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1 Fabricating BRDFs at High Spatial Resolution Using Wave Optics Anat Levin, Daniel Glasner, Ying Xiong, Fredo Durand, Bill Freeman, Wojciech Matusik, Todd Zickler. Weizmann Institute, Harvard University, MIT

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2 Appearance fabrication Goal: Fabricating surfaces with user defined appearance Applications: - Architecture -Product design -Security markers visible under certain illumination conditions -Camouflage - Photometric stereo (Johnson&Adelson 09) Reflectance Acquisition Fabrication

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3 BRDF (Bidirectional Reflectance Distribution Function) z Dot (pixel) unit on surface ? x

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4 Reflectance Diffuse Shiny Fabricating spatially varying BRDF

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5 Controlling reflectance via surface micro-structure Reflectance Diffuse Shiny Surface micro structure What surface micro- structure produces certain reflectances?

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6 Surface Reflectance Previous work: BRDF fabrication using micro- facets theory (Weyrich et al. 09) 3cm Surface: oriented planner facets Limited spatial resolution Dot size ~ 3cm x 3cm

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7 Micro-facet model: limitations 3cm 0.3cm 0.03cm 0.003cm Surface scale Reflectance Wave effects at small scales => Substantial deviation from geometric optics prediction

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8 Previous work: BRDF design Weyrich et al. (2009); Fabricating microgeometry for custom surface reflectance. Matusik et al. (2009); Printing spatially-varying reflectance Finckh et al. (2010); Geometry construction from caustic images Dong et al. (2010); Fabricating spatially-varying subsurface scattering. Papas et al (2011); Goal-based caustics. Malzbender et al. (2012); Printing reflectance functions Lan et al. (2013); Bi-Scale Appearance Fabrication Geometric Optics

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9 Previous work: Wave scattering Wave models for BRDF: He et al. 91; Nayar et al. 91; Stam 99; Cuypers et al. 12 Holography e.g. Yaroslavsky 2004; Benton and Bove 2008 No practical surface construction Specific illumination conditions (often coherent), not general BRDF

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10 Contributions: Extra high resolution fabrication Analyze wave effects under natural illumination Analyze spatial-angular resolution tradeoffs Practical surface design algorithm compatible with existing micro-fabrication technology 3cm 0.1mm

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11 Surface should be stepwise constant with a small number of different depth values x z Prototype: Binary depth values Restricts achievable BRDFs 11 Photolithography and its limitations Geometric optics predicts: surface is a mirror Wave optics: variety of reflectance effects

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12 Preview: reflectance = Fourier transform Reflectance Diffuse Shiny Surface micro-structure Anisotropic Wide Narrow Wide

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13 Background: understanding light scattering 1. Coherent illumination: laser in physics lab 2. Incoherent illumination: natural world

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14 Wave effects on light scattering z x

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15 Surface scattering Fourier transform 2 Fourier transform See also: He et al. 91 Stam 99 z x

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16 Inverse width relationship 2 Wide surface features Narrow (shiny) reflectance x

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17 Inverse width relationship 2 Wide (diffuse) reflectance x Narrow surface features

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18 Inverse width relationship 2 impulse (mirror) reflectance x Flat surface

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19 Reflectance design with coherent illumination: Fourier power spectrum of surface height to produce reflectance Challenges: Complex non-linear optimization May not have a solution with stepwise constant heights Inexact solutions: speckles

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20 Speckles Noisy reflectance from an inexact surface x

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21 Reflectance design with coherent illumination: Fourier power spectrum of surface height to produce reflectance Challenges: Complex non-linear optimization May not have a solution with stepwise constant heights Inexact solutions: speckles Our approach: Bypass problems utilizing natural illumination Pseudo random surface replaces optimization Need to model partial coherence

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22 Incoherent illumination: Point source=> Area source Area source = collection of independent coherent point sources x

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23 Incoherent reflectance: blurring coherent reflectance by source angle * x Angular Convolution Illumination angle Coherent reflectance

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24 Reflectance averaged over illumination angle is smooth x 24 Incoherent reflectance: blurring coherent reflectance by source angle

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25 Challenge: avoiding speckles Angular v.s. spatial resolution tradeoffs. Partial coherence. Our analysis:

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26 Angular resolution => Spatial coherence resolution x

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27 Angular resolution => spatial coherence resolution x Coherent area Phase change Coherent: Incoherent: Partial coherent:

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28 Angular resolution -> spatial coherence resolution x Coherent area Coherent: Incoherent: Partial coherent:

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29 Angular resolution => Spatial coherence resolution x Each coherent region emits a coherent field with speckles

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30 Angular resolution => Spatial coherence resolution x Each coherent region emits a coherent field with speckles

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31 Angular resolution => Spatial coherence resolution x Each coherent region emits a coherent field with speckles

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32 Angular resolution => Spatial coherence resolution Averaging different noisy reflectances from multiple coherent regions => smooth reflectance. x

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33 Angular resolution => Spatial coherence resolution x Dot size Coherent size

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34 Angular resolution => Spatial coherence resolution x Coherent size Dot size

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35 Angular resolution => Spatial coherence resolution x Dot size Coherent size Human eye resolution + typical angle of natural sources. => Smooth reflectance (see paper)

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36 Recap: Coherent BRDF = Fourier power spectrum of surface height. Incoherent BRDF = Fourier power spectrum of surface height, blurred by illumination angle.

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Next: Design surface height to produce desired BRDF. Coherent design: Fourier power spectrum to produce BRDF - Complex non linear optimization Incoherent design: Blurred Fourier power spectrum to produce BRDF - Pseudo randomness is sufficient

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38 Surface tiling algorithm x x z z

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39 Surface tiling algorithm x Coherent illumination => noisy reflectance

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40 Surface tiling algorithm x

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Step size distribution 41 Surface sampling Sampled surface micro-structure Reflectance Diffuse Glossy Shiny

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42 BRDFs produced by our approach Anisotropic Anisotropic anti-mirrors Isotropic Anti-mirror

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43 Fabrication results Electron microscope scanning of fabricated surface 20 m

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44 Imaging reflectance from fabricated surface Specular spike, artifact of binary depth prototype, can be removed with more etching passes (see paper)

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Imaging under white illumination at varying directions wafer camera Moving light

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Vertical illuminationHorizontal illumination Negative image Anisotropic BRDFs at opposite orientations

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VerticalHorizontal Negative image

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Narrow Isotropic Anti- mirror large incident angle: Anti-mirror kids: bright Background: dark Small incident angle: Anti-mirror kids: dark Background: bright

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49 Limitations

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50 Limitations

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51 Summary Spatially varying BRDF at high spatial resolution (220 dpi). Analyze wave effects under natural illumination. Account for photolithography limitations. Pseudo randomness replaces sophisticated surface design.

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Thank you! 52 20 m Wafer available after session