radiometry i: illumination - computer graphics at … matt pharr, spring 2003 • four key...
TRANSCRIPT
![Page 1: Radiometry I: Illumination - Computer Graphics at … Matt Pharr, Spring 2003 • Four key quantities • Power • Radiant intensity • Irradiance • Radiance • Radiometry and](https://reader036.vdocuments.us/reader036/viewer/2022081517/5b014e677f8b9a0c028e1098/html5/thumbnails/1.jpg)
cs348bMatt Pharr
Radiometry I: Illumination
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cs348b Matt Pharr, Spring 2003
• Extra copies of lrt book
• Bug fix for assignment 1 polynomial.h file
Administrivia
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cs348b Matt Pharr, Spring 2003
• Four key quantities• Power
• Radiant intensity
• Irradiance
• Radiance
• Radiometry and photometry
Onward To The Physical Description of Light
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cs348b Matt Pharr, Spring 2003
• The measurement of electromagnetic radiation• Radiation: propagation of energy through space
• We will ignore polarization, quantum mechanics
• Frequency distribution of radiation gives color
Radiometry
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cs348b Matt Pharr, Spring 2003
• Radiometric quantities are usually wavelength-dependent• (Usually not included in equations, for simplicity)
Spectral Distribution of Energy
Qλ = dQ/dλ
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cs348b Matt Pharr, Spring 2003
Blackbody Radiator
Most energy outside of the visible range
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cs348b Matt Pharr, Spring 2003
Sunlight
![Page 8: Radiometry I: Illumination - Computer Graphics at … Matt Pharr, Spring 2003 • Four key quantities • Power • Radiant intensity • Irradiance • Radiance • Radiometry and](https://reader036.vdocuments.us/reader036/viewer/2022081517/5b014e677f8b9a0c028e1098/html5/thumbnails/8.jpg)
cs348b Matt Pharr, Spring 2003
Fluorescent Light
400 500 600 700Wavelength
0
50
100
Brig
htne
ss
Spikes make accurate representation difficult
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cs348b Matt Pharr, Spring 2003
Lemon Skin
400 500 600 700Wavelength
0
0.2
0.4
0.6
Brig
htne
ss
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cs348b Matt Pharr, Spring 2003
• Arbitrarily complex spectral distributions represented with basis functions
• Classic efficiency vs accuracy trade-off• Polynomials, Gaussians, delta functions, step
functions, ...
• RGB is a poor / ill-defined choice!
Spectral Representations
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cs348b Matt Pharr, Spring 2003
• Energy (Q)• Joules
• Time usually not important in graphics
• (Film exposure, sunburn)
• Power ( )• Watts
• Energy per unit time
• Spectrum gives wavelength distribution of power
Radiant Energy and Power
Φ
Φ = dQ/dt
Φλ = dΦ/dλ
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cs348b Matt Pharr, Spring 2003
• Spectral emission distribution
• Angular emission distribution
• Spatial emission distribution
Light Sources
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cs348b Matt Pharr, Spring 2003
Intensity
I = dΦ/dω
Φ =
∫Ω
I(ω)dω
Φ = 4πIIsotropic point source:
Watts/steradian
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cs348b Matt Pharr, Spring 2003
• Plane angle (radians)• Length of arc subtended by object divided by
radius
• Solid angle (steredians)• Area of sphere subtended by object divided by
radius squared
• Examples...
Measuring Angles
θ = s/r
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cs348b Matt Pharr, Spring 2003
Differential Solid Angles
dω = sin θdθdφ
∫Ω
f(ω)dω =∫ 2π
0
∫ π
0
f(θ,φ) sin θdθdφ
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cs348b Matt Pharr, Spring 2003
Goniometric Diagrams
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cs348b Matt Pharr, Spring 2003
• How much light is arriving at a point on a surface?• Power per unit area
Irradiance
E = dΦ/dA
Φ =
∫A
E(x)dA
![Page 18: Radiometry I: Illumination - Computer Graphics at … Matt Pharr, Spring 2003 • Four key quantities • Power • Radiant intensity • Irradiance • Radiance • Radiometry and](https://reader036.vdocuments.us/reader036/viewer/2022081517/5b014e677f8b9a0c028e1098/html5/thumbnails/18.jpg)
cs348b Matt Pharr, Spring 2003
• Incident irradiance varies according to the cosine of the incident angle
Lambert’s Cosine Law
E = E0 cos θ
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cs348b Matt Pharr, Spring 2003
• Irradiance decreases with square of the distance from a point source
• Look at projected solid angles...
Inverse Square Falloff Law
![Page 20: Radiometry I: Illumination - Computer Graphics at … Matt Pharr, Spring 2003 • Four key quantities • Power • Radiant intensity • Irradiance • Radiance • Radiometry and](https://reader036.vdocuments.us/reader036/viewer/2022081517/5b014e677f8b9a0c028e1098/html5/thumbnails/20.jpg)
cs348b Matt Pharr, Spring 2003
• Area and solid angle density of flux• Think area lights, not point lights: intensity per
unit area, or irradiance per unit angle
• Unlike irradiance, flux, includes directional distribution
Radiance
L =dΦ
dωdA cos θ
![Page 21: Radiometry I: Illumination - Computer Graphics at … Matt Pharr, Spring 2003 • Four key quantities • Power • Radiant intensity • Irradiance • Radiance • Radiometry and](https://reader036.vdocuments.us/reader036/viewer/2022081517/5b014e677f8b9a0c028e1098/html5/thumbnails/21.jpg)
cs348b Matt Pharr, Spring 2003
• Invariant along rays• Carry radiance along rays in ray-tracer
• Response of sensor is proportional to incident radiance• Image is a 2D set of rays
• Fundamental quantity that characterizes light in environment• Other quantities can be derived from it
Key Properties of Radiance
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cs348b Matt Pharr, Spring 2003
• Total flux from Lambertian disk source?
• Total flux from cone spotlight
• Total flux from disk with cone angular distribution
• Irradiance from disk directly above surface
Exercises
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cs348b Matt Pharr, Spring 2003
• Quantities in terms of effect on standard human observer (photopic conditions)
• Luminous efficiency curve
Photometry
Xp = 683
∫λ
V (λ)Xr(λ)dλ
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cs348b Matt Pharr, Spring 2003
• Radiometry: physical measurement of electromagnetic energy
• Photometry: perceptually-based measurement
• But we don’t want to waste our time on radiation outside the visible range• So judiciously apply photometric computations
to help prioritize...
Photometry vs Radiometry
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cs348b Matt Pharr, Spring 2003
• Luminous flux / radiant flux
• Luminous intensity / radiant intensity
• Illuminance / irradiance
• Luminance / radiance
Photometric vs. Radiometric Quantities