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Illumination, Radiometry,and a (Very Brief) Introduction to the
Physics of Remote Sensing!
Course Philosophy"
4-Jan-2011 lhm - 2 ME/CS 132
Computer graphics!
Rendering!
Computer vision!
Estimation!
Remote sensing!
Robot vision"
What This Lecture is About"
4-Jan-2011 lhm - 3 ME/CS 132
• Characteristics of illumination sources!
• Atmospheric attenuation!
• Radiometry and reflectance models!
• Spectral characteristics of reflectance and thermal emission and their interrelationships!
In Context with Coming Lectures"
4-Jan-2011 lhm - 4 ME/CS 132
• Today: illumination, radiometry, physics of remote sensing!• Tuesday: cameras: optics, detectors!• Thursday: geometric camera modeling and calibration!• Reading material:!
– Szeliski sec 2.2 (today)!– Szeliski sec 2.3 (Tuesday)!– Forsyth ch. 1 (Tuesday)!– Szeliski sec 2.1 (Thursday)!
• Additional reference material:!– C. Elachi, Introduction to the Physical and Techniques of Remote
Sensing!– J. R. Jensen, Remote Sensing of the Environment!
Electromagnetic Spectrum"
4-Jan-2011 lhm - 5 ME/CS 132
Solar Spectrum"
4-Jan-2011 lhm - 6 ME/CS 132
Total irradiance ~ 1370 W/m2 above atmosphere (solar constant)!
Blackbody Emission: Planckʼs Law"
4-Jan-2011 lhm - 7 ME/CS 132
S(!) = 2"hc2
! 51
ech/!kT !1
Where!• S(λ) = spectral radiant emittance in W/m3 (watts per unit wavelength
per unit area)!• λ = radiation wavelength!• h = Planckʼs constant = 6.626 x 10-34 Wsec2!• T = absolute temperature in °K!• C = velocity of light = 2.9979 x 108 m/sec!• K = Boltzmann constant = 1.38 x 10-23 Wsec/K!
Blackbody Spectrum"
4-Jan-2011 lhm - 8 ME/CS 132
Blackbody Spectrum"
4-Jan-2011 lhm - 9 ME/CS 132
Stefan-Boltzmann and Wien Laws"
4-Jan-2011 lhm - 10 ME/CS 132
• Total flux emitted by a blackbody of unit area (Stefan-Boltzmann law):!
!– where σ = 5.669 x 10-8 W/m2K4!
• Wavelength of maximum emission (Wienʼs law):!
!– where a = 2898 μmK!– for sun (T ~ 6000 °K), λm = 480 nm; for Earth surface (T ~ 300 °K), λm = 9.66 μm!
• Photon energy = hc/λ (J/photon), so # photons = S(λ)λ/hc!
S(!)d! ="T 4!
!m =aT
Atmospheric Windows in the Infrared"
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Some Sources of Illumination"
4-Jan-2011 lhm - 12 ME/CS 132
• Sunlight!• Thermal emission!• Skylight!• Night sky glow (nightglow)!• Man-made lights: e.g. incandescent bulbs, fluorescent
bulbs, arc lamps!
Skylight"
4-Jan-2011 lhm - 13 ME/CS 132
Violet Indigo Blue Green Yellow Orange Red
Night Sky Glow"
4-Jan-2011 lhm - 14 ME/CS 132
Incandescent Bulb"
4-Jan-2011 lhm - 15 ME/CS 132
Violet Indigo Blue Green Yellow Orange Red
Tungsten bulb, 2800K!
Daylight model!
Metal Halide and Fluorescent Lights"
4-Jan-2011 lhm - 16 ME/CS 132
Violet Blue Green Yellow Orange Red
Some Illustrations"
4-Jan-2011 lhm - 17 ME/CS 132
SWIR nightglow image!(no moon)!
Visible vs. SWIR in haze!
Visible vs. thermal image at night!
Visible vs. thermal in smoke!
Atmospheric Propagation"
4-Jan-2011 lhm - 18 ME/CS 132
• In general, radiative transfer in the atmosphere has these elements:!
• We wonʼt study details of each!
Absorption!
Scattering!
Scattering!source!
Emission!source!
Together are “extinction”:!
I(D) = I0e!!D, T = e!!D
α is the extinction coefficient (km-1)!T is the transmission coefficient!
Visible" LWIR" 35 GHz MMW"
Haze! 0.02-2! 0.02-0.4! 0.001!Dust! 0.2-4! 0.2-4! < 0.005!
At 0.5 km:!TH! 0.37! 0.82! 0.9995!TD! 0.14! 0.14! 0.998!
Basic Radiometry: Motivation"
4-Jan-2011 lhm - 19 ME/CS 132
Goal: be able to model the light reaching a pixel in the image or to invert this to estimate scene properties from measured image brightness!
Solid Angles"
4-Jan-2011 lhm - 20 ME/CS 132
Angle!
Solid angle!
d! = dl cos"r
d! =dAcos"r2
Radiance and Irradiance"
4-Jan-2011 lhm - 21 ME/CS 132
Radiance:!• The amount of energy travelling at some point in a specified direction,
per unit time, per unit area perpendicular to the direction of travel, per unit solid angle (W m -2 sr -1). Usually denoted L(x,θ,φ).!
!!!!!Irradiance: !• Power per unit area of a collimated beam (W m -2 ). Usually denoted E.!• Power per unit area impinging on a surface.!
Definitions of Radiometric Terms"
4-Jan-2011 lhm - 22 ME/CS 132
• Radiance: L. Units: W m -2 sr -1!
• Irradiance: E. Units: W m -2 !
• Spectral quantities are per unit of wavelength, e.g.!– Spectral radiance, W m -2 sr -1 nm -1!
– Spectral irradiance, W m -2 nm -1!
• Radiant energy: Q. Units: J!
• Radiant flux: Φ. Units: W!
• Radiant intensity: I. Units: W/sr!
Surface Irradiance for Various Lighting Conditions"
4-Jan-2011 lhm - 23 ME/CS 132
Point source at infinity (e.g. sun)!
!nE, W/m2!
!i
dAsEi = E cos!id!i = Ei dAs
Point source at range r!
!nI, W/sr!
!i
dAs
d!s =dAs cos"i
r2
d!i = I d!s
Ei =I cos"ir2
d!s!nLi, W/sr/m2!
!i
dAsd!s
Extended source at range r!
d!i
dAi
d!s =dAs cos"i
r2, d!i =
dAir2
d!i = Li d!s dAi = Li d!i dAs cos"i
Ei =d!i
dAs= Li cos"i d!i
Same for extended source at infinity (e.g. sky)!
Given an incoming ray and outgoing raywhat proportion of the incoming light is reflected along outgoing ray?!
Bidirectional Reflectance Distribution Function"
4-Jan-2011 lhm - 24 ME/CS 132
Answer given by the BRDF:
Units: sr -1!f (!i,"i,!r,"r )Isotropic case: f (!i,!r, "i !"r )
(!i,"i ) (!r,"r )
BRDF as the Ratio of L and E"
4-Jan-2011 lhm - 25 ME/CS 132
f (!i,"i,!r,"r ) =dLr (!r,"r )dEi (!i,"i )
=dLr (!r,"r )
Li (!i,"i )cos!i d#i
!dLr = f dEi = f Li cos!i d"i
Diffuse Reflection"
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• Diffuse reflection!– Dull, matte surfaces like matte paper!– Often has a strong body color due to absorption by the material!
Internal scattering!
Diffuse Reflection"
4-Jan-2011 lhm - 27 ME/CS 132
• Diffuse reflection is governed by Lambertʼs law"• Viewed brightness does not depend on viewing direction • Brightness does depend on direction of illumination • This is the model most often used in computer vision
f (!i,"i,!r,"r ) = kEi = E cos!iLr = k E cos!i
What is k?"
4-Jan-2011 lhm - 28 ME/CS 132
Consider a point source at infinity. Total flux on the surface patch is:!
d!i = Ei dAs = E cos!i dAs
Flux leaving the surface patch through a given solid angle is:!
!n!i
dAs
d!r
!r
d!r = Lr dAs cos!r d"r
= k E cos!i dAs cos!r d"r
Assume a fixed fraction ρ is absorbed by the surface.!Equate total incoming with total outgoing:!
! d!i = d!r"
#
! = k cos"r d#r"
#
What is k?"
4-Jan-2011 lhm - 29 ME/CS 132
! = k0
" /2
!0
2"
! cos#r sin#rd#rd$r
! = 2"k cos#r sin#r d#r0
" /2
!
Substituting! 2sin! cos! = sin2!
! = k", k = !"
Lr =!"E cos#i
(patterned after Horn, Robot Vision, ch. 10)!
! = k cos"r d#r!
"
Lambertʼs Law is an Idealization;the Real World is More Complex"
4-Jan-2011 lhm - 30 ME/CS 132
S. Nayar and M. Oren, “Visual Appearance of Matte Surfaces”, Science, Vol. 267, pp. 1153-1156, 1995!
Rough cylinder! Smooth cylinder!
Other Reflectance Models"
4-Jan-2011 lhm - 31 ME/CS 132
Pure specular!
Specular lobe!
Varying roughness!
Varying incidence
angle!
Other Reflectance Models"
4-Jan-2011 lhm - 32 ME/CS 132
S. Nayar, K. Ikeuchi, T. Kanade, “Surface Reflection: Physical and Geometrical Perspectives”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 7, 1991!
Also: surface vs. body reflection (dichromatic
reflectance model)!
Other Reflectance Models:Opposition Effect"
4-Jan-2011 lhm - 33 ME/CS 132
B. Hapke, Theory of Reflectance and Emittance Spectroscopy, 1993!
Color"
4-Jan-2011 lhm - 34 ME/CS 132
050100150200250
050
100150
200
0
20
40
60
80
100
120
140
160
180
RedGreen
Blue
050100150200250
050
100150
200
0
20
40
60
80
100
120
140
160
180
RedGreen
Blue
green vegetation dry vegetation soil/rock
Spectral Reflectance:Visible and Near Infrared (VNIR)"
4-Jan-2011 lhm - 35 ME/CS 132
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
foliage
soil
dry grass
Wavelength (µm)
Reflectivity
Refle
ctiv
ity
Wavelength
Spectral Reflectance:Visible and Near Infrared (VNIR)"
4-Jan-2011 lhm - 36 ME/CS 132
650nm image 800nm image 650:800 ratio image
Classified image
: =
Spectral Reflectance:Visible and Near Infrared (VNIR)"
4-Jan-2011 lhm - 37 ME/CS 132
B-R R-IR
G-R-IR B-G-R
Spectral Reflectance:Short Wave Infrared (SWIR)"
4-Jan-2011 lhm - 38 ME/CS 132
Snow reflectance
Thermal Infrared"
4-Jan-2011 lhm - 39 ME/CS 132
• Seeing in the dark!• Seeing through atmospheric
obscurants!• Recognizing things due to:!
– Intrinsic heat!– Heat transfer characteristics!– Thermal “color”!
Visible
LWIR
Heat Transfer Characteristics:Thermal Inertia"
4-Jan-2011 lhm - 40 ME/CS 132 (U. Arizona)!
Open Problem:Terrain Classification for Mars Rovers"
4-Jan-2011 lhm - 41 ME/CS 132
Rovers sometimes get stuck in the ripples; easily cross the bedrock!!How to discriminate the two reliably at low cost for sensors and processing? !
Heat Transfer Characteristics"
4-Jan-2011 lhm - 42 ME/CS 132
Color crosswise view Color lengthwise view MWIR image 1 hr
after sundown Weatherproof sensor enclosure
Heat Transfer Characteristics:After Sundown, Holes Cool More Slowly than Surface"
4-Jan-2011 lhm - 43 ME/CS 132
• Radiation
• Evapotranspiration (ignored here)
A !
qnegobs1
2negobsq
terrainq
1sideT 2sideT
terrainT
skyT
airTterrainT
terrainq
negobsq
negobsT
C5020 °!=diurnalTterrainT
terrainq
negobsq
negobsT
• Convection
• Conduction
!
qterrain = "# (Tterrain4 $Tsky
4 )
!
qterrain = h(Tterrain "Tair)
!
qterrain = "k dTdx
Heat Transfer Characteristics"
4-Jan-2011 lhm - 44 ME/CS 132
3.8 m
3.7 m
0.53 m
0.53 m
North
9 pm 7 am
9 am 9 pm
5 pm 5 pm
10 pm 7 am
Thermal “Color”"
4-Jan-2011 lhm - 45 ME/CS 132
S !( ) = " !( ) C1
!5 eC2!T # 1
$
% &
'
( )
Spectral emittance:
Blackbody emittance
Emissivity
Issues: • Separate temperature and emissivity • Exploit thermal inertia information • Determine robust spectral features
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
7 8 9 10 11 12 13
Wavelength (µm)
Emissivity
soil
dry grass
foliage
