# Radiation and the Planck Function

0
0
2546 days ago, 693 views
PowerPoint PPT Presentation
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..

### Presentation Transcript

Slide 1

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

Slide 2

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.

Slide 3

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

Slide 4

Slide 5

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

Slide 6

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 __________________________________________________________________

Slide 7

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

Slide 8

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

Slide 9

Slide 10

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.

Slide 11

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 

Slide 12

Spectral Distribution of Energy Radiated from Blackbodies at Various Temperatures

Slide 14

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

Slide 15

B λ/B λ max

Slide 17

Area/3 2x Area/3

Slide 18

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 

Slide 20

B /B  max

Slide 21

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

Slide 22

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 

Slide 23

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

Slide 24

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)

Slide 25

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)

Slide 27

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

Slide 28

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

Slide 29

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