Light - Computer GraphicsSunlight plus skylight 100,000 lux ... Interior near window (daylight)...

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

Wavelength (NM)

From London and Upton


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


Radiant Energy and Power

Power: Watts vs. Lumens

Energy efficiency

Spectral efficacy

Energy: Joules vs. Talbot

ExposureFilm response

Skin - sunburn

( ) ( )Y V L dλ λ λ= ∫Luminance

Φ


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=


Blackbody Radiation


Tungsten Lamp


Fluorescent Bulb


Sunlight

Radiant Intensity


Radiant Intensity

Definition: The radiant (luminous) intensity is the

power per unit solid angle emanating from

a point source.

( )d

Id

ωωΦ

≡

W lmcd candela

sr sr = =


Angles and Solid Angles

Angle

Solid angle

l

rθ =

2

A

RΩ =

⇒ circle has 2π radians

⇒ sphere has 4π steradians


Differential Solid Angles

dφdθ

θ

φ

r

sinr θ

2

( )( sin )

sin

dA r d r d

r d d

θ θ φθ θ φ

=

=

2sin

dAd d d

rω θ θ φ= =


Differential Solid Angles

dφdθ

θ

φ

r

sinr θ 2sin

dAd d d

rω θ θ φ= =

2

2

0 0

1 2

1 0

sin

cos

4

S

d

d d

d d

π π

π

ω

θ θ φ

θ φ

π−

Ω =

=

=

=

∫

∫ ∫

∫ ∫


Isotropic Point Source

2

4S

I d

I

ω

π

Φ =

=

∫

4I

πΦ

=


Warn’s Spotlight

ω θ ω= = • ˆ( ) cos )s sI ( A

2 1

0 0

( ) cosI d dπ

ω θ ϕΦ = ∫ ∫

θ A

ω


Warn’s Spotlight

ω θ ω= = • ˆ( ) cos )s sI ( A

2 1 1

0 0 0

2( ) cos 2 cos cos

1sI d d d

s

π πω θ ϕ π θ θΦ = = =+∫ ∫ ∫

1( ) cos

2ss

I ω θπ+

= Φ

θ A

ω


Light Source Goniometric Diagrams


PIXAR Light Source

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

Shadows

Shadow Matte

Projected Slide Texture

Radiance


Definition: The surface radiance (luminance) is

the intensity per unit area leaving a surface

Radiance

ωω

ωω

≡

Φ=

2

( , )( , )

( , )

dI xL x

dA

d x

d dA

= =

2 2 2

W cd lmnit

sr m m sr mdA

dω

( , )L x ω


Typical Values of Luminance [cd/m2]

Surface of the sun 2,000,000,000 nit

Sunlight clouds 30,000

Clear day 3,000

Overcast day 300

Moon 0.03

Irradiance


The Invention of Photometry

Bouguer’s classic experimentCompare a light source and a candleIntensity is proportional to ratio of distances squared

Definition of a candelaOriginally a “standard”candleCurrently 550 nm laser w/ 1/683 W/sr1 of 6 fundamental SI units


Irradiance

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

Sometimes referred to as the radiant (luminous) incidence.

Φ≡( ) id

E xdA

2 2

W lmlux

m m =


Lambert’s Cosine Law

EAΦ =

EA

Φ=

A


Lambert’s Cosine Law

θ/ cosA

θ

Φ

cos/ cos

EA A

θθ

Φ Φ= =

A


Irradiance: Isotropic Point Source

θ h

r

4I

πΦ

=



θ

r

4I

πΦ

=dω

dA

h

ωΦ =d I d



θ

r

4I

πΦ

=

2

cosd dA

r

θω =

dω

dA

h



θ

r

4I

πΦ

=dω

dA

2

cos

4I d dA

r

θωπ

Φ=

h



θ

r

4I

πΦ

=dω

dA

2

cos

4I d dA E dA

r

θωπ

Φ= =

2

cos

4E

r

θπ

Φ=

h



θ

r

4I

πΦ

=dω

dA

3

2 2

cos cos

4 4E

r h

θ θπ π

Φ Φ= =

cosh r θ=


Directional Power Arriving at a Surface

ω ω θ ωΦ =2 ( , ) ( , )cosi id x L x dAd

ω( , )iL x

dAdω

θ

θ ω ω= icos dAd dA d2 ( , )id x ωΦ


Irradiance from the Environment

2

( ) ( , )cosi

H

E x L x dω θ ω= ∫

ω ω θ ωΦ = =2 ( , ) ( , )cosi id x L x dAd dEdA

( , ) ( , )cosidE x L x dω ω θ ω=

Light meter

ω( , )iL x

dA

θdω


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


The Sky Radiance Distribution

From Greenler, Rainbows, halos and glories


Gazing Ball ⇒ Environment Maps

Miller and Hoffman, 1984

Photograph of mirror ballMaps all spherical directions to a to circleReflection direction indexed by normalResolution function of orientation


Environment Maps

Interface, Chou and Williams (ca. 1985)


Irradiance Environment Maps

Radiance Environment Map

Irradiance Environment Map

R N( , )L θ ϕ ( , )E θ ϕ


Irradiance Map or Light Map

Isolux contours

Radiant Exitance(Radiosity)


Radiant Exitance

Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface.

In computer graphics, this quantity is oftenreferred to as the radiosity (B)

( ) odM x

dA

Φ≡

2 2

W lmlux

m m =


Directional Power Leaving a Surface

ω ω θ ωΦ =2 ( , ) ( , )coso od x L x dAd

dAdω

θ

( , )oL x ω

2 ( , )od x ωΦ


Uniform Diffuse Emitter

ω( , )oL x

dA

θdω

θ ω

θ ω

=

=

∫

∫2

2

cos

cos

o

H

o

H

M L d

L d


Projected Solid Angle

cos dθ ω

θ

θ ω πΩ = =∫2

cosH

d

dωcos dθ ω

Ω

Ω ≡ ∫


Uniform Diffuse Emitter

ω( , )oL x

dA

θdω

θ ω

θ ω

π

=

=

=

∫

∫2

2

cos

cos

o

H

o

H

o

M L d

L d

L

π=o

ML

Radiometry and PhotometrySummary


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


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 persteradian. Got it?”, James Kajiya

Light - Computer GraphicsSunlight plus skylight 100,000 lux ... Interior near window (daylight)...

Documents

Transcript of Light - Computer GraphicsSunlight plus skylight 100,000 lux ... Interior near window (daylight)...