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
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 1 Tungsten
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Flourescent
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Page 2 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. dΦ I()ω ≡ dω Φ=∫ Id()ωω S 2
Wlm ==cd candela sr sr
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 3 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
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 4 Warn’s Spotlight
Sˆ θ Aˆ I ()ωθ==• coss (Sˆˆ A )s
2π 1 1 2π Φ = I(ω) d cosθ dϕ = 2π coss θ d cosθ = ∫∫ ∫ + 0 0 0 s 1 s +1 I(ω) = Φ coss θ 2π
CS348B Lecture 5 Pat Hanrahan, Spring 2001
PIXAR Standard Light Source
Ronen Barzel UberLight( ) { Clip to near/far planes Clip to shape boundary foreach superelliptical blocker Inconsistent Shadows atten *= … foreach cookie texture atten *= … foreach slide texture color *= … foreach noise texture Projected Shadow Matte atten, color *= … foreach shadow map atten, color *= … Calculate intensity fall-off Calculate beam distribution } Projected Texture CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 5 Irradiance and Illuminance
Definition: The irradiance (illuminance) is the power per unit area incident on a surface. 2Φ ≡=d ωθω dE( x ) L ( x ,iii )cos d L(ω ) dA i = ωθω E()xLxd∫ (,iii )cos θ i H 2
Wlm = lux mm22
This is sometimes referred to as the radiant and luminous incidence.
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Isotropic Point Sources
Φ I (ω) = π θ r h 4
Φ cosθ Φ cos3 θ dΦ = E dA = I dω = dA = dA 4π r 2 4π h2 Note inverse square law fall off. Note cosine dependency
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 6 Distant or Directional Source
Es θ s E = ∫ Ldd(ωθ )cos cos θϕ H 2 θ ϕ = δ θ − θ δ ϕ −ϕ L( , ) Es (cos cos s ) ( s )
∫ Ldd(,θϕ )cos θ cos θ ϕ H 2 =−−δθ θδϕϕ θθϕ ∫ Esss(cos cos ) ( )cosdd cos H 2 = θ Esscos
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Irradiance Distribution
Isolux contours CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 7 Irradiance from Area Sources
==ωθω θω Ex()∫∫ Lx (,iii )cos d L cos ii d HH22 θ ∫ cosθωd = π i Η 2
Projected Solid Angle
Radiosity formulation = Differential Form Factor
Note: Things are considerably complicated by shadows
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 0.03 Moonless 0.00003
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 8 The Sky
From Greenler, Rainbows, halos and glories CS348B Lecture 5 Pat Hanrahan, Spring 2001
Disk Source
Geometric Derivation Algebraic Derivation θ cos d 2π r ELdd= ∫∫ cosθ φ cosθ 10 cosθ cos2 θ d = 2π L θ R 2 1 = πθ2 L sin d r 2 = Lπ rR22+
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 9 Spherical Source
Geometric Derivation Algebraic Derivation
= θ ω r E ∫ Lcos d R = Lπ sin 2 θ θ r 2 = Lπ R2
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-Lux Solar angle α = .25 degrees = .004 radians (half angle) ω = π sin2 α = 6 x 10-5 steradians Radiance E 1.353×103W / m2 W L = = = 2.25×107 ω 6×10−5sr m2 ⋅ sr
Pluto (6 tera-meters) 50 Lux - read a newspaper Deep space -> 20 micro-lux (see, but not read!)
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 10 Polygonal Source
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Lambert’s Formula
Ni γ i 3 ∑ A i A i=1 1 − A2 − A3 nn = γ • =•γ Ai i N Ni ∑∑AiiiNN ii==11
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 11 Radiosity and Luminosity
Definition: The radiosity (luminosity) is the energy per unit area leaving a surface. ω L( o )
θ = ω θ ω o B(x) ∫ L( o )cos o d o H 2
This is officially referred to as the radiant and luminous exitance.
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Uniform Diffuse Source
BL= ∫ cosθω d B L = = L∫ cosθωd π = π L
11 23− blondel=== apostilbππ nit cd/(10) m skot = apostilb
1 2 lamberts= π cd/ cm
1 23− foot−= lambertsπ cd/(10) ft glim =− foot lambert
CS348B Lecture 5 Pat Hanrahan, Spring 2001
Page 12 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 5 Pat Hanrahan, Spring 2001
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?” Kajiya
CS348B Lecture 5 Pat Hanrahan, Spring 2001
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