Satellite Meteorology Course, Alanya, Turkey 22-25
    • 11. Kirchoff’s law: Since no real body is perfect emitter, its emittance is less than that of a black body (Mb). Thus the emissivity of a real (gray,Mg) body is defined by εg= Mg/Mb
    • 12. • As the temperature increases, the peak wavelength emitted by the black body decreases. • As temperature increases, the total energy emitted increases, because the total area under the curve increases. • The curve gets infinitely close to the x-axis but never touches it.
    • 13. Derivation of Planck’s radiation law Assumptions: A cavity in a material that is maintained at constant temperature T The emission of radiation from the cavity walls is in equilibrium with the radiation that is absorbed by the walls Blackbody cavity: schematic The radiation field in an empty volume in thermal equilibrium with a container at T can be viewed as a superposition of standing harmonic waves M. Planck, Ann. Phys. Vol. 4, p.553 (1901)
    • 14. Rayleigh–Jeans Law: it describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a given temperature: c is the speed of light, k is Boltzmann's constant T is the temperature in kelvins. It predicts an energy output that diverges towards infinity as wavelengths grow smaller. This was not supported by experiments and the failure has become known as the ultraviolet catastrophe.
    • 15. The energy density (i.e., the energy per unit volume) is therefore given by a relation known as Rayleigh-Jeans' law. The expression is valid for but incorrect for , as it predicts that in this case the energy density should become infinite. This physically incorrect property of the equation would lead to what has been termed “UV catastrophy".
    • 16. Planck 1900: ...the whole procedure Wilhelm Wien (1864-1928). was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be...
    • 17. Planck’s radiation law The Planck’s radiation law can be written in dependence on frequency or on wavelength With L = spectral radiance (energy / unit time / unit surface area / unit solid angle / unit wavelenth), λ = wavelength, T = temperature, h = Planck const (6.62606896×10−34 J·s), c = speed of light (299,792,458 m/s), k =Boltzmann constant (1.380 6504 × 10−23 J /K) ν = frequency (c = λν). u = spectral energy density as energy / unit volume /unit wavelength 2 interpretations of Planck’s law: 1) A surface of a solid body with the highest possible emissivity emits exactly the radiation calculated from the Planck’s law. 2) Within a box with walls which have all the same temperature we get a gas of electromagnetic photons which are in equilibrium with the walls, meaning that in any time interval the walls absorb and emit an equal amount of photons. The energy density and spectral distribution of the photons are described by u .
    • 18. Planck’s radiation Law: For a radiating body with emissivity ε, the spectral radiant excitance (emittance) is given by Planck’s radiation law as: ε 8π hc 1 Mλ = ⋅ hc / λkT 5 λ e −1 W/(m2-μm) Using the relationship between frequency and wavelength of the electromagnetic radiation ν = c/λ, Planck’s law can be written as ε 8πh ν M ν = 3 ⋅ hν / kT c e −1 3 W/(m2-Hz)
    • 19. Black-body radiation is the type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (an opaque and nonreflective body) held at constant, uniform temperature. The radiation has a specific spectrum and intensity that depends only on the temperature of the body
    • 20. Planck to Einstein: I hereby award you the Planck Medal because you expanded my desperate idea of quantum of energy to the even more desperate idea of quantum of light.
    • 21. Stefan- Boltzmann Law: If we integrate Mλ or Mν over all wavelength or all frequencies, the total radiant emittance M will obtained for a radiating body of unit area i.e., M = ∫ M λ dλ = ∫ M v dv = (ε 8π κ / h c )T 5 = σεT ,...........W / m 4 4 3 3 4 2 Where σ is the Stefan-Boltzmann radiation constant, and has the numerical value = 5.669 10-8 W/(M2-K4) Wien’s Displacement Law: To obtain the peak spectral radiant emittance, we differentiate M λ with respect to λ and set it equal to 0 and the resulting equation is solved for λmax . Thus we get λmax = a / T ...............µm
    • 22. Radiance of EMR A black body is hypothetical material that absorbs and re-radiates ALL incident EMR. The Stephan-Boltzman equation describes the total amount of radiation emitted by a black body as a function of its surface temperature: M = σT4 where: M = energy (Wm-2) σ = Stephan-Boltzman constant T = temperature (K)
    • 23. • Wien’s Displacement Law λm = b/T λm = µm b = 2898 µm K • λ m(Sun) = 2898/6000 = 0.48 µm • λ m(Earth) = 2898/300 = 9.66 µm
    • 24. • Stefan-Boltzmann law MT = σT4 MT = W m-2 σ = 5.669 x 10-8 W m-2 K-4 λm(Sun) = 5.669e-8 X 60004 MT = 7.3 x 107 W m-2 • λm (Earth) = 5.669e-8 x 3004 MT = 4.6 x 102 W m-2
    • 25. Total EMR Emitted The higher the temperature the more total energy Total Energy = Area Under Curve
    • 26. Spectral Distribution of Energy Radiated from Blackbodies at Various Temperatures
    • 27. Wavelength of EMR Emitted The higher the temperature the lower/shorter the wavelength of maximum radiance • Wein’ Law states that λm = A/T where: A is a constant Shortwave EMR Longwave EMR
    • 28. Radiometric Quantities Quantities Radiant Energy (Q) Definition Unit Energy transferred by electromagnetic J waves Radiant Flux (Φ ) Rate of transfer of radiant energy (Φ = dQ/dt) W Radiant emittance/ Radiant excitance (M) Radiant flux emitted per unit area of a source (M = dΦ/ dA) W cm -2 Radiant Intensity (I) Radiant flux/ unit solid angle (I = dΦ/dω) W sr-1 Radiance (L) Radiant flux / unit solid angle/ unit area W cm-2 sr-1 (L=dI/dA Cosθ ) Irradiance (E) Radiant flux incident / unit area (E = dΦ/dA) W cm-2
    • 29. Selective transmission of EMR by Earth’s atmosphere Transmission through the atmosphere is very selective. Very high for wavelengths 0.3-1 µm and >1cm, moderately good for 1-20 µm and 0.1-1 cm, and very poor for <0.3 µm and 20-100 µm. This defines the “ATMOSPHERIC WINDOWS”.
    • 30. Absorption. Scattering
    • 31. Rayleigh Scattering: why the sky is blue
    • 32. The atmosphere affects electromagnetic energy through absorption, scattering and reflection. How these processes affect radiation seen by the satellite depends on the path length, the presence of particulates and absorbing gases, and wavelengths involved. transmitted absorbed, emitted and scattered by aerosols and molecules transmitted absorbed &scattered emitted reflected transmitted reflected absorbed emitted Land emitted reflected transmitted absorbed Ocean Figure-... Process of Atmospheric Radiation
    • 33. EM radiation from the sun interacts with the atmospheric constituents and gets absorbed or scattered. Essentially two types of scattering takes place: Elastic scattering in which the energy of radiation is not changed due to the scattering, and inelastic scattering in which the energy of the scattered radiation is changed. 3 types of elastic scattering is recognized in atmospheric scattering Rayleigh scattering Mie scattering Nonselective scattering
    • 34. Radiation scattered from a particle depends on: Size; Shape; Index of refraction; Wavelength of radiation; View geometry. For Rayleight scattering, λ >> φ •Scattering is diffuse (in all directions) and λ dependent or selective • Scattering = 1/ λ4 For Mie scattering, λ ≈φ Where φ is particle size.  Scattering properties of such aerosols as smoke, dust, haze in the visible part of the spectrum and of cloud droplets in the IR region can be explanined by Mie scattering, While of air molecules in the visible part can be explained by Rayleigh Scattering
    • 35. Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light. It is Rayleigh scattering off the molecules of the air which gives us the blue sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much smaller than the wavelength to be: Rayleigh scattering can be considered to be elastic scattering since the photon energies of the scattered photons is not changed. Scattering in which the scattered photons have either a higher or lower photon energy is called Raman scattering. Usually this kind of scattering involves exciting some vibrational mode of the molecules, giving a lower scattered photon energy, or scattering off an excited vibrational state of a molecule which adds its vibrational energy to the incident photon.
    • 36. Nonselective Scattering • Particles are much larger than the wavelength d>>l • All wavelength are scattered equally Effects of scattering • It causes haze in remotely sensed images • It decreases the spatial detail on the images • It also decreases the contrast of the images
    • 37. Mie Scattering The scattering from molecules and very tiny particles (< 1/10 wavelength) is predominantly Rayleigh scattering. For particle sizes larger than a wavelength, Mie scattering predominates. This scattering produces a pattern like an antenna lobe, with a sharper and more intense forward lobe for larger particles. Mie scattering is not strongly wavelength dependent and produces the almost white glare around the sun when a lot of particulate material is present in the air. It also gives us the white light from mist and fog. Greenler in his "Rainbows, Haloes and Glories" has some excellent color plates demonstrating Mie scattering and its dramatic absence in the particle-free air of the polar regions.
    • 38. Atmospheric scattering process Scattering process Rayleigh Mie Nonselective Wavelength Particle size dependence μm λ-4 <<0.1 λ0 to λ-4 0.1-10 λ0 >10 Kind of particles Air molecules Smoke , fume, Haze Dust , Fog, Cloud Nonselective scattering occurs when the particles are much larger than the wavelength of the radiation. Water droplets and large dust particles can cause this type of scattering. Nonselective scattering gets its name from the fact that all wavelengths are scattered about equally. This type of scattering causes fog and clouds to appear white to our eyes because blue, green, and red light are all scattered in approximately equal
    • 39. Atmospheric Windows     Atmospheric windows define wavelength ranges in which the atmosphere is particularly transmissive of energy. Visible region of the electromagnetic spectrum resides within an atmospheric window with wavelengths of about 0.3 to 0.9 µm Emitted energy from the earth's surface is sensed through windows at 3 to 5 µm and 8 to 14 µm. Radar and passive microwave systems operate through a window region of 1 mm to 1 m.
    • 40. Atmospheric Windows The dominant windows in the atmosphere are in the visible and radio frequency regions, while X-Rays and UV are very strongly absorbed and Gamma Rays and IR are somewhat less strongly absorbed.
    • 41. Those wavelength ranges in which radiation can pass through the atmosphere with relatively little attenuation. atmospheric windows.
    • 42. Atmospheric Windows • Those wavelengths that are relatively easily transmitted through the atmosphere
    • 43. Examples of Passive Sensors: • Advanced Very High Resolution Radiometer (AVHRR) Sea Surface Temperature • Sea-viewing Wide Field-of-View Sensor (SeaWiFS) Ocean Color
    • 44. Remote Sensing Examples •Global maps of land cover/land cover change from MODIS ….. • 69
    • 45. Key: land cover classes
    • 46. Geostationary vs. polar orbiting sensors Geostationary sensors orbit with the earth continually viewing the same hemispheric area Polar orbiters, continually view new areas of the earth as the planet rotates underneath the sensor. Keeps the same general solar time as it cross the equator on each orbit - called sun synchronous Polar orbit
    • 47. Many different systems - which to choose?
    • 48. ikonos-abbottabad-pakistan
    • 49. ikonos-fukushimadaiichi-after-web
    • 50. ikonosmanhattan-newyork-9-11-2001web
    • 51. IKONOS
    • 52. Remote Sensor Types: non-imaging non-scaning passive Monochrom IR imaging Camera imaging Sensor types Microwave radiometer Magnatic ensor Gravimeter Fourier spectrum scanning TV camera image plane scanning object plane scanning Solid scanner Optical mechanical scan. Microwave radiometer non-scaning non-imaging Microwave radiometer Microwave altimeter aktive scanning imaging image plane scanning object plane scanning WMO-RMTC-EUMETSAT Satellite Meteorology Course, Alanya, Turkey 22-25 Passive phased array radar Real aperture radar Synthetic aperture radar
    • 53. Orbits: The motion of the satellites around the earth is governed by the Newton’s law of motion. The attractive force is: r satellite earth Satellite orbit WMO-RMTC-EUMETSAT Satellite Meteorology Course, Alanya, Turkey 22-25 gMem F = r2
    • 54. However, real satellite orbit is nerly elliptical due to the external foreces(e.g. gravitational potential of earth, solar pressure). Eliptical orbit is to be explained by Kepler’s law. Six orbital elements are used to express the spacecraft position given by: •Semimajor axis,a (km); •Eccentricity,e; •Inclination,i (degree); •Right ascensing of ascending node, Ω (degree); •Argument of perigee, ω (degree); •And true anomaly, ν, degree. WMO-RMTC-EUMETSAT Satellite Meteorology Course, Alanya, Turkey 22-25
    • 55. Z spacecraft apogee earth a ν perigee Y ω Ascending node Orbit plane X Ω i Equator plane Ascending node For the meteorological satellites, mainly two orbits are used: and sunsynchronous and geostationary. WMO-RMTC-EUMETSAT Satellite Meteorology Course, Alanya, Turkey 22-25
    • 56. Sunsynchronous orbit have high inclination angle (e.g 98.7 for NOAA sat), pass the equator at the same local time, and located in the lower orbit (e.g . 850 km). Geostationary orbit consides with the earth’s equatorial plane, located nearly 36 km above the equator. Geostationary satellites drift from the desired orbit so that periodic orbit manoeuvres are needed in the east-west and north-south directions and vise versa. WMO-RMTC-EUMETSAT Satellite Meteorology Course, Alanya, Turkey 22-25