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Fabricating BRDFs at High Spatial Resolution Using Wave Optics

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. A ppearance fabrication. Reflectance Acquisition. Fabrication.

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Fabricating BRDFs at High Spatial Resolution Using Wave Optics

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  1. Fabricating BRDFs at High Spatial Resolution Using Wave Optics AnatLevin, Daniel Glasner, Ying Xiong, FredoDurand, Bill Freeman, WojciechMatusik, Todd Zickler. Weizmann Institute, Harvard University, MIT

  2. Appearance fabrication Reflectance Acquisition 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)

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

  4. Fabricating spatially varying BRDF Reflectance Diffuse Shiny ()

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

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

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

  8. Previous work: BRDF design • Weyrich et al. (2009); • Fabricating microgeometry for custom surface reflectance. • Matusik et al. (2009); Printingspatially-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 • Lanet 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; Cuyperset al. 12 • Holography • e.g. Yaroslavsky 2004; Benton and Bove2008 No practical surface construction Specific illumination conditions (often coherent), not general BRDF

  10. 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 0.1mm 3cm

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

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

  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 Narrow (shiny) reflectance Wide surface features x

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

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

  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 * Coherent reflectance Angular Convolution Illumination angle x

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

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

  26. Angular resolution => Spatial coherence resolution Size of spatial unit over which illumination is coherent x

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

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

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

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

  31. Angular resolution => Spatial coherence resolution Reflectance is smooth only if desired dot size Coherent size Dot size x

  32. Angular resolution => Spatial coherence resolution Reflectance is smooth only if desired dot size Coherent size Dot size x

  33. Angular resolution => Spatial coherence resolution Reflectance is smooth only if desired dot size Human eye resolution + typical angle of natural sources. => Smooth reflectance (see paper) Coherent size Dot size x

  34. Recap: Coherent BRDF = Fourier power spectrum of surface height. Incoherent BRDF = Fourier power spectrum of surface height, blurredby illumination angle.

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

  36. Surface tiling algorithm • Randomly sample steps: • Step width ~ • Step height ~(uniform) z x z x

  37. Surface tiling algorithm • Randomly sample steps: • Step width ~ • Step height ~(uniform) Coherent illumination => noisy reflectance x

  38. Surface tiling algorithm • Randomly sample steps: • Step width ~ • Step height ~(uniform) Width distribution defines reflectance: = Incoherent illumination + resolution conditions: coherent size dot size => smooth reflectance x

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

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

  41. Fabrication results 20mm Electron microscope scanning of fabricated surface

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

  43. Imaging under white illumination at varying directions wafer camera Moving light

  44. Vertical illumination Horizontal illumination Anisotropic BRDFs at opposite orientations Negative image

  45. Vertical Horizontal Negative image

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

  47. Limitations • Color and albedo cannot be controlled • Binary height restrictions: • Specular spike • BRDF must be symmetric • Simulation: eliminated with 4 different depths

  48. 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.

  49. 20mm Thank you! Wafer available after session

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