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All satellite remote detecting frameworks include the estimation of electromagnetic radiation. Electromagnetic radiation has the properties of both waves and discrete particles, in spite of the fact that the two are never show simultaneously.Electromagnetic radiation is normally evaluated by wave-like properties; for some applications it thought to be a ceaseless train of sinusoidal shapes..

Radiation and the Planck Function Lectures in Benevento June 2007 Paul Menzel UW/CIMSS/AOS

All satellite remote detecting frameworks include the estimation of electromagnetic radiation. Electromagnetic radiation has the properties of both waves and discrete particles, despite the fact that the two are never show at the same time. Electromagnetic radiation is generally measured by its wave-like properties; for some applications it thought to be a consistent prepare of sinusoidal shapes.

The Electromagnetic Spectrum Remote detecting utilizes brilliant vitality that is reflected and discharged from Earth at different "wavelengths" of the electromagnetic range Our eyes are delicate to the unmistakable bit of the EM range

Radiation is portrayed by wavelength and adequacy a

Terminology of brilliant vitality Energy from the Earth Atmosphere after some time is Flux which strikes the finder region Irradiance at a given wavelength interim Monochromatic Irradiance over a strong point on the Earth Radiance saw by satellite radiometer is depicted by The Planck capacity can be transformed to Brightness temperature

Definitions of Radiation __________________________________________________________________ QUANTITY SYMBOL UNITS __________________________________________________________________ Energy dQ Joules Flux dQ/dt Joules/sec = Watts Irradiance dQ/dt/dA Watts/meter 2 Monochromatic dQ/dt/dA/d W/m 2/micron Irradiance or dQ/dt/dA/d W/m 2/cm - 1 Radiance dQ/dt/dA/d /d W/m 2/micron/ster or dQ/dt/dA/d /d W/m 2/cm - 1/ster __________________________________________________________________

Radiation from the Sun The rate of vitality exchange by electromagnetic radiation is known as the brilliant flux, which has units of vitality per unit time. It is signified by F = dQ/dt and is measured in joules every second or watts. For instance, the brilliant flux from the sun is around 3.90 x 10**26 W. The brilliant flux per unit range is known as the irradiance (or brilliant flux thickness in a few writings). It is meant by E = dQ/dt/dA and is measured in watts per square meter. The irradiance of electromagnetic radiation going through the furthest reaches of the unmistakable plate of the sun (which has an inexact sweep of 7 x 10**8 m) is given by 3.90 x 10 26 E (sun sfc) = 6.34 x 10 7 W m - 2 . 4 (7 x 10 8 ) 2

The sun powered irradiance touching base at the earth can be figured by understanding that the flux is a steady, accordingly E (earth sfc) x 4πR es 2 = E (sun sfc) x 4πR s 2 , where R es is the mean earth to sun separate (around 1.5 x 10 11 m) and R s is the sun powered sweep. This yields E (earth sfc) = 6.34 x 10 (7 x 10 8/1.5 x 10 11 ) 2 = 1380 W m - 2 . The irradiance per unit wavelength interim at wavelength λ is known as the monochromatic irradiance, E λ = dQ/dt/dA/dλ , and has the units of watts per square meter per micrometer. With this definition, the irradiance is promptly observed to be E = E λ dλ . o

by and large, the irradiance upon a component of surface territory may comprise of commitments which originate from a limitlessness of various headings. It is here and there important to recognize the piece of the irradiance that is originating from headings inside some predefined microscopic circular segment of strong point dω. The irradiance per unit strong edge is known as the brilliance, I = dQ/dt/dA/dλ/dω, and is communicated in watts per square meter per micrometer per steradian. This amount is frequently likewise alluded to as force and indicated by the letter B (when alluding to the Planck work). On the off chance that the peak point, θ, is the edge between the course of the radiation and the typical to the surface, then the segment of the brilliance ordinary to the surface is then given by I cos θ. The irradiance speaks to the joined impacts of the typical segment of the radiation originating from the entire side of the equator; that is, E = I cos θ dω where in round directions dω = sin θ dθ dφ . Ω Radiation whose brilliance is autonomous of course is called isotropic radiation. For this situation, the incorporation over dω can be promptly appeared to be equivalent to so that E = I .

Radiation is represented by Planck's Law c 2/ T B( ,T) = c 1/{ 5 [e - 1] } Summing the Planck work at one temperature over all wavelengths yields the vitality of the transmitting source E = B(, T) = T 4 Brightness temperature is particularly identified with brilliance for a given wavelength by the Planck work.

Using wavelengths c 2/ T Planck's Law B( ,T) = c 1/ 5/[e - 1] (mW/m 2/ster/c m) where = wavelengths in cm T = temperature of radiating surface (deg K) c 1 = 1.191044 x 10-5 (mW/m 2/ster/cm - 4 ) c 2 = 1.438769 (cm deg K) Wien's Law dB( max ,T)/d = 0 where (max) = .2897/T demonstrates pinnacle of Planck capacity bend movements to shorter wavelengths (more noteworthy wavenumbers) with temperature increment. Note B( max ,T) ~ T 5 . Stefan-Boltzmann Law E = B( ,T) d = T 4 , where = 5.67 x 10-8 W/m2/deg4 . o expresses that irradiance of a dark body (territory under Planck bend) is corresponding to T 4 . Brilliance Temperature c 1 T = c 2/[ ln( _____ + 1)] is controlled by altering Planck work 5 B

Spectral Distribution of Energy Radiated from Blackbodies at Various Temperatures

B( max ,T) T 5 B( max,6000) ~ 3.2 x 10 7 B( max,300) ~ 1 x 10 1 so B( max,6000)/B( max,300) ~ 3 x 10 6 and (6000/300) 5 = (20) 5 = 3.2 x 10 6 which is the same

B λ/B λ max

Area/3 2x Area/3

Using wavenumbers c 2 /T Planck's Law B( ,T) = c 1 3/[e - 1] (mW/m 2/ster/cm - 1 ) where = # wavelengths in one centimeter (cm-1) T = temperature of emanating surface (deg K) c 1 = 1.191044 x 10-5 (mW/m 2/ster/cm - 4 ) c 2 = 1.438769 (cm deg K) Wien's Law dB( max ,T)/d = 0 where ν (max) = 1.95T demonstrates pinnacle of Planck capacity bend movements to shorter wavelengths (more noteworthy wavenumbers) with temperature increment. Note B( max ,T) ~ T**3. Stefan-Boltzmann Law E = B( ,T) d = T 4 , where = 5.67 x 10-8 W/m2/deg4 . o expresses that irradiance of a dark body (region under Planck bend) is relative to T 4 . Shine Temperature c 1 3 T = c 2 /[ln( ______ + 1)] is dictated by rearranging Planck work B

B /B max

B( max,T)~T 5 B(max,T)~T 3 B( ,T) B(,T) B( ,T) versus B(,T)

Using wavenumbers Using wavelengths c 2 /T c 2/ T B( ,T) = c 1 3/[e - 1] B( ,T) = c 1/{ 5 [e - 1] } (mW/m 2/ster/cm - 1 ) (mW/m 2/ster/ m) (max in cm-1) = 1.95T (max in cm)T = 0.2897 B( max ,T) ~ T**3. B( max ,T) ~ T**5. E = B( ,T) d = T 4 , E = B( ,T) d = T 4 , o o c 1 3 c 1 T = c 2 /[ln( ______ + 1)] T = c 2/[ ln( ______ + 1)] B 5 B

Temperature affectability , or the rate change in brilliance relating to a rate change in temperature, , is characterized as dB/B = dT/T. The temperature sensivity shows the ability to which the Planck brilliance relies on upon temperature, since B corresponding to T fulfills the condition. For infrared wavelengths, = c 2 /T = c 2/ T. __________________________________________________________________ Wavenumber Typical Scene Temperature Temperature Sensitivity 700 220 4.58 900 300 4.32 1200 300 5.76 1600 240 9.59 2300 220 15.04 2500 300 11.99

dB/B = dT/T or B = c T where = c2/ T for a little temperature window around T. B = B(T 0 ) + (dB/dT) 0 ( Δ T) + (d 2 B/dT 2 ) 0 ( Δ T) 2 + O(3) negligible So to first request c (T 0 + Δ T) = c T 0 + c T 0 -1 ( Δ T) c (T 0 + Δ T) - c T 0 = c T 0 -1 ( Δ T) Δ B = c T 0 -1 ( Δ T) Δ B/B = Δ T/T Also to first request (T 0 + Δ T) = T 0 + T 0 -1 ( Δ T)

Temperature Sensitivity of B( λ ,T) for run of the mill earth scene temperatures B ( λ , T)/B ( λ , 273K) 4 μ m 6.7 μ m 2 1 10 μ m 15 μ m microwave 250 300 Temperature (K)

B(10 um,T)/B(10 um,273) T 4 B(10 um,273)= 6.1 B(10 um,200)= 0.9 0.15 B(10 um,220)= 1.7 0.28 B(10 um,240)= 3.0 0.49 B(10 um,260)= 4.7 0.77 B(10 um,280)= 7.0 1 .15 B(10 um,273)= 9.9 1.62 1 200 300

B(4 um,T)/B(4 um,273) T 12 B(4 um,273)= 2.2 x 10 - 1 B(4 um,200)= 1.8 x 10 - 3 0.0 B(4 um,220)= 9.2 x 10 - 3 0.0 B(4 um,240)= 3.6 x 10 - 2 0.2 B(4 um,260)= 1.1 x 10 - 1 0.5 B(4 um,280)= 3.0 x 10 - 1 1.4 B(4 um,273)= 7.2 x 10 - 1 3.3 1 200 300

B(0.3 cm, T)/B(0.3 cm,273) T B(0.3 cm,273)= 2.55 x 10 - 4 B(0.3 cm,200)= 1.8 0.7 B(0.3 cm,220)= 2.0 0.78

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