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
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
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
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
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
Slide 50
50 Limitations
Slide 51
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.
