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
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