Light

Visible electromagnetic radiation Power spectrum

2 4 6 8 10 12 14 16 18 20 22 24 26 11010 10 10 10 10 10 10 10 10 10 10 10

Power Heat Radio Infra- Ultra- X-Rays Gamma Cosmic Red Violet Rays Rays

16 14 12 10 8 6 4 2 -2 -4 -6 -8 10 10 10 10 10 10 10 10 11010 10 10 Wavelength (NM)

IR R G B UV

700600 500 400

Polarization Photon (quantum effects) From London and Upton Wave (interference, diffraction)

CS348B Lecture 4 Pat Hanrahan, 2004

Topics

Light sources and illumination Radiometry and photometry Quantify spatial energy distribution „ Radiant intensity „ Irradiance and radiant exitance (radiosity) „ Inverse square law and cosine law „ Radiance Illumination calculations „ Irradiance from environment

CS348B Lecture 4 Pat Hanrahan, 2004

Page 1 Radiometry and Photometry

Radiant Energy and Power

Power: Watts vs. Lumens Φ „ Energy efficiency „ Spectral efficacy

Energy: Joules vs. Talbot „ Exposure „ Film response „ Skin - sunburn Luminance YVLd= ∫ ()()λ λλ

CS348B Lecture 4 Pat Hanrahan, 2004

Page 2 Radiometry vs. Photometry

Radiometry [Units = Watts] „ Physical measurement of electromagnetic energy Photometry and Colorimetry [Lumen] „ Sensation as a function of wavelength „ Relative perceptual measurement 1 Brightness [Brils] BY= 3 „ Sensation at different brightness levels „ Absolute perceptual measurement „ Obeys Steven’s Power Law

CS348B Lecture 4 Pat Hanrahan, 2004

Blackbody

CS348B Lecture 4 Pat Hanrahan, 2004

Page 3 Tungsten

CS348B Lecture 4 Pat Hanrahan, 2004

Fluorescent

CS348B Lecture 4 Pat Hanrahan, 2004

Page 4 Sunlight

CS348B Lecture 4 Pat Hanrahan, 2004

Radiant Intensity

Page 5 Radiant Intensity

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

dΦ I()ω ≡ dω

Wlm  ==cd candela sr sr 

CS348B Lecture 4 Pat Hanrahan, 2004

Angles and Solid Angles

l „ Angle θ = r

⇒ circle has 2π radians

A „ Solid angle Ω= R2

⇒ sphere has 4π steradians

CS348B Lecture 4 Pat Hanrahan, 2004

Page 6 Differential Solid Angles

rsinθ

dφ r dA= ()(sin) r dθ rθφ d dθ θ = rdd2 sinθθφ

φ dA dddω ==sinθθφ r 2

CS348B Lecture 4 Pat Hanrahan, 2004

Differential Solid Angles

dA dddω ==sinθθφ rsinθ r 2

dφ r Ω=∫ dω dθ 2 θ S ππ2 = ∫∫sinθ ddθφ φ 00 12π = ∫∫ddcosθ φ −10 = 4π

CS348B Lecture 4 Pat Hanrahan, 2004

Page 7 Isotropic Point Source

Φ=∫ I dω S2 = 4π I

Φ I = 4π

CS348B Lecture 4 Pat Hanrahan, 2004

Warn’s Spotlight ω θ Aˆ I()ωθω==• cosss(Aˆ )

21π Φ= ∫∫I()cosω ddθϕ 00

CS348B Lecture 4 Pat Hanrahan, 2004

Page 8 Warn’s Spotlight ω θ Aˆ I()ωθω==• cosss(Aˆ )

21π 1 2π Φ=∫∫Id(ωθϕπθθ ) cos d = 2 ∫ coss d cos = 00 0 s +1 s +1 I()ω =Φ coss θ 2π

CS348B Lecture 4 Pat Hanrahan, 2004

Light Source Goniometric Diagrams

CS348B Lecture 4 Pat Hanrahan, 2004

Page 9 PIXAR Light Source

UberLight( ) { Clip to near/far planes Clip to shape boundary foreach superelliptical blocker Shadows atten *= … foreach cookie texture atten *= … foreach slide texture color *= … foreach noise texture Shadow Matte atten, color *= … foreach shadow map atten, color *= … Calculate intensity fall-off Calculate beam distribution } Projected Slide Texture CS348B Lecture 4 Pat Hanrahan, 2004

Radiance

Page 10 Radiance

Definition: The surface radiance (luminance) is the intensity per unit area leaving a surface Lx(,ω ) dI(, x ω ) Lx(,ω )≡ dA dω dx2Φ(,ω ) = ddAω  Wcdlm   22== 2nit  dA sr m m sr m 

CS348B Lecture 4 Pat Hanrahan, 2004

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

CS348B Lecture 4 Pat Hanrahan, 2004

Page 11 Irradiance

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, 2004

Page 12 Irradiance

Definition: The irradiance (illuminance) is the power per unit area incident on a surface. dΦ Ex()≡ i dA

 Wlm  = lux mm22 

Sometimes referred to as the radiant (luminous) incidence.

CS348B Lecture 4 Pat Hanrahan, 2004

Lambert’s Cosine Law

A

Φ=EA

Φ E = A

CS348B Lecture 4 Pat Hanrahan, 2004

Page 13 Lambert’s Cosine Law

A A /cosθ

Φ

θ

Φ Φ E ==cosθ AA/cosθ

CS348B Lecture 4 Pat Hanrahan, 2004

Irradiance: Isotropic Point Source

Φ I = 4π θ h r

CS348B Lecture 4 Pat Hanrahan, 2004

Page 14 Irradiance: Isotropic Point Source

Φ I = dω 4π θ h r dA

dIdEdAΦ ==ω

CS348B Lecture 4 Pat Hanrahan, 2004

Irradiance: Isotropic Point Source

Φ I = dω 4π θ h r dA

cosθ ddAω = r 2

CS348B Lecture 4 Pat Hanrahan, 2004

Page 15 Irradiance: Isotropic Point Source

Φ I = dω 4π θ h r dA Φ cosθ I ddAω = 4π r 2

CS348B Lecture 4 Pat Hanrahan, 2004

Irradiance: Isotropic Point Source

Φ I = dω 4π θ h r dA Φ cosθ I ddAEdAω == 4π r 2 Φ cosθ E = 2 CS348B Lecture 44π r Pat Hanrahan, 2004

Page 16 Irradiance: Isotropic Point Source

Φ I = dω 4π θ hr= cosθ r dA

ΦΦcosθ cos3 θ E == 44ππrh22

CS348B Lecture 4 Pat Hanrahan, 2004

Directional Power Arriving at a Surface

Lx(,ω ) i dω dA 2 θ dxΦ=ii(,ω ) Lx (,ωθω )cos dAd = Lxi (,ωω ) dAdi dx2Φ (,ω ) i dAi dω = cosθω dAd

CS348B Lecture 4 Pat Hanrahan, 2004

Page 17 Irradiance from the Environment

2 dxΦ=ii(,ω ) Lx (,ωθ )cos dAd ω Lxi (,ω ) dE( x ,ω )= Li ( x ,ωθω )cos d dω θ

dA E()xLxd= (,ω )cosθω Light meter ∫ i H2 CS348B Lecture 4 Pat Hanrahan, 2004

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, 2004

Page 18 The Sky Radiance Distribution

From Greenler, Rainbows, halos and glories

CS348B Lecture 4 Pat Hanrahan, 2004

Gazing Ball ⇒ Environment Maps

Miller and Hoffman, 1984

„ Photograph of mirror ball „ Maps all directions to a to circle „ Reflection indexed by normal „ Resolution function of orientation

CS348B Lecture 4 Pat Hanrahan, 2004

Page 19 Environment Maps

Interface, Chou and Williams (ca. 1985) CS348B Lecture 4 Pat Hanrahan, 2004

Irradiance Environment Maps

L(,θ ϕ ) R E(,θ ϕ ) N

Radiance Irradiance Environment Map Environment Map

CS348B Lecture 4 Pat Hanrahan, 2004

Page 20 Irradiance Map or Light Map

Isolux contours CS348B Lecture 4 Pat Hanrahan, 2004

Radiant Exitance (Radiosity)

Page 21 Radiant Exitance

Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface. dΦ Mx()≡ o dA Wlm  = lux mm22 

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

CS348B Lecture 4 Pat Hanrahan, 2004

Directional Power Leaving a Surface

Lx(,ω ) o dω dA 2 θ dxΦ=oo(,ω ) Lx (,ωθω )cos dAd = Lxo (,ωω ) dAdi

2 dxΦo (,ω )

CS348B Lecture 4 Pat Hanrahan, 2004

Page 22 Uniform Diffuse Emitter

M = Ldcosθ ω ∫ o H2 Lo(,x ω ) = L cosθ dω o ∫ H2 dω

= πLo θ

M L = o π dA

CS348B Lecture 4 Pat Hanrahan, 2004

Projected Solid Angle Ω≡ ∫ cosθ dω Ω dω θ

cosθ dω Ω= ∫ cosθ dωπ = 2 CS348B Lecture 4H Pat Hanrahan, 2004

Page 23 Radiometry and Photometry Summary

Radiometric and Photometric Terms

Physics Radiometry Photometry

Energy Radiant Energy Luminous Energy

Flux (Power) Radiant Power Luminous Power

Flux Density Irradiance Illuminance

Radiosity Luminosity

Angular Flux Density Radiance Luminance

Intensity Radiant Intensity Luminous Intensity

CS348B Lecture 4 Pat Hanrahan, 2004

Page 24 Photometric Units

Photometry Units

MKS CGS British Luminous Energy Talbot

Luminous Power Lumen

Illuminance Lux Phot Footcandle Luminosity Luminance Nit Stilb Apostilb, Blondel 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?”, James Kajiya

CS348B Lecture 4 Pat Hanrahan, 2004

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