Rays. CS348B Lecture 4 Pat Hanrahan, 2004
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1 Page 1 Light Visible electomagnetic adiation Powe spectum Powe Heat Radio Ulta- X-Rays Gamma Cosmic Infa- Red Violet Rays Rays Wavelength (NM) IR R G B UV Polaization Photon (quantum effects) Fom London and Upton Wave (intefeence, diffaction) Topics Light souces and illumination Radiomety and photomety Quantify spatial enegy distibution Radiant intensity Iadiance and adiant exitance (adiosity) Invese squae law and cosine law Radiance Illumination calculations Iadiance fom envionment
2 Page Radiomety and Photomety Radiant Enegy and Powe Powe: Watts vs. Lumens Φ Enegy efficiency Spectal efficacy Enegy: Joules vs. Talbot Exposue Film esponse Skin - sunbun Luminance Y V( λ) L( λ) dλ
3 Page 3 Radiomety vs. Photomety Radiomety [Units Watts] Physical measuement of electomagnetic enegy Photomety and Coloimety [Lumen] Sensation as a function of wavelength Relative peceptual measuement Bightness [Bils] B Y 1 3 Sensation at diffeent bightness levels Absolute peceptual measuement Obeys Steven s Powe Law Blackbody
4 Page 4 Tungsten Fluoescent
5 Page 5 Sunlight Radiant Intensity
6 Page 6 Radiant Intensity Definition: The adiant (luminous) intensity is the powe pe unit solid angle emanating fom a point souce. I( ω) dφ W lm cd candela s s Angles and Solid Angles Angle l cicle has π adians Solid angle Ω A R sphee has 4π steadians
7 Page 7 Diffeential Solid Angles sin dφ φ d ( d )( sin dφ) sin d dφ sin d dφ Diffeential Solid Angles sin dφ φ d sin d dφ Ω S π π π 1 0 4π sin d dφ dcos dφ
8 Page 8 Isotopic Point Souce Φ S 4π I I I Φ 4π Wan s Spotlight ω Â s I ( ω) cos ( ω Aˆ ) s π 1 Φ 0 0 I( ω) dcos dϕ
9 Page 9 Wan s Spotlight ω Â s I ( ω) cos ( ω Aˆ ) s π 1 1 s π Φ I( ω) dcos dϕ π cos dcos s s + 1 s I( ω) Φ cos π Light Souce Goniometic Diagams
10 Page 10 PIXAR Light Souce Shadows Shadow Matte UbeLight( ) { Clip to nea/fa planes Clip to shape bounday foeach supeelliptical blocke atten * foeach cookie textue atten * foeach slide textue colo * foeach noise textue atten, colo * foeach shadow map atten, colo * Calculate intensity fall-off Calculate beam distibution } Pojected Slide Textue Radiance
11 Page 11 Radiance Definition: The suface adiance (luminance) is the intensity pe unit aea leaving a suface Lxω (, ) di( x, ω) Lx (, ω) d Φ( x, ω) W cd lm nit s m m s m Typical Values of Luminance [cd/m] Suface of the sun,000,000,000 nit Sunlight clouds 30,000 Clea day 3,000 Ovecast day 300 Moon 0.03
12 Page 1 Iadiance The Invention of Photomety Bougue s classic expeiment Compae a light souce and a candle Intensity is popotional to atio of distances squaed Definition of a candela Oiginally a standad candle Cuently 550 nm lase w/ 1/683 W/s 1 of 6 fundamental SI units
13 Page 13 Iadiance Definition: The iadiance (illuminance) is the powe pe unit aea incident on a suface. dφi Ex () W lm lux m m Sometimes efeed to as the adiant (luminous) incidence. Lambet s Cosine Law ΦEA A E A Φ
14 Page 14 Lambet s Cosine Law A A /cos Φ Φ Φ E cos A /cos A Iadiance: Isotopic Point Souce h Φ I 4π
15 Page 15 Iadiance: Isotopic Point Souce h I Φ 4π dφ I E Iadiance: Isotopic Point Souce h I Φ 4π cos
16 Page 16 Iadiance: Isotopic Point Souce h I Φ 4π I Φ cos 4π Iadiance: Isotopic Point Souce h I Φ 4π Φ cos I E 4π Φ cos E 4π
17 Page 17 Iadiance: Isotopic Point Souce Φ I 4π h cos E 3 Φ cos Φ cos 4π 4π h Diectional Powe Aiving at a Suface L ( x, ω) i d Φ i( x, ω) Li( x, ω)cos L ( x, ω) i i d Φ ( x, ω) i i cos
18 Page 18 Iadiance fom the Envionment (, ω) (, ω)cos ω d Φ i x Li x d de( x, ω) L ( x, ω)cos i L(, xω) i Light mete E() x Li (, xω)cos H Typical Values of Illuminance [lm/m ] Sunlight plus skylight 100,000 lux Sunlight plus skylight (ovecast) 10,000 Inteio nea window (daylight) 1,000 Atificial light (minimum) 100 Moonlight (full) 0.0 Stalight
19 Page 19 The Sky Radiance Distibution Fom Geenle, Rainbows, halos and gloies Gazing Ball Envionment Maps Mille and Hoffman, 1984 Photogaph of mio ball Maps all diections to a to cicle Reflection indexed by nomal Resolution function of oientation
20 Page 0 Envionment Maps Inteface, Chou and Williams (ca. 1985) Iadiance Envionment Maps L(, ϕ ) E(, ϕ) R N Radiance Envionment Map Iadiance Envionment Map
21 Page 1 Iadiance Map o Light Map Isolux contous Radiant Exitance (Radiosity)
22 Page Radiant Exitance Definition: The adiant (luminous) exitance is the enegy pe unit aea leaving a suface. dφo Mx ( ) W lm lux m m In compute gaphics, this quantity is often efeed to as the adiosity (B) Diectional Powe Leaving a Suface L (, ) o x ω d Φ o( x, ω) Lo( x, ω)cos L ( x, ω) i o d Φ (, ) o x ω
23 Page 3 Unifom Diffuse Emitte M L cos H L o πl H o o cos L (, o x ω ) L o M π Pojected Solid Angle Ω cos Ω cos Ω cos π CS348B Lectue 4 H Pat Hanahan, 004
24 Page 4 Radiomety and Photomety Summay Radiometic and Photometic Tems Physics Radiomety Photomety Enegy Radiant Enegy Luminous Enegy Flux (Powe) Radiant Powe Luminous Powe Flux Density Iadiance Radiosity Illuminance Luminosity Angula Flux Density Radiance Luminance Intensity Radiant Intensity Luminous Intensity
25 Page 5 Photometic Units Photomety Units MKS CGS Bitish Luminous Enegy Luminous Powe Illuminance Luminosity Talbot Lumen Lux Phot Footcandle Luminance Nit Stilb Apostilb, Blondel Lambet Footlambet Luminous Intensity Candela (Candle, Candlepowe, Cacel, Hefne) Thus one nit is one lux pe steadian is one candela pe squae mete is one lumen pe squae mete pe steadian. Got it?, James Kajiya
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