1. Diffusion Coding Photography for Extended Depth of Field SIGGRAPH 2010 Ollie Cossairt, Changyin Zhou, Shree Nayar Columbia University

2. Conventional Camera (F/1.8)

3. Focused Image PSFImage Noise Captured Image Camera Blur Model Spatial domain Focused ImageMTF Image Noise Captured Image Frequency domain

4. Deblurring Problems MTFCaptured image Low SNR low MTF values Problem 1: Focused image Lens Sensor P Object Q Problem 2: Variation with depth

5. Extending Depth of Field: Previous Work Focus Sweep Cameras [Hausler ’72] [Nagahara et al. ’08] LensFocal PlaneSensor Wavefront Coding Cameras [Dowski and Cathey ’95] [Chi and George ’01] [Garcia-Guerrero et al. ‘07] Other Related Work [Levin et al. ’07] [Veeraraghavan et al. ’07] [Levin et al. ’09]

6. Focus Sweep Camera Lens Scene Sensor ++++++ = Instantaneous PSF t = 1 t = 2t = 3t = 4t = 5t = 6t = 7 Final PSF [Hausler ’72] [Nagahara et al. ’08]

7. Focus Sweep Camera ++++++ = Instantaneous PSF t = 1t = 2t = 3t = 4t = 5t = 6t = 7 Final PSF Instantaneous PSF t = 1 + t = 2 + t = 3 + t = 4t = 5 + t = 6 + t = 7 + depth 1 depth 2 [Levin et al. ’09] 2D MTF = Final PSF Lens Scene Sensor [Hausler ’72] [Nagahara et al. ’08]

8. Wavefront Coding Lens Scene Sensor [Levin et al. ’09] 2D MTF Cubic Phase Plate xu [Dowski and Cathey ’95] Ambiguity Function slice MTF

9. Lens Resolution Target Sensor Focus Sweep Wavefront Coding EDOF Camera Comparison depth

10. Focus Sweep Wavefront Coding Deblurred image EDOF Camera Comparison

11. Deblurring Error vs. Depth Deblurring Error noise Deblurring Error Depth Wavefront Coding Focus Sweep Wavefront Coding

12. Is it possible to achieve the performance of focus sweep without moving parts?

13. Optical Diffusers Circular diffuser [http://www.luminitco.com] Diffuser sheets w SensorDiffuser Light ray x x Scatter function w SEM image

14. Diffuser Kernels LensSensor x u A u x A/2 -A/2 With diffuser A/2 -A/2 u x Without diffuser Light field space

15. w w A/2 -A/2 u x Without diffuser Diffuser Kernels LensSensor w u x With diffuser w Light field space x u

16. Diffuser Kernels LensSensor w u x A/2 -A/2 u x u x Diffuser kernel Light fieldDiffuser kernelCoded light field x u Without diffuserWith diffuser Light field space

17. Diffusion Coded PSF A/2 -A/2 u x Without diffuser u x With diffuser u x Diffuser kernel x project x Light field space x project Sensor space Camera PSFScatter functionCoded PSF

18. Radially Symmetric Light Field For an on-axis, isotropic point source:

19. Radially Symmetric Diffuser For a radially-symmetric diffuser kernel

20. Radially Symmetric Diffuser PSFs Radially symmetric diffuser Coded PSFScatter functionCamera PSF Coded PSFScatter functionCamera PSF Conventional diffuser Normalized frequency PSF Vs. Depth MTF Vs. Depth -50px50px-50px50px-50px50px-50px50px depth

21. Diffusion Coding Performance Deblurring Error vs. Depth Depth Wavefront Coding Focus Sweep noise Diffusion Coding (light field) Diffusion Coding (wave optics) Similar performance to focus sweep without moving parts

22. Diffuser Implementation Diffuser scatter function r (mm) 110 Thickness (um) 3 8 6 3 2 1 r (mm) [www.rpcphotonics.com] Diffuser heightmapFabricated Diffuser Diffuser surface profile [Sales et al. ‘03]

23. Garcia-Guerrero Comparison with Prior Work Deblurring Error vs. Depth Depth Diffusion Coding Diffusion coding significantly outperforms prior work

24. Diffusion Coding Experiments Fabricated DiffuserCannon 50mm EF lensCannon 450D Sensor Experimental Setup Measured PSFs depth Without diffuser with diffuser BM3D Deblurring Algorithm [Dabov et al. ‘08]

25. Examples

26. Conventional Camera f-number = 1.8, exposure time = 16ms

27. Conventional Camera f-number = 18, exposure time = 16ms

28. Diffusion Coding Captured f-number = 1.8, exposure time = 16ms

29. Diffusion Coding Deblurred f-number = 1.8, exposure time = 16ms

30. Conventional Camera f-number = 1.8 exposure time = 10ms

31. Diffusion Coding f-number = 1.8 exposure time = 10ms Captured

32. Diffusion Coding f-number = 1.8 exposure time = 10ms Deblurred

33. Conventional Camera f-number = 1.8 exposure time = 12.5ms

34. Diffusion Coding f-number = 1.8 exposure time = 12.5ms Captured

35. Diffusion Coding f-number = 1.8 exposure time = 12.5ms Deblurred

36. Conventional Camera f-number = 1.8, exposure time = 16ms

37. Diffusion Coding Captured f-number = 1.8, exposure time = 16ms

38. Diffusion Coding Deblurred f-number = 1.8, exposure time = 16ms

39. Limitations Conventional CameraDiffusion Coding Loss of image texture Loss of contrast Occlusion errors

40. Conclusions Diffusion Coding Theory Diffusion Coding Examples Radially Symmetric Diffusers Lens Sensor Diffuser Diffusion Coding Implementation