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

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

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

4 Reflectance Diffuse Shiny Fabricating spatially varying BRDF

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

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

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

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

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

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

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

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

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

14 Wave effects on light scattering z x

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

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

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

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

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

20 Speckles Noisy reflectance from an inexact surface x

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

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

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

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

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

26 Angular resolution => Spatial coherence resolution x

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

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

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

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

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

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

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

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

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

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

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

38 Surface tiling algorithm x x z z

39 Surface tiling algorithm x Coherent illumination => noisy reflectance

40 Surface tiling algorithm x

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

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

43 Fabrication results Electron microscope scanning of fabricated surface 20  m

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

Imaging under white illumination at varying directions wafer camera Moving light

Vertical illuminationHorizontal illumination Negative image Anisotropic BRDFs at opposite orientations

VerticalHorizontal Negative image

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

49 Limitations

50 Limitations

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.

Thank you!  m Wafer available after session