CS348B Lecture 4 Pat Hanrahan, 2005

Light

Visible electromagnetic radiation

Power spectrum

Polarization

Photon (quantum effects)

Wave (interference, diffraction)

1 102 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024 1026

1016 1014 1012 1010 108 106 104 102 1 10-2 10-4 10-6 10-8

CosmicRays

GammaRays

X-RaysUltra-Violet

Infra-Red

RadioHeatPower

700 400600 500

IR R G B UV

Frequency (Hertz)

Wavelength (NM)

From London and Upton

CS348B Lecture 4 Pat Hanrahan, 2005

Topics

Light sources and illumination

Radiometry and photometry

Quantify spatial energy distribution

Radiant intensity

Irradiance Inverse square law and cosine law

Radiance

Radiant exitance (radiosity)

Illumination calculations

Irradiance from environment

Radiometry and Photometry

CS348B Lecture 4 Pat Hanrahan, 2005

Radiant Energy and Power

Power: Watts vs. Lumens

Energy efficiency

Spectral efficacy

Energy: Joules vs. Talbot

Exposure Film response

Skin - sunburn

( ) ( )Y V L d Luminance

CS348B Lecture 4 Pat Hanrahan, 2005

Radiometry vs. Photometry

Radiometry [Units = Watts]

Physical measurement of electromagnetic energy

Photometry and Colorimetry [Lumen]

Sensation as a function of wavelength

Relative perceptual measurement

Brightness [Brils]

Sensation at different brightness levels

Absolute perceptual measurement

Obeys Steven’s Power Law

13B Y

CS348B Lecture 4 Pat Hanrahan, 2005

Blackbody Radiation

CS348B Lecture 4 Pat Hanrahan, 2005

Tungsten Lamp

CS348B Lecture 4 Pat Hanrahan, 2005

Fluorescent Bulb

CS348B Lecture 4 Pat Hanrahan, 2005

Sunlight

Radiant Intensity

CS348B Lecture 4 Pat Hanrahan, 2005

Radiant Intensity

Definition: The radiant (luminous) intensity is the

power per unit solid angle emanating from

a point source.

( )d

Id

W lmcd candela

sr sr

CS348B Lecture 4 Pat Hanrahan, 2005

Angles and Solid Angles

Angle

Solid angle

l

r

2

A

R

circle has 2 radians

sphere has 4 steradians

CS348B Lecture 4 Pat Hanrahan, 2005

Differential Solid Angles

dd

r

sinr

2

( )( sin )

sin

dA r d r d

r d d

2sin

dAd d d

r

CS348B Lecture 4 Pat Hanrahan, 2005

Differential Solid Angles

dd

r

sinr 2sin

dAd d d

r

2

2

0 0

1 2

1 0

sin

cos

4

S

d

d d

d d

CS348B Lecture 4 Pat Hanrahan, 2005

Isotropic Point Source

2

4S

I d

I

4I

CS348B Lecture 4 Pat Hanrahan, 2005

Warn’s Spotlight

ˆ( ) cos )s sI ( A

2 1

0 0

( ) cosI d d

A

CS348B Lecture 4 Pat Hanrahan, 2005

Warn’s Spotlight

ˆ( ) cos )s sI ( A

2 1 1

0 0 0

2( ) cos 2 cos cos

1sI d d d

s

1( ) cos

2ss

I

A

CS348B Lecture 4 Pat Hanrahan, 2005

Light Source Goniometric Diagrams

CS348B Lecture 4 Pat Hanrahan, 2005

PIXAR Light Source

UberLight( ){ Clip to near/far planes Clip to shape boundary foreach superelliptical blocker atten *= … foreach cookie texture atten *= … foreach slide texture color *= … foreach noise texture atten, color *= … foreach shadow map atten, color *= … Calculate intensity fall-off Calculate beam distribution}

Shadows

Shadow Matte

Projected Slide Texture

Radiance

CS348B Lecture 4 Pat Hanrahan, 2005

Definition: The surface radiance (luminance) is

the intensity per unit area leaving a surface

Radiance

2

( , )( , )

( , )

dI xL x

dA

d x

d dA

2 2 2

W cd lmnit

sr m m sr mdA

d

( , )L x

CS348B Lecture 4 Pat Hanrahan, 2005

Typical Values of Luminance [cd/m2]

Surface of the sun2,000,000,000 nit

Sunlight clouds 30,000

Clear day 3,000

Overcast day 300

Moon 0.03

Irradiance

CS348B Lecture 4 Pat Hanrahan, 2005

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 candela Originally a “standard”

candle Currently 550 nm laser w/

1/683 W/sr 1 of 6 fundamental SI units

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance

Definition: The irradiance (illuminance) is the

power per unit area incident on a surface.

Sometimes referred to as the radiant (luminous)

incidence.

( ) id

E xdA

2 2

W lmlux

m m

CS348B Lecture 4 Pat Hanrahan, 2005

Lambert’s Cosine Law

EA

EA

A

CS348B Lecture 4 Pat Hanrahan, 2005

Lambert’s Cosine Law

/ cosA

cos/ cos

EA A

A

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance: Isotropic Point Source

h

r

4I

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance: Isotropic Point Source

r

4I

d

dA

h

d I d

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance: Isotropic Point Source

r

4I

2

cosd dA

r

d

dA

h

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance: Isotropic Point Source

r

4I

d

dA

2

cos

4I d dA

r

h

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance: Isotropic Point Source

r

4I

d

dA

2

cos

4I d dA E dA

r

2

cos

4E

r

h

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance: Isotropic Point Source

r

4I

d

dA

3

2 2

cos cos

4 4E

r h

cosh r

CS348B Lecture 4 Pat Hanrahan, 2005

Directional Power Arriving at a Surface

2 ( , ) ( , )cosi id x L x dAd

( , )iL x

dA d

cos dAd dA d

2 ( , )id x

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance from the Environment

2

( ) ( , )cosi

H

E x L x d

2 ( , ) ( , )cosi id x L x dA d dEdA

( , ) ( , )cosidE x L x d

Light meter

( , )iL x

dA

d

CS348B Lecture 4 Pat Hanrahan, 2005

Typical Values of Illuminance [lm/m2]

Sunlight plus skylight 100,000 lux

Sunlight plus skylight (overcast) 10,000

Interior near window (daylight) 1,000

Artificial light (minimum) 100

Moonlight (full) 0.02

Starlight 0.0003

CS348B Lecture 4 Pat Hanrahan, 2005

The Sky Radiance Distribution

From Greenler, Rainbows, halos and glories

CS348B Lecture 4 Pat Hanrahan, 2005

Gazing Ball Environment Maps

Miller and Hoffman, 1984

Photograph of mirror ball Maps all spherical directions to a to

circle Reflection direction indexed by normal Resolution function of orientation

CS348B Lecture 4 Pat Hanrahan, 2005

Environment Maps

Interface, Chou and Williams (ca. 1985)

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance Environment Maps

Radiance Environment Map

Irradiance Environment Map

R N( , )L ( , )E

CS348B Lecture 4 Pat Hanrahan, 2005

Irradiance Map or Light Map

Isolux contours

Radiant Exitance(Radiosity)

CS348B Lecture 4 Pat Hanrahan, 2005

Radiant Exitance

Definition: The radiant (luminous) exitance is the

energy per unit area leaving a surface.

In computer graphics, this quantity is often

referred to as the radiosity (B)

( ) odM x

dA

2 2

W lmlux

m m

CS348B Lecture 4 Pat Hanrahan, 2005

Directional Power Leaving a Surface

2 ( , ) ( , )coso od x L x dAd

dA d

( , )oL x

2 ( , )od x

CS348B Lecture 4 Pat Hanrahan, 2005

Uniform Diffuse Emitter

( , )oL x

dA

d

2

2

cos

cos

o

H

o

H

M L d

L d

CS348B Lecture 4 Pat Hanrahan, 2005

Projected Solid Angle

cos d

2

cosH

d

d cos d

CS348B Lecture 4 Pat Hanrahan, 2005

Uniform Diffuse Emitter

( , )oL x

dA

d

2

2

cos

cos

o

H

o

H

o

M L d

L d

L

oM

L

Radiometry and PhotometrySummary

CS348B Lecture 4 Pat Hanrahan, 2005

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 4 Pat Hanrahan, 2005

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 IntensityCandela (Candle, Candlepower, Carcel, Hefner)

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