Page 1

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Light Sources and Illumination

Properties of light sources� Power Spectrum� Radiant and luminous intensity� Directional distribution – goniometric diagram� Shape

Illumination� Irradiance and illuminance� Area light sources

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Blackbody

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Tungsten

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Flourescent

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Sunlight

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Radiant and Luminous Intensity

Definition: The radiant (luminous) intensity is the power per unit solid angle from a point.

( ) dId

ωωΦ≡

W lm cd candelasr sr

= =

2

( )S

I dω ωΦ = ∫

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

The Invention of Photometry

Bouguer’s classic experiment� Compare a light source and a candle� Intensity is proportional to ratio of

distances squared

Definition of a standard candle� Originally “standard” candle� Currently 550 nm laser w/ 1/683 W/sr� 1 of 6 fundamental SI units

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Goniometric Diagrams

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Warn’s Spotlight

ˆ ˆ( ) cos )s sI ω θ= = •(S A

12coscos2cos)(

1

0

2

0

1

0 +===Φ ∫∫ ∫ s

dddI s πθθπϕθωπ

θπ

ω ssI cos2

1)( +Φ=

θ A

S

CS348B Lecture 5 Pat Hanrahan, Spring 2001

PIXAR Standard Light Source

Ronen Barzel UberLight( ){

Clip to near/far planesClip to shape boundaryforeach superelliptical blocker

atten *= …foreach cookie texture

atten *= …foreach slide texture

color *= …foreach noise texture

atten, color *= …foreach shadow map

atten, color *= …Calculate intensity fall-offCalculate beam distribution

}

Inconsistent Shadows

Projected Shadow Matte

Projected Texture

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Irradiance and Illuminance

Definition: The irradiance (illuminance) is the power per unit area incident on a surface.

This is sometimes referred to as the radiant and luminous incidence.

2

( ) ( , ) cosi i iH

E x L x dω θ ω= ∫

)( iL ω

iθ

2

( ) ( , ) cosi i iddE x L x ddA

ω θ ωΦ≡ =

2 2

W lm luxm m

=

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Isotropic Point Sources

� Note inverse square law fall off.� Note cosine dependency

πω

4)( Φ=I

dAh

dAr

dIdAEd 2

3

2

cos4

cos4

θπ

θπ

ω Φ=Φ===Φ

θ hr

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Distant or Directional Source

2

( ) cos cosH

E L d dω θ θ ϕ= ∫

)()cos(cos),( sssEL ϕϕδθθδϕθ −−=

2

2

( , ) cos cos

(cos cos ) ( ) cos cos

cos

H

s s sH

s s

L d d

E d d

E

θ ϕ θ θ ϕ

δ θ θ δ ϕ ϕ θ θ ϕ

θ

= − −

=

∫

∫

sθsE

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Irradiance Distribution

Isolux contours

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Irradiance from Area Sources

2

cosΗ

dθ ω π=∫

2 2

( ) ( , ) cos cosi i i i iH H

E x L x d L dω θ ω θ ω= =∫ ∫

Projected Solid Angle

Radiosity formulation = Differential Form Factor

Note: Things are considerably complicated by shadows

iθ

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Luminance of Common Light Sources

Surface of the sun 2,000,000,000. cd/m2

Sunlight clouds 30,000.Clear day 3,000.Overcast day 300.Moonlight 0.03Moonless 0.00003

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

The Sky

From Greenler, Rainbows, halos and glories

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Disk Source

r

R θ

cos 2

1 0cos2

12

2

2 2

cos cos

cos22

sin

d

d

d

E L d d

L

LrL

r R

θ π

θ

θ φ θ

θπ

π θ

π

=

=

=

=+

∫ ∫

Geometric Derivation Algebraic Derivation

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Spherical Source

2

2

2sin

cos

RrL

L

dLE

π

θπ

ωθ

=

=

= ∫rR

θ

Geometric Derivation Algebraic Derivation

CS348B Lecture 5 Pat Hanrahan, Spring 2001

The Sun

Solar constant (normal incidence at zenith)Irradiance 1353 W/m2

Illuminance 127,500 Lumen/m2 = 127.5 Kilo-LuxSolar angle

αααα = .25 degrees = .004 radians (half angle)ωωωω = ππππ sin2 αααα = 6 x 10-5 steradians

Radiance

Pluto (6 tera-meters) 50 Lux - read a newspaperDeep space -> 20 micro-lux (see, but not read!)

srmsrmWEL

⋅×=

××== − 2

75

23 W1025.2106

/10353.1ω

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Polygonal Source

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Lambert’s Formula

1 1

n n

i i ii iA γ

= =

= •∑ ∑ N N� �

iiiA NN��

•=γ

iN�

iγ∑

=

3

1iiA

1A

2A−

3A−

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Radiosity and Luminosity

Definition: The radiosity (luminosity) is the energy per unit area leaving a surface.

This is officially referred to as the radiant and luminousexitance.

∫=2

cos)()(H

ooo dLxB ωθωoθ

)( oL ω

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Uniform Diffuse Source

2 31 / ( 10 )foot lamberts cd ft glim foot lambertπ−− = = −

21 /lamberts cd cmπ=

2 31 1 / ( 10 )blondel apostilb nit cd m skot apostilbπ π−= = = =

cos

cos

B L d

L d

L

θ ω

θ ω

π

=

=

=

∫

∫ πBL =

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CS348B Lecture 5 Pat Hanrahan, Spring 2001

Radiometric and Photometric Terms

Physics Radiometry Photometry

Energy Radiant Energy Luminous Energy

Flux (Power) Radiant Power Luminous Power

Flux Density Irradiance

Radiosity

Illuminance

Luminosity

Angular Flux Density Radiance Luminance

Intensity Radiant Intensity Luminous Intensity

CS348B Lecture 5 Pat Hanrahan, Spring 2001

Photometric Units

Photometry Units

MKS CGS British

Luminous Energy Talbot

Luminous Power Lumen

Illuminance

Luminosity

Lux Phot Footcandle

Luminance Nit

Apostilb, Blondel

Stilb

Lambert Footlambert

Luminous Intensity Candela (Candle, Candlepower, Carcel, Hefner)

“Thus one nit is one lux per steradian is one candela per square meter is one lumen per square meter per steradian. Got it?” Kajiya