GNR401 Dr. A. Bhattacharya 1

FUNDAMENTALS OF RADIOMETRY

Lecture 5 Radiometry

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 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

GNR401 Dr. A. Bhattacharya Solid angle

3 3D analogue of 2D angle

l angle   , circle  2 radians r a solid angle   , sphere  4 steradians R r 2  dAcos d  R2 1 m2 subtends a solid angle of 1 steradian (sr). Sphere  4 , hemisphere  2 steradians. Solid angle of a small planar patch of area dA at a distance R :

GNR401 Dr. A. Bhattacharya Radiometry

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Radiometric Quantities : • Radiant Energy Q Joules • Radiant flux  Watts d  sindd • Irradiance E Watts/m2 • Radiant Intensity I Watts/sr • Radiance L Watts/sr/m2

GNR401 Dr. A. Bhattacharya 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 dQ Q   d GNR401 Dr. A. Bhattacharya 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

dQ   dt

 Spectral radiant flux

d    d

GNR401 Dr. A. Bhattacharya Irradiance/Radiance

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 Irradiance:  The measure of radiant flux per unit area d d  dQ  E     dA dA  dt   Radiant Intensity  Radiant flux leaving a source per unit solid angle in a given direction d I  d  Radiance:  Radiant flux per unit solid angle in a given direction per unit projected source area in that direction

GNR401 Dr. A. Bhattacharya Radiance

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 Foreshortened surface in measuring radiance

GNR401 Dr. A. Bhattacharya Radiance

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d 2x, y,, Lx, y,,  dda cos

Radiance is a function of position in a defined surface as well as the direction through the point to the observer (sensor)

GNR401 Dr. A. Bhattacharya E   dL, 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 Irradiance is incident power per surface power per foreshortened surface area per area (not foreshortened); it is not a steradian in a specific direction directional quantity. Radiance (Wsr-1m-2) Irradiance (Wm-2) Radiance describes light emitted from a Irradiance describes light incident on a surface surface From the radiance emitted from one surface we can compute the incident irradiance at a nearby surface.

GNR401 Dr. A. Bhattacharya Radiometry

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GNR401 Dr. A. Bhattacharya Surface characteristics for radiometric measurements 12

 Reflection and emission from targets are two important phenomenon used in RS

 Smooth surface  Snell’s law  Specular reflection

 Specular reflection does not mean that the amount of reflected flux is independent of the angle of incidence

GNR401 Dr. A. Bhattacharya Surface characteristics for radiometric measurements 13

 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

GNR401 Dr. A. Bhattacharya Surface characteristics for radiometric measurements 14

 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

  h  h  8cos 32cos

h  RMS height variation above a reference plane in units of  h  RMS height variation above a reference plane in units of    Wavelength   Wavelength   Angle of incidence   Angle of incidence

GNR401 Dr. A. Bhattacharya Surface characteristics for radiometric measurements 15

 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 I  I0 cos .

 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 I0 is reduced.

GNR401 Dr. A. Bhattacharya Bi-directional Reflectance Distribution (BRDF) 16

 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

GNR401 Dr. A. Bhattacharya BRDF

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The BRDF f   i ,  r  is given by

dLr i ,r   f i ,r dEi i 

or

dLr i ,r  1 f i ,r   sr dEi i    ,

BRDF essentially transform the incident irradiance into reflected radiance.

GNR401 Dr. A. Bhattacharya BRDF

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dEi  : The elemental irradiance from the direction i

within a solid angle di

dLi ,r  : The elemenatl reflected radiance in the direction r

into the solid angle dr

Since reflection depends on wavelength

dEi and dLi are spectral quantities dependent on  (omitted)

dEi  Li cosi di dL  ,  f  ,  r i r i r Li cosidi GNR401 Dr. A. Bhattacharya 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 :

f i ,r   0

Energy conservation :  , f  , cos d i   i r  0 0 

GNR401 Dr. A. Bhattacharya BRDF Measurement

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An example of field goniometers for BRDF measurements

GNR401 Dr. A. Bhattacharya 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. GNR401 Dr. A. Bhattacharya