Light Sources and Illumination. Blackbody. Page 1

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1 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 Blackbody Page 1

2 Tungsten Flourescent Page

3 Sunlight Radiant and Luminous Intensity Definition: The radiant (luminous) intensity is the power per unit solid angle from a point. dφ I ( ω) dω Φ= I( ω) dω S W lm = cd = candela sr sr Page 3

4 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 Goniometric Diagrams Page 4

5 Warn s Spotlight θ Ŝ Â s I ( ω) = cos θ = (Sˆ Aˆ) s Φ = π s π I ( ω) d cosθ dϕ = π cos θ d cosθ = s s + 1 I ( ω) = Φ cos π s θ PIXAR Standard Light Source Inconsistent Shadows Projected Shadow Matte Projected Texture Ronen Barzel UberLight( ) { Clip to near/far planes Clip to shape boundary foreach superelliptical blocker atten *= foreach cookie texture atten *= foreach slide texture color *= foreach noise texture atten, color *= foreach shadow map atten, color *= Calculate intensity fall-off Calculate beam distribution } Page 5

6 Irradiance and Illuminance Definition: The irradiance (illuminance) is the power per unit area incident on a surface. d Φ de( x) = L( x, ωi)cosθi dωi da E( x) = L( x, ωi)cosθidωi W lm = lux m m This is sometimes referred to as the radiant and luminous incidence. θ i L( ωi ) Isotropic Point Sources θ r h I ( ω) = Φ 4π 3 Φ cosθ Φ cos θ dφ = E da = I dω = da = da 4π r 4π h Note inverse square law fall off. Note cosine dependency Page 6

7 Distant or Directional Source E s θ s E = L( ω)cosθ dcosθdϕ L( θ, ϕ) = E s δ (cosθ cosθ s) δ ( ϕ ϕs ) L( θϕ, )cosθdcosθdϕ = E δ(cosθ cos θ ) δ( ϕ ϕ ) cosθ dcosθ dϕ = E cosθ s s s s s Irradiance Distribution Isolux contours Page 7

8 Irradiance from Area Sources Ex ( ) = Lx (, ω )cosθ dω = L cosθ dω i i i i i Η cosθ dω = π θ i Projected Solid Angle Radiosity formulation = Differential Form Factor Note: Things are considerably complicated by shadows Luminance of Common Light Sources Surface of the sun,000,000,000. cd/m Sunlight clouds 30,000. Clear day 3,000. Overcast day 300. Moonlight 0.03 Moonless Page 8

9 The Sky From Greenler, Rainbows, halos and glories Disk Source Geometric Derivation R θ r Algebraic Derivation cosθ π d E = Lcosθ dφ dcosθ 1 0 cos θ = π L = Lπsin θ d r = Lπ r + R cosθ 1 d Page 9

10 Spherical Source Geometric Derivation Algebraic Derivation R θ r E = Lcosθdω = = Lπ sin r Lπ R θ The Sun Solar constant (normal incidence at zenith) Irradiance 1353 W/m Illuminance 17,500 Lumen/m = 17.5 Kilo-Lux Solar angle α =.5 degrees =.004 radians (half angle) ω = π sin α = 6 x 10-5 steradians Radiance 3 E W / m 7 W L = = = ω 6 10 sr m sr Pluto (6 tera-meters) 50 Lux - read a newspaper Deep space -> 0 micro-lux (see, but not read!) Page 10

11 Polygonal Source Lambert s Formula N i Ai = γ N N i γ i i 3 A i i= 1 A 1 A A 3 n n A = γ N N i i i i= 1 i= 1 Page 11

12 Radiosity and Luminosity Definition: The radiosity (luminosity) is the energy per unit area leaving a surface. L( ωo) θ o B( x) = L( ω )cosθ dω o o o This is officially referred to as the radiant and luminous exitance. Uniform Diffuse Source B = Lcosθ dω = L = π L cosθ dω L = B π blondel = apostilb = nit = cd m skot = apostilb lamberts = cd cm 1 π / π π / ( 10 ) foot lamberts = cd ft glim = foot lambert 1 3 π / ( 10 ) Page 1

13 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 Luminous Power Illuminance Luminosity Talbot Lumen Lux Phot Footcandle Luminance Nit Apostilb, Blondel Stilb Lambert Footlambert Luminous Intensity Candela (Candle, Candlepower, Carcel, efner) 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 Page 13