MV4920

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MV-4920 Physical Modeling Remote Sensing Basics
Nomenclature Atmospherics Illumination Surface
physics EO/IR
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Why NOMENCLATURE?
Computer Graphics
Remote Sensing
Photometrics
Radiometrics
THESE FOUR COMMUNITIES DIFFER NOMENCLATURE EQ
UATIONS APPROACH
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Components of the Radiometric Sensing Problem.
Sensor Model
Illumination Model
Atmospheric Propagation Model
Surface Rendering Model
Thermal Load Model
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Radiometric Nomenclature
ance ending implies radiation measurement
quantities
Spectral radiance L (x,y,?,?,?)
watts/cm2 sr ?
Radiance L ?L (x,y,?,?,?) d?
watts/cm2 sr
Irradiance E ? ? ? L (x,y,?,?,?) d? sin(?)
d? d? or Emittance when radiation is from a
surface watts/cm2
Flux(power) ? ? ? ? ? ?L (x,y,?,?,?) sin(?)
d? d? d? dx dy watts
Radiant Intensity I ? ? ? L (x,y,?,?,?) d?
dxdy watts/ sr
Also used alternative definition Radiance N
?N (x,y,?,?,?) d?
watts/cos(? )cm2 sr
Collimated incident flux J ? ? ? N
(x,y,?,?,?) d? sin(?) d? d? watts
/cmp2
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Radiometric Nomenclature
Radiance -L- radiance means watts flowing into a
unit area ( As ) from a solid angle ?i watts/
cms2 sri
Incident spectral radiance Li(x,y,?i,? i,?)
?e Ae /R2
?
Emitted spectral radiance Le(x,y,?e,? e,?)
Alternative definition(causes lots of
confusion) Radiance- N - radiance means watts
flowing into a unit area ( Ap ) perpendicular to
the ray from a solid angle ?i watts/ cmp2 sri
cmp2 cos (?) cms2 and N cos (?) L
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Radiometric Nomenclature
H irradiance the watts flowing into a unit
surface from all angles watts/ cms2 sri
?i
Li
? i
As
1cm
irradiance ?radianced ?
irradiance ?Li(x,y,?i,? i,?) sin(?i) d?id? i
emittance the watts flowing out of a unit
surface from all angles
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Radiometric Nomenclature
I radiant intensity the watts flowing into a
unit solid angle from a point source watts/ sri

Power in (Pin)
1cm
? A /R2
1m
radiant intensity ?radiancedxdy
Point source radiance Li (x,y, ?,?,?) Pin
watts/4?sr ?(x-xi)? (y-yi) radiant intensity
? Pin watts/4?sr ?(x-xi)? (y-yi) dxdy Pin
w/4?sr example Radiant intensity from a 100 watt
bulb on a 1cm radius surface at 1 meter is (100/
4?) ?.012.0025w
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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 ?abs /?in
Add spectral to indicate wavelength
dependence. Spectral reflectivity ?(?) power
reflected/power incident at wavelength ?
No standard but general indicators add
bidirectional And function to indicate
directional dependence.
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Radiometric Nomenclature
SBDRF - Spectral Bidirectional Reflectance
Distribution Function ?(?i,? i?r,?
r,?) sr-1 ratio of the spectral reflected
radiance to the incident flux per unit area
?(?i,? i?r,? r,?) N (xr,yr, ?r,? r,?)/E(xs,ys
?i,? i)
When wavelength independent it is called
BDRF - Bidirectional Reflectance Distribution
Function - ??(?i,? i?r,? r)
Simplistic Interpretation BDRF relates the
power in at one angle to power out at another
Jout watts/cmp
Al
Ai
Jin watts/cmp
E(xs,ys ?i,? i)
As
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Radiometric Nomenclature
But that is too simple
Power out is collected from a detector area Ad
projected through a lens of area Al onto a
surface area As .
Power out (Pout)
?l As AdAl/(f2 cos(?r))
Ad area of detector
?l Solid angle of lens at surface
f focal length
Al area of lens
As
The power leaving the surface at angles to hit
the detector is L (x,y, ?r,? r,) ?l As L
(x,y, ?r,? r,) AdAl/(f2 cos(?r)) N (xp,yp, ?r,?
r,) AdAl/ f2
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Radiometric Nomenclature
Look how BDRF is measured.
Power in (Pin)
Power out (Pout)
Illumination Surface Sensor
Pin ?in cos(?i) ?(?i,? i?r,? r) AdAl/ f2 Pout
?in
Ai
Ar
Jin Pin ?in
As
N (xp,yp, ?r,? r,) ?l Ar
Incident power E(x,y,?i,? i) As Jin cos(?i) Ai
Power leaving the surface in the direction of the
lens L (x,y, ?r,? r,) ?l As
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Lambertian Surface
Most natural surfaces are Lambertian to first
order. How bright a Lambertian surface looks
Does not depend upon the view angles ?r,? r
Depends upon the illumination power Jin and
angles ?i,? i
Ad
?r
?i
I
Jin
Power leaving the surface L (x,y, ?r,? r,)
cos(?r) must decrease as the cos(?r) since As
increases as 1/ cos(?r)
As
The BDRF for a Lambertian surface as ? (?i,?
i?r,? r) ? / ?. ? Ein /Eout the
reflectivity
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Solar Radiation Example
Solar radiance at the top of the atmosphere is
Li (x,y, ?,?,?) Jin watts/cmp2
cos(?)?(?-?i)? (?-?i) Solar irradiance on a
surface x,y is Ein ? ? L (x,y,?,?) sin(?) d?
d? Jin cos(?i) .14 cos(?i) Reflected radiance
from the surface is L (xs,ys, ?r,? r,) (? / ?)
.14 cos(?i) cos(?r) The Emittance from the
surface into the upper hemisphere is Eout ? ?
L (xs,ys, ?r,? r,) sin(?) d? d? ? .14
cos(?i) The power hitting a detector size Ad
through lens Al focal length f assuming the
surface covers the field of view is Pout (? /
?) (Ad Al /(f2 cos(?r))).14 cos(?i) cos(?r)
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Power out (Pout)
Solar Radiation Example
(.0078)(10-2)(3.14)(102) / (.5x 202 ) .12mw
?i 60deg
?r 60deg
Lens radius 10cm focal length 20 cm detector 1 sq
mm 1 km from surface
Ai
Jin .14 watts/cmp
Ar
As
Emittance .049w/ cms2
Irradiance .07
Lambertian surface with reflectivity of
.7 Reflected radiance L at ?r
60deg .0078watts/cms2 sr
Ground area in m (105 /20)2(10-2)/ (.5) 50 m2
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Radiometric Nomenclature vs. Hapke Nomenclature
i , ?i incidence angle e, ?r emission angle ?
, ? i -? r azimuthal angle between the planes
of incidence and emission g phase angle (angle
between incidence and emission angles) 0,? i
incident azimuth angle, set to zero in Hapke
nomenclature
?/?, ? single scattering albedo, Jin,J
irradiance at the upper surface of the medium
source is highly collimated radiation infinite
distance from medium N,I radiance at the
detector I(i,e,g)? ?(?i,? i?r,? r)cos(?i),
r(i,e, ?) reflectance function
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Photometric Units
Photometric units are similar to radiometric
units however the radiation is weighted to match
the human eye using a photometric curve(luminous
efficacy) K(?).
Radiometric Photometric
Flux watts ? K(?) ??
Luminous flux Lumens
K(?) - At a frequency of 540x1012 Hertz is
defined as 1 lm/683watts of radiant power
Irradiance watts/cm2 E K(?) 10-4 E?
Illuminance Lux Lumens/m2
Radiance watts/sr-cm2 L K(?) 10-4 L?
Luminance Lux /sr
Ref //www.schorsch.com/kbase/glossary/index.html
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1Handbook of Military Infrared Technology, W.L
Wolfe ,1965 ONR Dep of Navy Washington p4 2
Ref A Survey of BRDF Representation for Computer
Graphics, Szymon Rusinkiewicz http//www-graphics.
stanford.edu/smr/cs348c/surveypaper.html 3
Hapke, B., (1993). Theory of Reflectance and
Emittance Spectroscopy. Cambridge University
Press, 4 Shepard, M.K., R.E. Arvidson, and
E.A.Guinness (1993) Specular Scattering on a
Terrestrial Playa and Implications for Planetary
Surface Studies. JGR, vol. 98, no. E10, pgs.
18,707 - 18,718. 5Toward A Standard Rendering
Equation For Intrinsic Earth Surface
Classification 00S-SIW-070.doc 6 Toward
Standards for Interoperability and Reuse in IR
Simulation 7R. Driggers, P Cox, T.
Edwards,Introduction to Infrared And
Electro-Optical Systems, Artech House, Inc., 1999
ISBN 0-89006-470-9