MV4920

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MV-4920 Physical Modeling Remote Sensing Basics
Nomenclature Atmospherics Illumination Surface
physics EO/IR
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Radiometric Nomenclature
ivity ending implies intrinsic surface
measurement quantities absorbtivity ? power
absorbed / power incident ?abs
/?in reflectivity ? power reflected/power
incident ?ref /?in transmissivity ? power
transmitted/power incident ?trans
/?in emissivity ? power emitted/power emitted
from a blackbody ?bb /?in
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Intrinsic Surface Reflectivity Is Characterized
by BDRF
Light source
Sensor

Power into the surface Jin cos(?i ) watts/cm2
Ein(xs,ys ?i,? i)
Radiance Reflected from a surface.
Measured perpendicular to the direction of
travel N watts cm-2cos-1(?r)
As
Ein( xs,ys ?i,? i) ?(?i,? i?r,? r,?) N (xr,yr,
?r,? r,?)
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BDRF MODELS
BDRF of a Lambertian Surface ?
?o / ?
BDRF of a specular surface is ? R(?I)
?(?-?I ? )? (?-?i) cos(?r) sin(?r)
where R(?I) is the Fresnel reflectance R(?I)
½ sin2(?i - ?t) / sin2(?i ?t) tan2(?i -
?t) / tan2(?i ?t) where ?t the transmitted
ray angle n sin(?i)/sin(?I) n the index of
refraction of the media
All Surfaces can be considered as something
between Lambertian and Specular, hence, two
extremes form the first order starting points for
all approximations.
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?i
?r
Pure spectral
Increasing roughness
Pure Lambertian
Foreward Scatterer
Backward Scatterer
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Term Incident Surface Description Light
Lambertian directional flat surface
mat finish Specular, directional gloss
surface, mirror Foreward Scattering Opposition
effect, directional rough surface,
shadowing Back scattering Ambient-
diffuse any surface, all angles in all
angles out approx.
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Minneart BDRF ? (?o / ? ) cos(?r) cos(?i)
k-1 Where k empirically derived limb
darkening parameter ?o empirically
derived reflectivity Originally derived to
characterize the reflectance of the lunar
disk. Extension of Lambertian surface As kgt1 the
limb darkens Used for Topographic Normalization
to correct remote sensing reflectance . Does not
handle forward or back scattering.
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Microfacet Emperical models Basic correction to
spectral reflection BDRF is incorporated in two
factors D an G such that ? D G ?(?,
?i) Where ?(?, ?i) is the spectral reflection
of an optically smooth surface. D is the
fractional surface area oriented at an angle a to
the surface normal N G is the self shadowing
factor
V
N
H
L
a
shadow
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Examples of BDRF Models
B(b(a, f, g)) P(a ,f) D
Description d(b) exp(-(4phcos(?i)/l)2
Davies h average height (4m2cos4(a))1
exp(-tan2(a)/m2) Beckman m rms slope
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Geometric Definitions
N
H
f
g
a
b
LV
V
L
The sum of unit vectors LV bisects the plane
made by L and V. LV makes an angle b with the
facet normal H and g with the surface normal N. N
and H make an angle a. The angle f is the azimuth
angle about the surface normal.
Cos(a) N H Cos(b) H (LV) /LV Cos(g)
N (LV) /LV Cos(b) -cos(a)cos(g)
sin(a)sin(g)cos(f)
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Calculating D G ?(?, ?i)
H
N
Assume each facet acts like a smooth finished
surface whose reflection function is symmetric
about H. Then ?(?, ?i) gt ?0 B(b ) equal the
fraction of the total reflected energy the facet
reflects in the V direction. Let P(a,f) equal
the probability of the facets that make and angle
alpha and phi with the surface normal so that it
contributes B(b) to the energy at the sensor.
g
f
a
LV
b
The fraction of energy contributed by the facet
is then, DG?(?, ?i) ?a ?f G(a, f)?0B(b(a,
f, g)) P(a ,f) cos(a )dfda
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Calculating the Shadow effect G
?i
?r
Shadowing depends strongly on the relative
geometry of the surface. The two most critical
parameters are the standard deviation of height
?h and vertical spacing ?v . We also use the
slope m ?h /?v .
?v
?h
Illuminated Visible Both
The Probability that a particular facet will be
illuminated is Pi cosm(?i)
The probability that a particular facet will be
visible is Pv cosm(?v)
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Calculating the Shadow effect G
?i
?r
The length l of the overlap between illuminated
and visible portions is l R (cos(?i)
cos(?v)) The fraction of the whole is (?v - R
(cos(?i) cos(?v))) / ?v
?v
?h
Illuminated Visible Both
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Calculating the Shadow effect G
?i
?r
?v
?h
When the view and illumination angle are from the
same direction these probabilities are in phase
so we add a phase factor (1-cos(fi- fv))/2
The probability that a particular facet is both
illuminated and visible is Pi Pv cosm(?i)
cosm(?v)
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References Alan Watt, Mark Watt , Advanced
Animation and Rendering Techniques, Addison
Wesley, ISBN 0-201-54412-1, Chap. 2 The theory
and practice of light/object interaction