illumination, radiometry, and a (very brief) introduction...
TRANSCRIPT
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Illumination, Radiometry,and a (Very Brief) Introduction to the
Physics of Remote Sensing!
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Course Philosophy"
4-Jan-2011 lhm - 2 ME/CS 132
Computer graphics!
Rendering!
Computer vision!
Estimation!
Remote sensing!
Robot vision"
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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!
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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!
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Electromagnetic Spectrum"
4-Jan-2011 lhm - 5 ME/CS 132
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Solar Spectrum"
4-Jan-2011 lhm - 6 ME/CS 132
Total irradiance ~ 1370 W/m2 above atmosphere (solar constant)!
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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!
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Blackbody Spectrum"
4-Jan-2011 lhm - 8 ME/CS 132
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Blackbody Spectrum"
4-Jan-2011 lhm - 9 ME/CS 132
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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
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Atmospheric Windows in the Infrared"
4-Jan-2011 lhm - 11 ME/CS 132
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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!
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Skylight"
4-Jan-2011 lhm - 13 ME/CS 132
Violet Indigo Blue Green Yellow Orange Red
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Night Sky Glow"
4-Jan-2011 lhm - 14 ME/CS 132
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Incandescent Bulb"
4-Jan-2011 lhm - 15 ME/CS 132
Violet Indigo Blue Green Yellow Orange Red
Tungsten bulb, 2800K!
Daylight model!
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Metal Halide and Fluorescent Lights"
4-Jan-2011 lhm - 16 ME/CS 132
Violet Blue Green Yellow Orange Red
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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!
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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!
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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!
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Solid Angles"
4-Jan-2011 lhm - 20 ME/CS 132
Angle!
Solid angle!
d! = dl cos"r
d! =dAcos"r2
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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.!
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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!
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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)!
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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 )
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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
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Diffuse Reflection"
4-Jan-2011 lhm - 26 ME/CS 132
• Diffuse reflection!– Dull, matte surfaces like matte paper!– Often has a strong body color due to absorption by the material!
Internal scattering!
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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
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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"
#
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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!
"
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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!
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Other Reflectance Models"
4-Jan-2011 lhm - 31 ME/CS 132
Pure specular!
Specular lobe!
Varying roughness!
Varying incidence
angle!
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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)!
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Other Reflectance Models:Opposition Effect"
4-Jan-2011 lhm - 33 ME/CS 132
B. Hapke, Theory of Reflectance and Emittance Spectroscopy, 1993!
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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
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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
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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
: =
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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
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Spectral Reflectance:Short Wave Infrared (SWIR)"
4-Jan-2011 lhm - 38 ME/CS 132
Snow reflectance
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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
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Heat Transfer Characteristics:Thermal Inertia"
4-Jan-2011 lhm - 40 ME/CS 132 (U. Arizona)!
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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? !
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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
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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
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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
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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