FUNDAMENTALS OF RADIOMETRY
Transcript of FUNDAMENTALS OF RADIOMETRY
FUNDAMENTALS OF RADIOMETRY Lecture 5
1GNR401 Dr. A. Bhattacharya
Radiometry
Quantitative measurement of the properties of EM radiation interaction with matter or emission from it
Radiometry deals with total EM radiation
We extend the concept of radians in 3d to explain solid angle
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Solid angle
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steradians 4 sphere ,ra angle solid
radians 2 circle ,rl angle
2
3D analogue of 2D angle
: distance aat area ofpatch planar small a of angle Solid.steradians 2 hemisphere ,4Sphere(sr).steradian 1 of angle solid a subtends m 1 2
RdA
d dAcos
R2
R
Radiometry
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ddd sin
Radiometric Quantities :• Radiant Energy Joules• Radiant flux Watts• Irradiance E Watts/m2
• Radiant Intensity I Watts/sr• Radiance L Watts/sr/m2
Q
Radiant Energy
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Quantity of energy carried by the EM radiation
Quantity of energy propagated into/through/emerging from a specified surface (RS) in a given area in a given period of time
All wavelengths contained in the radiation is included
When considered at a particular wavelength Spectral radiant energy
ddQQ
Radiant Flux
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Radiant flux is the rate at which radiant energy is emitted/transferred/received in the form of EM radiation from a point/surface to another
Spectral radiant flux
dtdQ
dd
Irradiance/Radiance
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Irradiance: The measure of radiant flux per unit area
Radiant Intensity Radiant flux leaving a source per unit solid angle in a
given direction
Radiance: Radiant flux per unit solid angle in a given direction per
unit projected source area in that direction
dtdQ
dAd
dAdE
ddI
Radiance
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Foreshortened surface in measuring radiance
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Radiance
cos,,,,,,
2
dadyxdyxL
Radiance is a function of position in a defined surface as well as the direction through the point to the observer (sensor)
Radiance vs. Irradiance
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Radiance and irradiance are very similar concepts, both describe an amount of light transmitted in space but it is important to recognize the distinctions between them. There are several ways of thinking about the difference:
Radiance is a function of direction; it is power per foreshortened surface area per steradian in a specific direction
Irradiance is incident power per surface area (not foreshortened); it is not a directional quantity.
Radiance (Wsr-1m-2) Irradiance (Wm-2)
Radiance describes light emitted from a surface
Irradiance describes light incident on a surface
From the radiance emitted from one surface we can compute the incident irradiance at a nearby surface.
,dLE
Radiometry
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Surface characteristics for radiometric measurements
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Reflection and emission from targets are two important phenomenon used in RS
Smooth surface Snell’s law Specularreflection
Specular reflection does not mean that the amount of reflected flux is independent of the angle of incidence
Surface characteristics for radiometric measurements
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The angular distribution of the reflected ray varies with the surface properties
Lambertian Surface If the emergent radiance is constant for all direction
in a hemispherical solid angle then the surface is said to be Lambertian reflector/emitter
The real surface we encounter is neither a perfect specular nor a perfect Lambertian surface
Surface characteristics for radiometric measurements
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Whether a surface behaves as Lambertian or specular depends on the surface’s unevenness (that is height of variation from reference surface) relative to the wavelength of observation
Rayleigh’s criteria Fraunhofer’s criteria
incidence of Angle h Wavelengt
of unitsin plane reference a aboveiation height var RMS
cos8
h
h
incidence of Angle h Wavelengt
of unitsin plane reference a aboveiation height var RMS
cos32
h
h
Surface characteristics for radiometric measurements
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The radiance in any one direction is, on average, the same as any other; in other words, radiance is constant at any viewing position on the hemisphere and is therefore independent of .
However, the radiant intensity at any position will vary according to the relation .
This states that as the angle of incident radiation Iθ is varied, the intensity of outgoing radiation also changes. For normal incidence (from the zenith), θ is 0 and cosθ is 1, so Iθ = I0. For all other angles cosθ is less than 1 and I0is reduced.
cos0II
Bi-directional Reflectance Distribution (BRDF)
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The reflectance property of a surface can be completely described by a bi-directional reflectance distribution (BRDF).
Reflectance of a target as a function of the illumination geometry and view geometry
BRDF is a mathematical representation of our practical experience that the reflectance from an object is generally different when viewed from different angles and when illuminated from different directions
BRDF
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,
,,
,,
1
srdE
dLf
or
dEfdL
ii
rirri
iiririr
The BRDF is given by rif ,
BRDF essentially transform the incident irradiance into reflected radiance.
BRDF
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r
rri
i
ii
ddL
ddE
angle solid theintodirection in the radiance reflected elemenatl The : ,
angle solid awithin direction thefrom irradiance elemental The :
Since reflection depends on wavelength(omitted) on dependent quantities spectral are and ii dLdE
iii
riri
iiii
dLdLf
dLdE
r
cos,,
cos
Radiometers
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The radiometers gives the radiance values corresponding to a number of broad spectral bands, usually matching the satellite sensors (MSS, TM, IRS-LISS) characteristics
BRDF properties :
00cos,, :onconservatiEnergy
0,
df
f
rii
ri
BRDF Measurement
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An example of field goniometers for BRDF measurements
BRDF Example
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Bidirectional reflectance effect on a grass lawn, observed under different viewing angles from a mounted camera in the solar principal plane. Solar zenith angle is 35°, indicated with red arrows. The view directions are given in blue.