AA&A spring 20021

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 “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 A “perfect”color space y = “perfect” green x = “perfect” red “perfect” blue

AA&A spring Coordinates of the CIE plot y = “perfect” green x = “perfect” red “perfect” blue

AA&A spring Mixing spectral color with white Hue –Which spectral color Saturation –How little white Brightness –How much of everything

AA&A spring ****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 Hue, saturation and brightness brightness saturation

AA&A spring 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 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 ground substrate

AA&A spring 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 10 8 m/s –n = index of refraction –typically 1 < n < 2 sin  1 /sin  2 = n 2 /n 1 –Bending ~ (n 2 - n 1 ) –More refraction if n’s are very different Speed of light fastslow n1n1 n 2 > n 1 11 22

AA&A spring Reflection Light is reflected as goes from air to water (or glass, or …) Velocity of light in medium –s = c/n c = 3 x 10 8 m/s –n = index of refraction –typically 1 < n < 2 specular reflection  i =  r Reflected intensity ~ (n 2 - n 1 ) 2 / (n 2 + n 1 ) 2 –More reflection if n’s are very different Speed of light fastslow n1n1 n 2 > n 1 ii rr

AA&A spring *****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 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 also reduces reflection—see T&M)

AA&A spring 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 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 Scattering of light Parallel light beam incident on sphere Refracted as enters the sphere Refracted again as leave the sphere Typical scattering angle  ~ (n 1 - n 2 ) (scattering by reflection as well!) 

AA&A spring 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 Effect of binder index of refraction Smaller (n 2 - n 1 ) implies: smaller  more scatterings to randomize direction longer mean free path L deeper penetration D

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AA&A spring Effect of binder index of refraction Smaller (n 2 - n 1 ) implies: smaller  more scatterings to randomize direction longer mean free path L deeper penetration glass/airglass/linseed oil

AA&A spring Particle size Larger particles of pigment implies: –larger mean free path L –longer total path in paint and –thicker paint (larger D) for same R and T Very small particles: –Scattering decreases with size as size becomes small compared with wavelength –L becomes large (perhaps as large as D) –Pigment + binder can become transparent

AA&A spring Colored pigment Each pigment particle like a filter Subtractive combination Multiply transmission spectra Saturation of color depends on total path length in pigment particles transmission

AA&A spring 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 Filtering by multiple particles transmission Suppose light passes through n = 1, 2, …, 64 particles 32 64

AA&A spring Change of hue with particle number transmission

AA&A spring Index of refraction difference (for fixed particle size) Binder and pigment—large (n 1 - n 2 ) –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 *****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 Pigment particle size (for fixed difference of index of refraction) Large particle size –Long mean free path L –Plenty of pathlength in pigment –Saturated colors Small particle size –Short mean free path L –Little pathlength in pigment –Unsaturated colors Even smaller (smaller than wavelength) –Really need different description –Talking now about ink or dye, not paint!

AA&A spring 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: ????

AA&A spring