The 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

CS348B Lecture 4 Pat Hanrahan, Spring 2002

Page 1 and Photometry

Power: vs. Lumens Φ  Energy efficiency  Spectral efficacy

Energy: vs. Talbot  Exposure  Film response  Skin - sunburn YVLd= ∫ ()()λ λλ

CS348B Lecture 4 Pat Hanrahan, Spring 2002

Radiometry [Units = Watts]  Physical measurement of electromagnetic energy Photometry and Colorimetry []  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

Definition: The radiant (luminous) intensity is the power per unit from a point.

dΦ I()ω ≡ dω

Wlm  ==cd sr sr 

CS348B Lecture 4 Pat Hanrahan, Spring 2002

Page 6 Angles and Solid Angles

l  Angle θ = r

A  Solid angle Ω= R2

⇒ sphere has 4π

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

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

Definition: The irradiance (illuminance) is the power per unit area incident on a surface. dΦ Ex()≡ dA

 Wlm  = 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

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

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

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

Flux (Power) Radiant Power Luminous Power

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 Apostilb, Blondel Footlambert

Luminous Intensity Candela (Candle, Candlepower, Carcel, Hefner)

“Thus one nit is one lux per 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