pigmented colorants: dependence on media and time - Cornell ...

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Figure A.2: The path of light between two homogeneous layers. Adapted from [Kub54] Summing the portions reflected by the layered specimen, we have T1T1 ′R2 Rtotal = R1 + T1T1 ′R2(1 + R1 ′R2 + R 2 1 ′R2 2 + ···)=R1 + 1 − R1 ′R2 207 (A.23) For any homogeneous layer, R1 = R1 ′, or the material reflects light equally when illuminated from both sides. Also, it can be shown that T1 = T1 ′,orthe transmittance has the same value, if we illuminate a homogeneous layer from one side or the other. Therefore, the formulas simplify to: Ttotal = T1T2 1 − R1R2 Rtotal = R1 + T 2 1 R2 1 − R1R2 (A.24) (A.25) The compositing equations can be used to calculate the reflectance of spec- imens that contain more than two layers (which is often the case in painting).
One concatenates the layers into a single reflectance value by obtaining R and T from two layers, and using that value for the next compositing operation. For instance, a specimen with three homogeneous layers has reflectance R1,R2,R3 and transmittance T1,T2,T3: R1,2 = T1T2 1 − R1R2 T1,2 = R1 + T 2 1 R2 1 − R1R2 R1,2,3 = T1,2T3 1 − R1,2R3 T1,2,3 = R1,2 + T 2 1,2R3 1 − R1,2R3 208 (A.26) (A.27) (A.28) (A.29)
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PIGMENTED COLORANTS: DEPENDENCE ON
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ABSTRACT We present a physically ba
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Acknowledgements This work would no
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Table of Contents 1 Introduction 1
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List of Tables 2.1 Average pigment
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3.15 Photoreceptor absorption .....
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B.15 Variation of spectral reflecta
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corrode the surfaces of materials.
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Figure 1.1: Detail of the Azor-Sado
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However, since mural artwork is typ
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at a very high quality (albeit limi
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heterogeneous sum of very different
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which linseed oil derives (the most
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oration of a rigidly painted layer
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ing will hit the ground and reflect
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tion of paint tubes in 1841 and the
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Figure 2.8: Natural pigments of ant
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ecome more common recently. The Ame
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A V = O(r2 ) O(r3 ) = 1 O(r) 24 (2.
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Table 2.2: Pigment specific gravity
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provide the underlying color to a p
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though the speed of light in air is
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In general, when light travels from
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materials while lit from behind. Li
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Table 2.4: Index of refraction η f
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to completely congeal. Hence, these
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ond together to form proteins. Exam
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to its original state by any means.
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While it has been used since the 19
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organic binder found in more conven
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3.1.1 Visible Light Spectrum Light
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Figure 3.2: Hue, brightness and sat
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measures how much light is reflecte
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Figure 3.6: Additive color mixing o
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Figure 3.9: The physical amount of
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The vascular tunic lies on the wall
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Figure 3.11: Cross section of the r
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Not all areas have the same sensiti
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identify and distinguish between va
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that range between zero and full in
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spectrum. This insures that the res
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Figure 3.19: Graphical representati
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X x = (X + Y + Z) Y y = (X + Y + Z)
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color into the appropriate RGB colo
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components in the image (the smalle
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haviors of subtractive mixing and i
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of perceptually equal sizes. Unfort
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enabling one to transform between t
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andwidth as converted signals are s
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Figure 3.28: Retinal ganglion recep
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example shown in Figure 3.28. Under
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Figure 3.31: The work of Josef Albe
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sensations for each trial and picke
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Chapter 4 Previous Work There is no
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different location. Subsurface scat
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describes the scattering and absorp
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only accounts for a small percentag
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σ ′ t = σa + σ ′ s and α
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104 Figure 4.4: A model of an alaba
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effects or are too computationally
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108 Figure 4.6: Results using Kubel
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specifying pigments works adequatel
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color representation, it is not fea
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time. A metallic surface patina is
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the system consisted of wetness and
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or darkening enables the museum per
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in front of a displayed work. Felle
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light exposure. This effect is espe
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over time. Perceptually, these hues
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The rate of change of the concentra
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over white grounds) suffer the grea
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protects the deeper remaining color
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light source. This method is used w
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chemical smog and have been identif
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Chapter 5 Preparation & Measurement
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tending transparent pigments used i
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140 Figure 5.1: Spectral reflectanc
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the requirements of the work at han
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144 Figure 5.2: Left: Magnified vie
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Table 5.2: Relevant data regarding
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historically one of the best grades
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created far too strong of a binder,
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too brittle and cracking. While wor
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154 Figure 5.4: Reflectance values
Page 169 and 170: 5.1.5 Painting After the layers of
Page 171 and 172: The gray card reflected 18% of the
Page 173 and 174: 160 Figure 5.8: The optical setup f
Page 175 and 176: Note that harmonics reflect at the
Page 177 and 178: Note that the calibration factors f
Page 179 and 180: Chapter 6 Experimental Results 6.1
Page 181 and 182: 168 Figure 6.1: Lapis Lazuli in dif
Page 183 and 184: (such as CIE standards C, D50, orD6
Page 185 and 186: 172 Table 6.2: Perceptual differenc
Page 187 and 188: 174 Figure 6.3: Munsell plots of La
Page 189 and 190: and j has a saturation of red rsat,
Page 191 and 192: 178 Figure 6.4: Variation of spectr
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Page 195 and 196: 182 Figure 6.5: Munsell plots of La
Page 197 and 198: trying to match color ca from the p
Page 199 and 200: as it ages. This is in direct contr
Page 201 and 202: teractive viewer. In our applicatio
Page 203 and 204: 190 Figure 7.1: Our simulated canva
Page 205 and 206: where n is the normal at the curren
Page 207 and 208: In summary, our implementation prov
Page 209 and 210: Chapter 8 Conclusion We have studie
Page 211 and 212: inks are beginning to find their wa
Page 213 and 214: Appendix A Derivation of K-M theory
Page 215 and 216: ∆i − =(K + S) idx 202 ∆j −
Page 217 and 218: Equation A.8 is now: Rearranging yi
Page 219: and if the paint is infinitely thic
Page 223 and 224: 210 Figure B.1: Cold Glauconite in
Page 225 and 226: Table B.1: Color conversions from t
Page 227 and 228: 214 Figure B.4: Munsell plots of Co
Page 229 and 230: 216 Figure B.5: Burnt Sienna in dif
Page 233 and 234: 220 Figure B.8: Munsell plots of La
Page 235 and 236: 222 Figure B.9: Red Ochre Tint in d
Page 239 and 240: 226 Figure B.12: Munsell plots of C
Page 241 and 242: 228 Figure B.13: Variation of spect
Page 243 and 244: 230 Figure B.15: Variation of spect
Page 245 and 246: Table B.13: Color conversions of Bu
Page 247 and 248: 234 Figure B.18: Munsell plots of C
Page 249 and 250: 236 Figure B.20: Munsell plots of R
Page 251 and 252: References [Alb71] Josef Albers. In
Page 253 and 254: 240 [GLL + 04] Michael Goesele, Hen
Page 255 and 256: 242 [KM31] Paul Kubelka and Franz M
Page 257 and 258: [Rat72] Floyd Ratliff. Contour and
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