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Light Sources and Illumination Blackbody 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 CS348B Lecture 5 Pat Hanrahan, Spring 2001 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 Page 13.
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