A J Gasiewski remote sensing course notes lecture4 PDF
Preview A J Gasiewski remote sensing course notes lecture4
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 1 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 3 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 4 ECEN 5254 Remote Sensing Signals & Systems Spring 2012 University of Colorado at Boulder Planck Spectrum 5 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 6 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) == 7 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: 8 Cavity Resonant Frequencies pp n ellipsoid m 9 Average # Photons per Mode (same as 1-D) EEnneerrggyy ppeerr PPhhoottoonn ((= hhff, ssaammee aass 11-DD )) 3-D Thermal Energy Spectral Density 10 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:: 11
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