Illumination, Radiometry, and a (Very Brief) Introduction...

Illumination, Radiometry,and a (Very Brief) Introduction to the

Physics of Remote Sensing!

Course Philosophy"

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Computer graphics!

Rendering!

Computer vision!

Estimation!

Remote sensing!

Robot vision"

What This Lecture is About"

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•  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"

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•  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"

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Solar Spectrum"

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Total irradiance ~ 1370 W/m2 above atmosphere (solar constant)!

Blackbody Emission: Planckʼs Law"

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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"

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Blackbody Spectrum"

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Stefan-Boltzmann and Wien Laws"

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•  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"

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•  Sunlight!•  Thermal emission!•  Skylight!•  Night sky glow (nightglow)!•  Man-made lights: e.g. incandescent bulbs, fluorescent

bulbs, arc lamps!

Skylight"

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Violet Indigo Blue Green Yellow Orange Red

Night Sky Glow"

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Incandescent Bulb"

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Violet Indigo Blue Green Yellow Orange Red

Tungsten bulb, 2800K!

Daylight model!

Metal Halide and Fluorescent Lights"

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Violet Blue Green Yellow Orange Red

Some Illustrations"

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SWIR nightglow image!(no moon)!

Visible vs. SWIR in haze!

Visible vs. thermal image at night!

Visible vs. thermal in smoke!

Atmospheric Propagation"

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•  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"

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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"

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Angle!

Solid angle!

d! = dl cos"r

d! =dAcos"r2

Radiance and Irradiance"

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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"

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•  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"

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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"

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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"

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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"

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•  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?"

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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?"

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! = 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"

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S. Nayar and M. Oren, “Visual Appearance of Matte Surfaces”, Science, Vol. 267, pp. 1153-1156, 1995!

Rough cylinder! Smooth cylinder!

Other Reflectance Models"

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Pure specular!

Specular lobe!

Varying roughness!

Varying incidence

angle!

Other Reflectance Models"

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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"

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B. Hapke, Theory of Reflectance and Emittance Spectroscopy, 1993!

Color"

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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)"

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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)"

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650nm image 800nm image 650:800 ratio image

Classified image

: =

Spectral Reflectance:Visible and Near Infrared (VNIR)"

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B-R R-IR

G-R-IR B-G-R

Spectral Reflectance:Short Wave Infrared (SWIR)"

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Snow reflectance

Thermal Infrared"

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•  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"

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Open Problem:Terrain Classification for Mars Rovers"

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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"

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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"

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• 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"

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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”"

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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