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

2

GNR401 Dr. A. Bhattacharya

Solid angle


3

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


4

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


5

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


6

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


7

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


8

Foreshortened surface in measuring radiance


9

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


10

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


11

Surface characteristics for radiometric measurements


12

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



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



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

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



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 .

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)


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

BRDF


17

,

,,

,,

1

srdE

dLf

or

dEfdL

ii

rirri

iiririr

The BRDF is given by rif ,

BRDF essentially transform the incident irradiance into reflected radiance.

BRDF


18

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


19

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


20

An example of field goniometers for BRDF measurements

BRDF Example


21

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.

fundamentals of radiometry

Documents