AA&A spring 2002 1

AA&A spring 2002 2

Interaction of light with paint

• Review of some color ideas

• Histories of light rays coming to our eyes

• Index of refraction

• 1—Front surface of painting

• 2—Thick white paint

• 3—Thick red paint

AA&A spring 2002 3

“Perfect” R, G and B

• Suppose we could find sources which excite either ONLY the R, only the G or only the B cones. (Hard to see how, but let’s suppose!)

AA&A spring 2002 4

A “perfect”color space

0.9

1.0

y = “perfect”

green

1.00.90.8

x = “perfect”

red

“perfect”blue

AA&A spring 2002 5

Coordinates of the CIE plot

0.9

1.0

y = “perfect”

green

1.00.90.8

x = “perfect”

red

“perfect”blue

AA&A spring 2002 6

Mixing spectral color with white

• Hue– Which spectral

color

• Saturation – How little white

• Brightness – How much of

everything

AA&A spring 2002 7

****Hue, saturation, brightness****• I have a color A with source intensities (R,G,B) = (128, 64, 64), i.e., 128 units of

R, 64 units of G and B.• I make another color B with (R,G,B) = (64,128,64).• I make another color C with (R,G,B) = (116,70,70).• I make another color D with (R,G,B) = (140,70,70).• I make another color E with (R,G,B) = (120,120,100).

• Comparing each of B, C, D and E with A, fill in the table giving the change in hue, saturation and brightness using the code L = less, D = different, M = more, S= same.

• hue saturation brightness• B D S S

• C S L S

• D S S M

• E D L M

AA&A spring 2002 8

Hue, saturation and brightness

brightness

saturation

AA&A spring 2002 9

Saturation of color

• Can make any color in chromaticity diagram by mixing a spectral color with white

• Highly saturated means mostly spectral

• Unsaturated means mostly white

AA&A spring 2002 10

Cross-section of painting

• What do we see??• How many different things can happen??• Critical properties — index of refraction,

particle size, transmission spectra

varnish

binder

pigment

groundsubstrate

AA&A spring 2002 11

Index of refraction

• Light bends (refracts) as goes from air to water (or glass, or …)

• Velocity of light in medium– s = c/n c = 3 x 108 m/s– n = index of refraction– typically 1 < n < 2

• sin 1/sin 2 = n2/n1

– Bending ~ (n2 - n1)

– More refraction if n’s are very different

Speed of light

fast slown1 n2 > n1

1

2

AA&A spring 2002 12

Reflection

• Light is reflected as goes from air to water (or glass, or …)

• Velocity of light in medium– s = c/n c = 3 x 108 m/s– n = index of refraction– typically 1 < n < 2

• specular reflection i = r

• Reflected intensity ~ (n2 - n1)2/ (n2 + n1)2

– More reflection if n’s are very different

Speed of light

fast slown1 n2 > n1

i

r

n1 −n2

n1 +n2

⎛

⎝ ⎜ ⎞

⎠ ⎟

2n1 −n2

n1 +n2

⎛

⎝ ⎜ ⎞

⎠ ⎟

2

AA&A spring 2002 13

*****Reflection*****• I have a painting with a varnish overcoat. The varnish

has an index of refraction n = 1.6 and the paint (assume it to b a flat, smooth surface) has n = 2.0. Will the front surface reflection for this painting be dominantly from the air/varnish interface or the varnish/paint interface?

air/varnish interface

AA&A spring 2002 14

Surface finish—physics• Varnish

– Flat, smooth surface

– Specular reflection

– Reflected beams—single direction—(and “white”)

• Raw paint– Rough, uneven surface

– Diffuse reflection

– Reflected beams—random directions—(and “white”)

• (Two-step index change alsoreduces reflection—see T&M)

AA&A spring 2002 15

Surface finish—what do we see• Consequences

– Specular• Annoying reflections from lamps, windows

– Diffuse• Avoids annoying reflection problem by killing specular reflection • But get weak reflection of white light at all angles—“light fog,” i.e.,

colors less saturated

– Specular• Avoids reduction of color saturation• Most museums: lights and windows, if any, will be high

• Examples– Raw paint versus varnish on paintings– Matte versus glossy finish on photos– Anti-reflection versus normal glass– Unfinished versus polished (or wet) stone

AA&A spring 2002 16

White paint• White paint made of transparent

pigment and binder– Why is it white?– Why is it not transparent?

• Clouds made of transparent water– Why are clouds white?– Why are cloudy days dark?

AA&A spring 2002 17

Scattering of light

• Parallel light beam incident on sphere

• Refracted as enters the sphere

• Refracted again as leave the sphere

• Typical scattering angle ~ (n1 - n2)

• (scattering by reflection as well!)

AA&A spring 2002 18

Multiple scattering

• L = “mean free path” = typical distance before directional memory is lost

• Transmission (fraction that gets through) T = L/D

• Fraction diffusely reflected = R = (1 - L/D)

• Color reflected = color incident (usually = white)

D

AA&A spring 2002 19

Effect of binder index of refractionSmaller (n2 - n1) implies: smaller more scatterings to randomize direction longer mean free path L

deeper penetration

D

AA&A spring 2002 21

Effect of binder index of refractionSmaller (n2 - n1) implies: smaller more scatterings to randomize direction longer mean free path L

deeper penetration

glass/air glass/linseed oil

AA&A spring 2002 24

Colored pigment

• Key new property of pigment— selective absorption

• Each pigment particle like a filter

• Subtractive combination of filtering by number of particles

• Multiply transmission spectra• What are the consequences?

AA&A spring 2002 25

Filtering by multiple particles

400 500 600 700

1

0

0.5

transmission

1

2

8

16

4

Suppose light passes through n = 1, 2, …, 64 particles

32 64

AA&A spring 2002 26

Change of hue with particle number

400 500 600 700

1

0

0.5

transmission

1

2

4

8

AA&A spring 2002 27

Index of refraction difference(for fixed particle size)

• Binder and pigment—large (n1 - n2)– Short mean free path L– Typical ray gets out very quickly– Total pathlength is small– Color unsaturated and bright

• Binder and pigment better “index matched”– Long mean free path L– Typical ray penetrates deeply– Total pathlength is long– Saturated color but less bright– Possible change of hue

AA&A spring 2002 28

*****miscellaneous*****• We didn’t talk about thin paint layers, but you should be able to answer these

anyway!!!! Think about two cases, one with a white ground (reflecting any light that reaches it), the other (unconventional, but I’m a physicist) with a black one (absorbing all of the light that reaches it).

• A) Each has a thin layer of red paint on it. (Thin means some of the light reaches the ground.) Which will show the brighter color?

• B) Each has a thin layer of red paint on it. See if you argue why the one with the white ground will show the greater saturation? (If anyone asks, the answer will appear in the FAQs later in the week/)

• C) If a binder contains a mixture of two different pigments, do we need to combine the colors of the two pigments additively or subtractively?

• D) I’m mixing my own paints and find that a paint I have made gives a rather pale washed out color. Should I try to add more binder to allow the light to penetrate more deeply? Should I try to use less binder so that the light has to go through more pigment? Should I use a binder with an index of refraction closer to that of the pigment?

• A) The one with the white ground• C) Subtractively• D) no, no, yes

AA&A spring 2002 30

Light, paint and color

• A few basic ideas:– Hue, saturation and brightness– Index of refraction—refraction/reflection– Front surface of painting—diffuse/specular– Thick white paint—clear pigment/white paint– Thick red paint—many-filter model

• The subtleties: ????