A J Gasiewski remote sensing course notes lecture4

61 Pages·00.979 MB·English

by  A J Gasiewski

EECCEENN 55225544
Remote Sensing Signals and Systems
Professor Albin J. Gasiewski
Lecture #4 – January 26, 2012
EECCOOTT 224466
303-492-9688 (O)
[email protected]
Classes: ECCS 1B14 TR 8:00-9:15 AM
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ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder
Last Lecture
• Coherence
• Transmission line radiation
• Rayleigh-Jeans approximation
•• JJoohhnnssoonn tthheerrmmaall nnooiissee
• 1-D radiative transfer
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ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder
Today’s Lecture
• Planck ((3-D)) sppectrum
• Rayleigh-Jeans approximation
•• WWiieenn’ss llaaww
• Stefan-Boltzmann law
• Plane wave review
• Stochastic EM pplane waves
• Stokes parameters
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ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder
Planck Spectrum
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Thermal Radiation in Free Space
T (K) S+(f) → (W/Hz)
T (K)
Previously: 1-D single mode thermal radiation
I(θ,ϕ,f ) (W/m2-st-Hz)
TT ((KK))
NNooww:: CCoonnssiiddeerr 33-DD ppllaannee wwaavvee ssppeeccttrruumm,, ttwwoo
polarization states for each direction of propagation
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Derivation of Planck Spectral Density
CConsiidder a cllosedd condducttiing caviitty iin tthhermall equiilliibbriium
at temperature T (K):
yy
z
b
V = abd
TT ((KK))
d
x
a
WW((ff)) = EEnneerrggyy ssppeeccttrraall ddeennssiittyy iinn JJ//((HHzz-mm3)) ooff EEMM rraaddiiaattiioonn
in the cavity (all TEM plane wave modes)
==
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Cavity Resonator Modes
TE Comprised of uniform plane
mnp
TM waves (UPWs) of the form:
mnp
Standing waves patterns
(all three dimensions):
a,,b,, or d
From boundary conditions of
caviitty - m, n, p iinttegers:
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Cavity Resonant Frequencies
pp
n
ellipsoid
m
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Average # Photons per Mode (same as 1-D)
EEnneerrggyy ppeerr PPhhoottoonn ((= hhff, ssaammee aass 11-DD ))
3-D Thermal Energy Spectral Density
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3-D Thermal Noise Power Spectral Density
TToo ffiinndd II((θθ,ϕϕ, ff )) ccoonnssiiddeerr tthhee ffllooww ooff rraaddiiaattiioonn
I
z
through a thin slab:
θ
EEnergy wiillll propagate out off
box as isotropic density I
Area A
((W/m2-Hz-st))
T (K)
If energy escapes without
Δz
rreeppllaacceemmeenntt tthheenn::
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