Light Visible electromagnetic radiation Power spectrum 2 4 6 8 10 12 14 16 18 20 22 24 26 11010 10 10 10 10 10 10 10 10 10 10 10 Power Heat Radio Infra- Ultra- X-Rays Gamma Cosmic Red Violet Rays Rays 16 14 12 10 8 6 4 2 -2 -4 -6 -8 10 10 10 10 10 10 10 10 11010 10 10 Wavelength (NM) IR R G B UV 700600 500 400 Polarization Photon (quantum effects) From London and Upton Wave (interference, diffraction) CS348B Lecture 4 Pat Hanrahan, 2004 Topics Light sources and illumination Radiometry and photometry Quantify spatial energy distribution Radiant intensity Irradiance and radiant exitance (radiosity) Inverse square law and cosine law Radiance Illumination calculations Irradiance from environment CS348B Lecture 4 Pat Hanrahan, 2004 Page 1 Radiometry and Photometry Radiant Energy and Power Power: Watts vs. Lumens Φ Energy efficiency Spectral efficacy Energy: Joules vs. Talbot Exposure Film response Skin - sunburn Luminance YVLd= ∫ ()()λ λλ CS348B Lecture 4 Pat Hanrahan, 2004 Page 2 Radiometry vs. Photometry Radiometry [Units = Watts] Physical measurement of electromagnetic energy Photometry and Colorimetry [Lumen] Sensation as a function of wavelength Relative perceptual measurement 1 Brightness [Brils] BY= 3 Sensation at different brightness levels Absolute perceptual measurement Obeys Steven’s Power Law CS348B Lecture 4 Pat Hanrahan, 2004 Blackbody CS348B Lecture 4 Pat Hanrahan, 2004 Page 3 Tungsten CS348B Lecture 4 Pat Hanrahan, 2004 Fluorescent CS348B Lecture 4 Pat Hanrahan, 2004 Page 4 Sunlight CS348B Lecture 4 Pat Hanrahan, 2004 Radiant Intensity Page 5 Radiant Intensity Definition: The radiant (luminous) intensity is the power per unit solid angle emanating from a point source. dΦ I()ω ≡ dω Wlm ==cd candela sr sr CS348B Lecture 4 Pat Hanrahan, 2004 Angles and Solid Angles l Angle θ = r ⇒ circle has 2π radians A Solid angle Ω= R2 ⇒ sphere has 4π steradians CS348B Lecture 4 Pat Hanrahan, 2004 Page 6 Differential Solid Angles rsinθ dφ r dA= ()(sin) r dθ rθφ d dθ θ = rdd2 sinθθφ φ dA dddω ==sinθθφ r 2 CS348B Lecture 4 Pat Hanrahan, 2004 Differential Solid Angles dA dddω ==sinθθφ rsinθ r 2 dφ r Ω=∫ dω dθ 2 θ S ππ2 = ∫∫sinθ ddθφ φ 00 12π = ∫∫ddcosθ φ −10 = 4π CS348B Lecture 4 Pat Hanrahan, 2004 Page 7 Isotropic Point Source Φ=∫ I dω S2 = 4π I Φ I = 4π CS348B Lecture 4 Pat Hanrahan, 2004 Warn’s Spotlight ω θ Aˆ I()ωθω==• cosss(Aˆ ) 21π Φ= ∫∫I()cosω ddθϕ 00 CS348B Lecture 4 Pat Hanrahan, 2004 Page 8 Warn’s Spotlight ω θ Aˆ I()ωθω==• cosss(Aˆ ) 21π 1 2π Φ=∫∫Id(ωθϕπθθ ) cos d = 2 ∫ coss d cos = 00 0 s +1 s +1 I()ω =Φ coss θ 2π CS348B Lecture 4 Pat Hanrahan, 2004 Light Source Goniometric Diagrams CS348B Lecture 4 Pat Hanrahan, 2004 Page 9 PIXAR Light Source UberLight( ) { Clip to near/far planes Clip to shape boundary foreach superelliptical blocker Shadows atten *= … foreach cookie texture atten *= … foreach slide texture color *= … foreach noise texture Shadow Matte atten, color *= … foreach shadow map atten, color *= … Calculate intensity fall-off Calculate beam distribution } Projected Slide Texture CS348B Lecture 4 Pat Hanrahan, 2004 Radiance Page 10 Radiance Definition: The surface radiance (luminance) is the intensity per unit area leaving a surface Lx(,ω ) dI(, x ω ) Lx(,ω )≡ dA dω dx2Φ(,ω ) = ddAω Wcdlm 22== 2nit dA sr m m sr m CS348B Lecture 4 Pat Hanrahan, 2004 Typical Values of Luminance [cd/m2] Surface of the sun 2,000,000,000 nit Sunlight clouds 30,000 Clear day 3,000 Overcast day 300 Moon 0.03 CS348B Lecture 4 Pat Hanrahan, 2004 Page 11 Irradiance 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 candela Originally a “standard” candle Currently 550 nm laser w/ 1/683 W/sr 1 of 6 fundamental SI units CS348B Lecture 4 Pat Hanrahan, 2004 Page 12 Irradiance Definition: The irradiance (illuminance) is the power per unit area incident on a surface. dΦ Ex()≡ i dA Wlm = lux mm22 Sometimes referred to as the radiant (luminous) incidence. CS348B Lecture 4 Pat Hanrahan, 2004 Lambert’s Cosine Law A Φ=EA Φ E = A CS348B Lecture 4 Pat Hanrahan, 2004 Page 13 Lambert’s Cosine Law A A /cosθ Φ θ Φ Φ E ==cosθ AA/cosθ CS348B Lecture 4 Pat Hanrahan, 2004 Irradiance: Isotropic Point Source Φ I = 4π θ h r CS348B Lecture 4 Pat Hanrahan, 2004 Page 14 Irradiance: Isotropic Point Source Φ I = dω 4π θ h r dA dIdEdAΦ ==ω CS348B Lecture 4 Pat Hanrahan, 2004 Irradiance: Isotropic Point Source Φ I = dω 4π θ h r dA cosθ ddAω = r 2 CS348B Lecture 4 Pat Hanrahan, 2004 Page 15 Irradiance: Isotropic Point Source Φ I = dω 4π θ h r dA Φ cosθ I ddAω = 4π r 2 CS348B Lecture 4 Pat Hanrahan, 2004 Irradiance: Isotropic Point Source Φ I = dω 4π θ h r dA Φ cosθ I ddAEdAω == 4π r 2 Φ cosθ E = 2 CS348B Lecture 44π r Pat Hanrahan, 2004 Page 16 Irradiance: Isotropic Point Source Φ I = dω 4π θ hr= cosθ r dA ΦΦcosθ cos3 θ E == 44ππrh22 CS348B Lecture 4 Pat Hanrahan, 2004 Directional Power Arriving at a Surface Lx(,ω ) i dω dA 2 θ dxΦ=ii(,ω ) Lx (,ωθω )cos dAd = Lxi (,ωω ) dAdi dx2Φ (,ω ) i dAi dω = cosθω dAd CS348B Lecture 4 Pat Hanrahan, 2004 Page 17 Irradiance from the Environment 2 dxΦ=ii(,ω ) Lx (,ωθ )cos dAd ω Lxi (,ω ) dE( x ,ω )= Li ( x ,ωθω )cos d dω θ dA E()xLxd= (,ω )cosθω Light meter ∫ i H2 CS348B Lecture 4 Pat Hanrahan, 2004 Typical Values of Illuminance [lm/m2] Sunlight plus skylight 100,000 lux Sunlight plus skylight (overcast) 10,000 Interior near window (daylight) 1,000 Artificial light (minimum) 100 Moonlight (full) 0.02 Starlight 0.0003 CS348B Lecture 4 Pat Hanrahan, 2004 Page 18 The Sky Radiance Distribution From Greenler, Rainbows, halos and glories CS348B Lecture 4 Pat Hanrahan, 2004 Gazing Ball ⇒ Environment Maps Miller and Hoffman, 1984 Photograph of mirror ball Maps all directions to a to circle Reflection indexed by normal Resolution function of orientation CS348B Lecture 4 Pat Hanrahan, 2004 Page 19 Environment Maps Interface, Chou and Williams (ca. 1985) CS348B Lecture 4 Pat Hanrahan, 2004 Irradiance Environment Maps L(,θ ϕ ) R E(,θ ϕ ) N Radiance Irradiance Environment Map Environment Map CS348B Lecture 4 Pat Hanrahan, 2004 Page 20 Irradiance Map or Light Map Isolux contours CS348B Lecture 4 Pat Hanrahan, 2004 Radiant Exitance (Radiosity) Page 21 Radiant Exitance Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface. dΦ Mx()≡ o dA Wlm = lux mm22 In computer graphics, this quantity is often referred to as the radiosity (B) CS348B Lecture 4 Pat Hanrahan, 2004 Directional Power Leaving a Surface Lx(,ω ) o dω dA 2 θ dxΦ=oo(,ω ) Lx (,ωθω )cos dAd = Lxo (,ωω ) dAdi 2 dxΦo (,ω ) CS348B Lecture 4 Pat Hanrahan, 2004 Page 22 Uniform Diffuse Emitter M = Ldcosθ ω ∫ o H2 Lo(,x ω ) = L cosθ dω o ∫ H2 dω = πLo θ M L = o π dA CS348B Lecture 4 Pat Hanrahan, 2004 Projected Solid Angle Ω≡ ∫ cosθ dω Ω dω θ cosθ dω Ω= ∫ cosθ dωπ = 2 CS348B Lecture 4H Pat Hanrahan, 2004 Page 23 Radiometry and Photometry Summary 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 4 Pat Hanrahan, 2004 Page 24 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?”, James Kajiya CS348B Lecture 4 Pat Hanrahan, 2004 Page 25.