1 Fabricating BRDFs at High Spatial Resolution Using Wave Optics Anat Levin, Daniel Glasner, Ying...
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- Slide 1
- 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
- Slide 43
- 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.
- Slide 52
- Thank you! 52 20 m Wafer available after session