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Radiant and Luminous IntensityDefinition: The radiant (luminous) intensity is the powerper unit solid angle from a point.dΦ I (ω )dωΦ I (ω ) dω W candela cd lm sr sr S2CS348B Lecture 5Pat Hanrahan, Spring 2000The Invention of PhotometryBouguer’s Classic experimentCompare two light sourcesOne is a candleDefinition of a standard candlenOriginally “standard” candlenCurrently550 nm laser with 1/683 W/srCS348B Lecture 5Pat Hanrahan, Spring 2000Page 1
Luminance of Common SourcesSkySurface of the sun2,000,000,000. cd/m2Sunlight clouds30,000.Clear day3,000.Overcast day300.Moonlight0.03Moonless0.00003CS348B Lecture 5Pat Hanrahan, Spring 2000Light SourcesPropertiesnSpectraln Blackbody (incandescent)n FlourescentnPoint or areanDirectional distribution – goniometric diagramCS348B Lecture 5Pat Hanrahan, Spring 2000Page 2
Warn’s SpotlightθΦ 2π 1I (ω ) cos s θ12π I (ω ) d cosθ dϕ 2π cos θ d cos θ s 1s0 0I (ω ) Φ0s 1 scos θ2πCS348B Lecture 5Pat Hanrahan, Spring 2000Goniometric DiagramsIsocandle diagram forNovalux sodium luminaireFrom Parry MoonThe Scientific Basic ofIlluminating Engineeringp. 236CS348B Lecture 5Pat Hanrahan, Spring 2000Page 3
Irradiance and IlluminanceDefinition: The irradiance (illuminance) is the power perunit area incident on a surface.L (ω i )dE ( x) L (ω i ) cos θ i dω iE (x) θi L(ωi ) cosθ i dωH2 W Lux lm m 2 m 2 This is sometimes referred to as the radiant andluminous incidence.CS348B Lecture 5Pat Hanrahan, Spring 2000Irradiance DistributionIsolux contoursCS348B Lecture 5Pat Hanrahan, Spring 2000Page 4
Isotropic Point SourcesθI (ω ) rhΦ4πΦ cosθΦ cos 3 θdΦ E dA I dω dA dA224π r4π hn Note inverse square law fall off.n Note cosine dependencyCS348B Lecture 5Pat Hanrahan, Spring 2000Distant SourceEsθsE E s cos θ sCS348B Lecture 5Pat Hanrahan, Spring 2000Page 5
Hemisphere: Projected Solid Angle cosθ dω π? 2CS348B Lecture 5Pat Hanrahan, Spring 2000DiskrE cos θ d 2π 1R θL cosθ dφ d cosθ0cos2 θ 2πL2cosθ d1 Lπ sin θ d2r2 Lπ 2r R2CS348B Lecture 5Pat Hanrahan, Spring 2000Page 6
SphererE L cosθ dω Lπ sin 2 θRθr2 Lπ 2RCS348B Lecture 5Pat Hanrahan, Spring 2000The SunSolar constant (normal incidence at zenith)Irradiance1353 W/m2Illuminance127,500 Lumen/m2 127.5 Kilo-LuxSolar anglea .25 degrees .004 radians (half angle)ω π sin2 a 6 x 10-5 steradiansRadianceL E 1.353 103W / m 2W 2.25 107 2 5ω6 10 srm srPluto (6 tera-meters) 50 Lux - read a newspaperDeep space - 20 micro-lux (see, but not read!)CS348B Lecture 5Pat Hanrahan, Spring 2000Page 7
Polygonal SourceCS348B Lecture 5Pat Hanrahan, Spring 2000Lambert’s FormularNiγi3 AiA1i 1 A2 A3r rAi γ i N NinnrrAi γ i N N i i 1i 1CS348B Lecture 5Pat Hanrahan, Spring 2000Page 8
Form Factorx′θ′θcosθ ′dω dA′2x x′x x′cos θ dω dAcosθ cos θ ′dA′2x x′cosθ ′ cos θ′2 d A dAA A′ π x x′T CS348B Lecture 5Pat Hanrahan, Spring 2000Form eFinite-finiteFAi , A jFdAi , dA j cos θ o′cosθ idA j2π x x′cos θ o′cosθ iFdAi , A j dA′2A j π x x′1cos θ o′cos θ i′ 2 d A dAAi Ai A j π x x′CS348B Lecture 5Pat Hanrahan, Spring 2000Page 9
Form Factor PropertiesForm factor is the percentage of light transferredbetween surfaces1. Reciprocitycos θ o′cos θ i′Tij Ai Fij 2 dA dA T ji A j F jiAi A j π x x′2. Summation Fij Fji 1jiCS348B Lecture 5Pat Hanrahan, Spring 2000Radiosity and LuminosityDefinition: The radiosity (luminosity) is the energy perunit area leaving a surface.L (ω o )θoB ( x) L(ω o ) cos θ o dω oH2lm W Lux m2 m2 This is officially referred to as the radiant and luminousexitance.CS348B Lecture 5Pat Hanrahan, Spring 2000Page 10
Uniform Diffuse SourceB L cosθ dωL L cosθ dω πLblondel apostilb π1 nit π1 cd / m 2Bπ(skot 10 3 apostilb)lamberts π1 cd / cm 2foot lamberts π1 cd / ft 2( glim 10 3 foot lambert )CS348B Lecture 5Pat Hanrahan, Spring 2000Radiometric and Photometric TermsPhysicsRadiometryPhotometryEnergyRadiant EnergyLuminous EnergyFlux (Power)Radiant PowerLuminous PowerFlux ular Flux DensityRadianceLuminanceIntensityRadiant IntensityLuminous IntensityCS348B Lecture 5Pat Hanrahan, Spring 2000Page 11
Photometric UnitsPhotometryUnitsMKSCGSLuminous EnergyTalbotLuminous dleLuminosityLuminanceApostilb, BlondelLambertFootlambertLuminous Intensity Candela (Candle, Candlepower, Carcel, Hefner)“Thus one nit is one lux per steradian is one candela per squaremeter is one lumen per square meter per steradian. Got it?” KajiyaCS348B Lecture 5Pat Hanrahan, Spring 2000Page 12
Radiant and Luminous Intensity Definition: The radiant (luminous) intensityis the power per unit solid angle from a point. (w) w I d d Φ sr lm candela cd sr Φ W 2 S I w dw CS348B Lecture 5 Pat Hanrahan, Spring 2000 The Invention of Photometry Bouguer’s Classic experiment Compare two light sou
