Light Field: New opportunities and applications

2,463 views

Published on

CVPR 2009 Short Course on Light Field: Present and Future
slide 5/6

Published in: Technology, Spiritual
0 Comments
4 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
2,463
On SlideShare
0
From Embeds
0
Number of Embeds
10
Actions
Shares
0
Downloads
0
Comments
0
Likes
4
Embeds 0
No embeds

No notes for slide

Light Field: New opportunities and applications

  1. 1. Light Fields in Ray and Wave Optics Introduction to Light Fields: Ramesh Raskar Wigner Distribution Function to explain Light Fields: Zhengyun Zhang Augmenting LF to explain Wigner Distribution Function: Se Baek Oh Q&A Break Light Fields with Coherent Light: Anthony Accardi New Opportunities and Applications: Raskar and Oh Q&A: All
  2. 2. New opportunities and Applications Se Baek Oh & Ramesh Raskar
  3. 3. Message • LF is a very powerful tool to understand wave-related phenomena • and potentially design and develop new systems and applications 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 3
  4. 4. Outline On wavefront coding holography 315 rendering the screen was very large. As expected, we see (Fig. 9) th Fraunhofer diffraction pattern. 1.1. Double-helix point spread function (DH-PSF) A DH-PSF system can be implemented by introducing a phase mask in the Fourier plane of an otherwise standard imaging system. The phase mask is designed such that its transmittance function generates a rotating pattern in the focal region of a Fourier transform lens [15-18]. Specifically, the DH-PSF exhibits two lobes that spin around the opticalaperture. An animate Figure 9: Diffraction from a square axis as shown in Fig. 1(a). Note that DH-PSF displays this experiment with of orientation with defocusappears in of a significant change varying the aperture size over an gaussian beam rotating PSF extended depth. In contrast, the standard PSF presents a slowly changing and expanding plementary material as a video. The distance from the ap symmetrical pattern throughout the same region [Fig. 1(b)]. the screen is 1 m. 316 317 Double rectangular apertures: Next we created two r lar apertures and probe them with the AMP. Note that we 3D Optical Fig. 1. Comparison of the (a) DH-PSF and the (b) standard PSF at different axial planes for a Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future system with 0.45 numerical aperture (NA) and 633nm wavelength. 4
  5. 5. Augmented LF light field transformer WDF LF LF LF LF negative radiance Augmented LF (diffractive) optical element Light Field LF propagation LF propagation 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 5
  6. 6. Wavefront coding • ALF of a phase mask(slowly varying ϕ(x)) λ ∂φ T (x, θ) = δ θ − 2π ∂x conventional wavefront coding extended DOF (w/ deconvolution) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 6
  7. 7. Holography Recording Reconstruction object hologram 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  8. 8. Holography Recording Reconstruction laser object object wave hologram 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  9. 9. Holography Recording Reconstruction laser object object wave reference wave hologram 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  10. 10. Holography Recording Reconstruction laser object object wave reference wave hologram hologram 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  11. 11. Holography Recording Reconstruction laser object object wave reference reference wave hologram wave hologram 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  12. 12. Holography Recording Reconstruction laser object object wave reference reference wave hologram wave hologram 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  13. 13. Holography Recording Reconstruction laser object virtual image object wave reference reference wave hologram wave hologram observer 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  14. 14. Holography Recording Reconstruction laser object virtual image object wave real image reference reference wave hologram wave hologram observer 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
  15. 15. Holography • For a point object recording reconstruction 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 8
  16. 16. Rendering Online Submi the screen was very large. As expected, we see (Fig. 9) the typical 315 3 • Using virtual Fraunhofer light sources in photon mapping diffraction pattern. 3 3 3 3 3 white light 3 3 3 3 3 3 3 rectangular aperture screen Augmented Photon Mapping for Wavefront Transmission Effects 3D Optical Figure 9: Diffraction S. B. Oha square aperture. An animated version from et al. (2009) Se Baek Oh Systems Group of this experiment with varying the aperture sizePresent and Future 9 CVPR 2009 - Light Fields: appears in the sup-
  17. 17. Gaussian Beam (from a laser pointer) • Beam from a laser • a solution of paraxial wave equation 20 mm beam width 20 m distance 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 10
  18. 18. Gaussian Beam • ALF (and WDF) of the Gaussian Beam is also Gaussian in x-θ space θ x z x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 11
  19. 19. Gaussian Beam • ALF (and WDF) of the Gaussian Beam is also Gaussian in x-θ space θ x z x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 11
  20. 20. Gaussian Beam • ALF (and WDF) of the Gaussian Beam is also Gaussian in x-θ space θ x z x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 11
  21. 21. Gaussian Beam • ALF (and WDF) of the Gaussian Beam is also Gaussian in x-θ space θ x z x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 11
  22. 22. Gaussian Beam x-θ space z-x space 20 mm beam 20 m distance width 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 12
  23. 23. Unusual PSF for depth Double-helix point spread function (DH-PSF) from defocus -PSF system can be implemented by introducing a phase mask in the Fourier plane of an wise standard imaging system. The phase mask is designed such that its transmittance on generates a rotating pattern in the focal region of a Fourier transform lens [15-18]. fically, the DH-PSF exhibits two lobes that spin around the optical axis as shown in Fig. Note that DH-PSF displays a significant change of orientation with defocus over an standard PSF DH PSF ded depth. In contrast, the standard PSF presents a slowly changing and expanding Defocus circle with distance metrical pattern throughout the same region [Fig. 1(b)]. 1µm 1µm 3D positions 3 5 2 1 4 Fig. 1. Comparison of the (a) DH-PSF and the (b) standard PSF at different axial planes for a system with 0.45 numerical aperture (NA) and 633nm wavelength. hile Prof. Rafael Piestun’s group provide valuable insight on wave propagation analytical solutions for helical beams Courtesy of S. R. P. Pavani and Univ. of Colorado@Boulder can be used in photon-unlimited applications [16], they do not provide the high- ency transfer functions required for photon-limited systems. Hence, we use a design that U. of Colorado@Boulder nes the helical pattern Optical specific axial range of interest to attain high efficiency 3D Se Baek Oh standardto aGroup ms [15]. Unlike Systems CVPR 2009 - Light and astigmatic PSFs, the DH-PSF concentrates its energy in its Fields: Present and Future 13
  24. 24. Reference • “Wave propagation with rotating intensity distributions,” Y.Y. Schechner, R. Piestun, and J. Shamir, Phys. Rev. E 54: R50–R53 (1996) Concept • “Wave fields in three dimensions: analysis and synthesis,” R. Piestun, B. Spektor, and J. Shamir, J. Opt. Soc. Am. A 13:1837-1848 (1996) • “Propagation-invariant wave fields with finite energy,” R. Piestun,Y.Y. Schechner, and J. Shamir, J. Opt. Soc. Am. A 17:294-303 (2000) Implement • "Depth from diffracted rotation," A. Greengard,Y.Y. Schechner, and R. Piestun, Opt. Lett., 31(2):181-183, (2006) ation • "High-efficiency rotating point spread functions", S. R. P. Pavani and R. Piestun, Opt. Express, 16(5):3484-3489, (2008) • “Three-Dimensional Single-Molecule Fluorescence Imaging Beyond the Diffraction Limit Using a Double-Helix Point Spread Function,” S. R. P. Pavani, M. A. Thompson, Microscope J. S. Biteen, S. J. Lord, N. Liu, R. I. Twieg, R. Piestun, and W. E. Moerner, PNAS, 106: 2995, (2009) • “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system, “ S. R. P. Pavani, A. Greengard, and R. Piestun, APL (2009)  In Press 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 14
  25. 25. Gauss-Laguerre mode 2 1/2 w(ˆ) = w0 1 + z z ˆ √ U(r, t) = u(r) exp [i(kz − ωt)] 2w0 w 0 Orthogonal basis in the cylindrical coordinate unm (r) = G(ˆ, z )Rnm (ˆ)Ψm (φ)Zn (ˆ) ρ ˆ ρ z z0 (0,0): Gaussian beam ρ z ρ= ˆ z= ˆ w(ˆ) z z0 w0 G(ˆ, z ) = ρ ˆ exp −ˆ2 exp iˆ2 z exp (−iψ(ˆ)) ρ ρ ˆ z πw0 2 w(ˆ) z z0 = √ |m| λ |m| Rnm (ˆ) = ρ 2ˆ ρ L(n−|m|)/2 (2ˆ2 ) ρ Zn (ˆ) = exp {−inψ(ˆ)} z z Ψ(φ) = exp(imφ) ψ(ˆ) = arctan(ˆ) : Gouy phase z z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 15
  26. 26. Rotating PSF GL modal plane • Rotating beams 10 • Superposition along a straight line n • Rotation rate related to slope of 5 line • Both intensity and phase rotate 0 • Maximum rotation rate in Rayleigh -10 -5 0 m 5 10 range intensity Courtesy of S. R. P. Pavani 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
  27. 27. Rotating PSF Rotating PSF HER-PSF 1.84% 57.01% Courtesy of S. R. P. Pavani 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 17
  28. 28. Conceptually... y x z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 18
  29. 29. Conceptually... y x z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 18
  30. 30. Conceptually... y x z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 19
  31. 31. Conceptually... y x z other modes need to be balanced... 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 19
  32. 32. WDF (ALF) of (1,1) order GL modal plane 10 intensity n 5 0 -10 -5 0 5 10 m R. Simon and G. S. Agarwal, "Wigner representation of Laguerre-Gaussian beams", Opt. Lett., 25(18), (2000) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 20
  33. 33. intensity in x-y y x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 21
  34. 34. intensity in x-y WDF in θx- θy y θy x θx 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 21
  35. 35. intensity in x-y WDF in θx- θy y θy x θx WDF in θx- θy θy 3D Optical θx Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 21
  36. 36. WDF in θx- θy θy intensity in x-y WDF in θx- θy θx y θy x θx WDF in θx- θy θy 3D Optical θx Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 21
  37. 37. Future direction • Reflectance (e.g. BRDR/BTF) model • Tomography & Inverse problems • Beam shaping/phase mask design by ray- based optimization • New processing w/ virtual light source 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 22
  38. 38. Space of LF representations Time-frequency representations Phase space representations Quasi light field
  39. 39. Space of LF representations Time-frequency representations Phase space representations Quasi light field incoherent coherent
  40. 40. Space of LF representations Time-frequency representations Phase space representations Quasi light field Traditional light field incoherent coherent
  41. 41. Space of LF representations Time-frequency representations Phase space representations Quasi light field WDF Traditional light field incoherent coherent
  42. 42. Space of LF representations Time-frequency representations Phase space representations Quasi light field Observable LF WDF Traditional light field incoherent coherent
  43. 43. Space of LF representations Time-frequency representations Phase space representations Quasi light field Observable LF WDF Augmented LF Traditional light field incoherent coherent
  44. 44. Space of LF representations Time-frequency representations Phase space representations Quasi light field Observable LF WDF Augmented LF Traditional light field incoherent Rihaczek Distribution Function coherent
  45. 45. Space of LF representations Time-frequency representations Phase space representations Quasi light field Other LF representations Observable LF WDF Augmented LF Other LF Traditional representations light field incoherent Rihaczek Distribution Function coherent
  46. 46. Property of the Representation Constant along Interference Non-negativity Coherence Wavelength rays Cross term Traditional LF always always only zero no constant positive incoherent nearly always any Observable LF constant positive coherence any yes state only in the positive and Augmented LF paraxial region negative any any yes only in the positive and WDF paraxial region negative any any yes Rihaczek DF no; linear drift complex any any reduced 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 24
  47. 47. Benefits & Limitations of the Representation Adaptability Ability to Modeling Simplicity of to current Near Field Far Field propagate wave optics computation pipe line Traditional Light Fields x-shear no very simple high no yes Observable not x- yes modest low yes yes Light Fields shear Augmented Light Fields x-shear yes modest high no yes WDF x-shear yes modest low yes yes better than Rihaczek DF x-shear yes WDF, not as low no yes simple as LF 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 25
  48. 48. Conclusions • Wave optics phenomena can be understood with geometrical ray based representation • There are many different phase-space representations • We hope to inspire researchers in computer vision/graphics as well as in optics graphics to develop new tools and algorithms based on joint exploration of geometric and wave optics concepts 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 26

×