The Light Field Electromagnetic waves and 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 Ignore polarization Ignore photons Spatial distribution From London and Upton CS348B Lecture 4 Pat Hanrahan, Spring 2002 Topics Radiometry and photometry Light sources Radiant intensity Irradiance Inverse square law and cosine law Radiance Exposure proportional to radiance Radiance constant along a ray CS348B Lecture 4 Pat Hanrahan, Spring 2002 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, Spring 2002 Page 2 Radiometry vs. Photometry Radiometry [Units = Watts] Physical measurement of electromagnetic energy Photometry and Colorimetry [Lumen] Relative perceptual measurement Sensation as a function of wavelength 1 Brightness [Brils] BY= 3 Absolute perceptual measurement Sensation at different intensities CS348B Lecture 4 Pat Hanrahan, Spring 2002 Blackbody CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 3 Tungsten CS348B Lecture 4 Pat Hanrahan, Spring 2002 Fluorescent CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 4 Sunlight CS348B Lecture 4 Pat Hanrahan, Spring 2002 Light Source Properties Power spectrum Directional distribution (goniometric diagram) Spatial distribution (area sources) CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 5 Intensity Radiant and Luminous Intensity Definition: The radiant (luminous) intensity is the power per unit solid angle from a point. dΦ I()ω ≡ dω Wlm ==cd candela sr sr CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 6 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, Spring 2002 Differential Solid Angles rsinθ dA= ()(sin) r dθ rθφ d 2 dφ r = rddsinθθφ dθ θ dA dddω ==sinθθφ φ r 2 ππ2 Sdd==∫∫sinθ θφ 4 π 00 CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 7 Isotropic Point Source Φ=∫ I dω S2 = 4π I Φ I = 4π CS348B Lecture 4 Pat Hanrahan, Spring 2002 Light Source Goniometric Diagrams CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 8 Warn’s Spotlight Sˆ θ Aˆ I()ωθ==• cosss(Sˆˆ A ) 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, Spring 2002 PIXAR Standard 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, Spring 2002 Page 9 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 standard candle Originally a “standard” candle Currently 550 nm laser w/ 1/683 W/sr 1 of 6 fundamental SI units CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 10 Irradiance and Illuminance Definition: The irradiance (illuminance) is the power per unit area incident on a surface. dΦ Ex()≡ dA Wlm = lux mm22 Sometimes referred to as the radiant (luminous) incidence. CS348B Lecture 4 Pat Hanrahan, Spring 2002 Lambert’s Cosine Law A /cosθ A Φ θ Φ Φ E ==cosθ AA/cosθ CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 11 Illumination: Isotropic Point Source Φ I()ω = 4π θ r h dIdEdAΦ ==ω Φ cosθ I ddAEdAω == 4π r 2 Φ cosθ ΦΦcosθ cos3 θ E = ⇒ 4π r 2 44ππrh22 CS348B Lecture 4 Pat Hanrahan, Spring 2002 Radiance Page 12 Radiance Definition 1: The surface radiance (luminance) is the intensity per unit area leaving a surface Lx(,ω ) dI(, x ω ) Lx(,ω )≡ dA dω dxΦ(,ω ) = ddAω Wcd = nit 22 dA sr m m CS348B Lecture 4 Pat Hanrahan, Spring 2002 Typical Values of Luminance [cd/m2] Surface of the sun 2,000,000,000. Sunlight clouds 30,000. Clear day 3,000. Overcast day 300. Moon 0.03 CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 13 Typical Values of Illuminance [lm/m2] Sunlight plus skylight 100,000 lm/m2 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, Spring 2002 Properties of Radiance 1. Radiance invariant along a ray. ∴ Radiance is associated with rays in ray tracer 2. Response of a sensor proportional to radiance. ∴ Image is a 2D set or rays 3. Fundamental field quantity that characterizes the distribution of light in an environment. ∴ All other quantities are derived from it. CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 14 1st Law: Conversation of Radiance The radiance in the direction of a light ray remains constant as the ray propagates from one surface to another surface dLddALddAdΦ1111222==ω ω =Φ 2 dA1 dA2 L L 1 2 2 ddArω12= 2 ddArw21= dω1 dA dA ddAωω==12 ddA 11r 2 2 2 dω2 ∴L12= L CS348B Lecture 4 Pat Hanrahan, Spring 2002 Quiz Does radiance increase under a magnifying glass? No!! CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 15 Radiance: 2nd Law The response of a sensor is proportional to the radiance of the surface visible to the sensor. Ω Aperture A Sensor RLddALT==∫∫ ω A Ω TddA= ∫∫ ω A Ω L is what should be computed and displayed. CS348B Lecture 4 Pat Hanrahan, Spring 2002 Quiz Does the brightness that a wall appears to the eye depend on the distance of the viewer to the wall? No!! CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 16 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, Spring 2002 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, Spring 2002 Page 17.