Light and reflection, Exams of Optics

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Light and reflection

Marc Levoy

Computer Science Department Stanford University

CS 178, Spring 2014

Begun 5/20/14, finished 5/

Outline

✦ measures of light

• radiometry versus photometry
• luminous intensity of a point light
• luminance leaving an area light
• luminance arriving on a surface
• illuminance on a surface

✦ reflection of light

• diffuse
• specular
• goniometric diagrams
• Fresnel equations and other effects

2

Relationship to tristimulus theory

✦ the response of the human visual system to a spectrum is

✦ the total response can be expressed as

✦ where

4

(ρ,γ , β) = L (^) e ( λ) 400 nm

700 nm ∫ ρ^ (^ λ)^ d^ λ,^ L^ e^ (^ λ) 400 nm

700 nm ∫ γ^ (^ λ)^ d^ λ,^ L^ e^ (^ λ) 400 nm

700 nm ∫ β^ (^ λ)^ d^ λ

V ( λ) = ρ ( λ) + γ ( λ) + β ( λ)

L = ρ + γ + β = L e ( λ) V ( λ)

400 nm

700 nm ∫ d^ λ

luminance radiance (Stone)

V(λ), or luminous efficiency curve

S is actually much lower than M or L

Luminous intensity of a point light

✦ power given off by the light per unit solid angle

✦ related radiometric quantity

• radiant intensity (watts/steradian) 5

I =

P

lumens steradian

⎝⎜^

(Reinhard)

Luminous intensity of a point light

✦ power given off by the light per unit solid angle

✦ related units

• 1 candela = 1 lumen / sr

✦ examples

• a standard Bouguer candle gives off 1 candela
• a 100W light bulb with a luminous efficiency of 2.6% (the other 97.4% we don’t see) gives off 17.6 lumens per watt × 100W ÷ 4π sr in the sphere = 140 candelas = 140 lumens through each steradian, which is a 12.7’ circle 10’ feet away from the bulb 7

I =

P

lumens steradian

⎝⎜^

Pierre Bouguer (1698-1758) As I mentioned in class, if the (incandescent) light bulb were 100% efficient (i.e. no energy wasted as heat outside the visible spectrum), it would give off 683 lumens per watt of input power, instead of 17.6 lumens per watt. That’s a big difference, and it explains the increasing popularity of compact fluorescent light bulbs, which give off up to 75 lumens per watt.

Photography by candlelight

✦ need SLR-sized pixels, fast lens, tripod, patient subject

• moderate shutter speed (1/15 sec) and ISO (400) 8

(digital-photography-school.com)

Luminance leaving an area light

✦ power given off by the light per unit solid angle per unit

area, viewed at a declination of θ relative to straight-on

✦ related units

• 1 nit = 1 candela / m^2 = 1 lumen / (sr m^2 )

✦ example

• viewed perpendicularly, a computer display gives off 50-300 candelas per meter^2 of the display surface, about the same as a 100W light bulb but spread over the surface of the display 10

L =

P

Ω A cos^ θ

lumens steradian m 2

⎝⎜^

Luminance arriving on a surface

✦ power arriving on a surface per unit solid angle per unit

area, illuminated from a declination of θ

11

L =

P

Ω A cos^ θ

lumens steradian m 2

⎝⎜^

Luminance from sun → reflection from surface (contents of whiteboard)

✦ Q. Why is the sun 160,000 candelas/cm^2 but its reflection by a diffuse white surface is only 1.6 cd/cm^2? ✦ A. the sun doesn’t occupy the entire sky, but diffuse reflection does. ✦ luminance arrives from the sun through 0.001% of the celestial hemisphere (0.00006 sr), hence the amount arriving is 160,000 cd/cm^2 = 160,000 lumens/sr cm^2 × 0.00006 sr = 10 lumens/cm^2 ✦ if we assume a diffuse white surface reflects all the light it receives, then it reflects these 10 lumens/cm^2 into 100% of hemisphere (2π sr), hence the surface’s outgoing luminance is 10 lumens/cm^2 ÷ 2π sr = 1.6 lumens/sr cm^2 13 or 1.6 cd/cm^2

you won’t be asked to perform calculations like this on your final exam (whew!)

✦ power accumulating on a surface per unit area,

considering light arriving from all directions

Illuminance on a surface

14

E =

P

A

lumens m 2

⎝⎜^

(Reinhard)

To help yourself remember the difference bet ween luminous intensity, luminance, and illuminance, keep your eye on the units of each. The luminous intensity of a point light source is given in power per unit solid angle (lumens/sr); the luminance of an area light source (or the luminance arriving at an extended surface) is given in power per unit solid angle per unit area on the surface (lumens/(sr m given in power per unit area (lumens/m^2 ); the illuminance accumulating on a surface is (^2) ). Note that each of these three concepts has different units.

The effect of distance to the subject

✦ for a point light, illuminance on a surface falls as d^2

16

Q. How does illuminance change with distance from an area light?

(Thomson)

Georges de La Tour The Carpenter, 1640

How does illuminance change with distance from an area light?

(contents of whiteboard)

✦ assume the light is a diffuse surface of infinite extent (at right in drawings) ✦ assume the receiver (at left) is a camera or light meter (or human eye), having a given lens (or iris) diameter and a pixel (or retinal cell) width ✦ the solid angle captured by the lens from each point on the light source falls as d^2 (left drawing) ✦ but the number of source points seen by the pixel rises as d^2 (right drawing) ✦ these effects cancel, so the illuminance at a pixel is independent of d 17

Recap

✦ to convert radiometric measures of light into photometric measures, multiply the spectral power distribution as measured by a spectroradiometer wavelength-by-wavelength by the human luminous efficiency curve V(λ) ✦ useful measures of light are the^ luminous^ intensity^ emitted by a point source (power per solid angle), the luminance emitted by (or arriving at) an area source (power per solid angle per unit area), and the illuminance accumulating on a surface (power per unit area) ✦ bright objects (like the sun) may be more luminous (measured in lumens/sr cm^2 ) than darker objects (like the blue sky), but typically cover a smaller fraction of the incoming hemisphere ✦ outdoor shadows are 1/5 as bright as lit areas (2.2 f/stops)

19 Que s t ions?

Outline

✦ measures of light

• radiometry versus photometry
• luminous intensity of a point light
• luminance leaving an area light
• luminance arriving on a surface
• illuminance on a surface

✦ reflection of light

• diffuse
• specular
• goniometric diagrams
• Fresnel equations and other effects

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