Chapter 2. Production and measurement of light

Chapter 2. Production and measurement of light

• Radiometry : measurement of EM radiation• Photometry : psycho-physical (human response) measurement of radiation• Blackbody radiation• Sources of optical radiation• Light Detectors

Radiometric and Photometric Definitions and Units

Radiometric and Photometric Definitions and Units

Solid Angle : steradianSolid Angle : steradian

Fundamentals of Heat and Mass Transfer, F. P. Incropera and D. P. DeWitt

2ndAd sr

rω =

Radiant Intensity : Ie (W/sr)Radiant Intensity : Ie (W/sr)

Assume a point source emits radiation uniformly in all directions (solid angles) at the rate of radiant flux Φe (W). The radiant intensity at every position surrounding the point source will be

4e e

eWIsrω π

Φ Φ= =

Irradiance : Ee (W/m2)Irradiance : Ee (W/m2)

For a sphere of radius r surrounding the point source, the irradiance Ee (W/m2) at each point on the surface will be given by

2 2 24e e

eI WE

r r mπΦ

= =

r

Radiance : Le (W/sr-m2)Radiance : Le (W/sr-m2)The radiance Le is defined per unit solid angle and per unit projected area(in most radiation heat transfer texts, this is termed the intensity). Consider the differential area element dA as a source of radiation. The radiant flux that passes through the small area element on the surface of the sphere is proportional to differential solid angle dω of the area element on the sphere, and the projected differential area of the source dAp = dAcosθ as seen from the sphere area element. The radiance Le is given by

Thermal Radiation Heat Transfer, R. Siegel and J. R. Howell

Le2

2

cos

ee

p

e

dLd dA

dd dA

ω

ω θ

Φ=

Φ=

Radiance of Lambertian surface Radiance of Lambertian surface The radiance Le is a constant, independent of direction, for a blackbody source area element, or, a Lambertian surface (it radiates uniformly in all direction).

( )eL θ

( ) ( )0 cose eI Iθ θ=

Radiant intensity decreases as θ increases.

Lambert’s cosine law

( ) ( ) (0)cos (0) constantcos coseI I IL

A A Aθ θθθ θ

= = = =

Invariance of radianceInvariance of radiance

Radiance Le is constant at any point along a ray propagating in a uniform, lossless medium.

2 21 1

11 1 1 2 2 12 1 1( cos ) ( cos / )( cos )

d dLd dA dA r dAω θ θ θ

Φ Φ= =

1dω

The radiance at dA1 :

2 22 2

22 2 2 1 1 12 2 2( cos ) ( cos / )( cos )

d dLd dA dA r dAω θ θ θ

Φ Φ= =The radiance at dA2 :

Therefore, L1 = L2 , since the power remains constant.

Photometric Units Photometric Units 555 nm Radiant flux

of 1 Watt at 555 nmis

the luminous fluxof 685 lm (lumen)

Radiant flux of 1 Watt at 610 nm

is the luminous flux

of 342.5 lm (lumen)

Photometric unit=

685 x V(λ) x radiometric unit

Photometric Units Photometric Units

( )

2

photometric unit 685 radiometric unit

lumens (lm) = Watts ; lux (lx) = ; candela (cd) =

VW Wm sr

λ= ×

Blackbody Exitance (W/m2) Blackbody Exitance (W/m2)

4 : Stefan-Boltzman lawbbM Tσ=

Wien displacement law

Planck’s blackbody radiation

Color temperature of light source ?

: the blackbody temperature with the closest spectral energy distribution

-> the sun has a color temperature rangeof 5000 K ~ 6000 K

Light Sources: Xenon Arc Lamp Light Sources: Xenon Arc Lamp

Light Sources: Xenon Arc Lamp Light Sources: Xenon Arc Lamp

Light Sources: Hg-Xe Arc Lamp Light Sources: Hg-Xe Arc Lamp

Light Sources: Deuterium Arc Lamp Light Sources: Deuterium Arc Lamp