Light Fields in Ray and Wave Optics

Introduction to Light Fields: 
    
      
           
   
     Ramesh Raskar

Wigner...
Space of LF representations
Time-frequency representations
Phase space representations
Quasi light field

                 ...
Augmenting Light Fields
explaining Wigner Distribution Function with LF



                       Se Baek Oh
             ...
Traditional
                             Light Field




             3D Optical
Se Baek Oh   Systems Group            CVP...
Motivation


       Traditional
       Light Field




             3D Optical
Se Baek Oh   Systems Group         CVPR 200...
Motivation

                                           light field
                                          direction
    ...
Motivation


       Traditional
       Light Field




                                                  http://graphics.s...
Motivation


       Traditional
       Light Field


 ray optics based
 simple and powerful

                             ...
Motivation

                             Wigner
                             Distribution
                             Fun...
Motivation
                             rigorous but cumbersome
                             wave optics based

          ...
Motivation
                              rigorous but cumbersome
                              wave optics based

        ...
Augmented LF
                              rigorous but cumbersome
                              wave optics based

      ...
Augmented LF
                              rigorous but cumbersome
                              wave optics based

      ...
Augmented LF
                              rigorous but cumbersome
                              wave optics based

      ...
Augmented LF
                              rigorous but cumbersome
                              wave optics based

      ...
Augmented LF
             • not a new light field
             • a new methodology/framework to create,
               modu...
Augmented LF framework

             LF


                              (diffractive)
                                 opt...
Augmented LF framework

             LF                    LF


                                        (diffractive)
    ...
Augmented LF framework
                                      light field
                                    transformer

 ...
Augmented LF framework
                                      light field
                                    transformer

 ...
Augmented LF framework
                                      light field
                                    transformer

 ...
Augmented LF framework
                                           light field
                                         tran...
outline




             3D Optical
Se Baek Oh   Systems Group       CVPR 2009 - Light Fields: Present and Future   10
outline
             • Limitations of Light Field analysis




               3D Optical
Se Baek Oh     Systems Group     ...
outline
             • Limitations of Light Field analysis
             • Augmented Light Field
              • free-space...
outline
             • Limitations of Light Field analysis
             • Augmented Light Field
              • free-space...
outline
             • Limitations of Light Field analysis
             • Augmented Light Field
              • free-space...
Assumptions
             • monochromaticinto polychromatic coherent)
                                (= temporally
       ...
Young’s experiment
                                                     screen
   light from       double
      a laser   ...
Young’s experiment
                                                     screen
   light from       double
      a laser   ...
Young’s experiment
                                                     screen
   light from       double
      a laser   ...
Young’s experiment
                                                          screen
   light from       double
      a las...
Young’s experiment
      x        θ+

                                        θ                         u (= θ/λ)
  A


  ...
Young’s experiment
              θ+                  x

                                                    θ             ...
Young’s experiment
                                                     projection                      projection


     ...
Wigner Distribution Function
                                      x                   x
             Wg (x, u) =         ...
Wigner Distribution Function
                                   x              x
             Wg (x, u) =      g x+     g ...
Wigner Distribution Function
                                   x              x
             Wg (x, u) =      g x+     g ...
Wigner Distribution Function
                                   x              x
             Wg (x, u) =      g x+     g ...
Wigner Distribution Function
                                   x                x
             Wg (x, u) =      g x+     ...
Wigner Distribution Function
                                   x                x
             Wg (x, u) =      g x+     ...
Wigner Distribution Function
                                   x                x
             Wg (x, u) =      g x+     ...
Wigner Distribution Function
                                   x                x
             Wg (x, u) =      g x+     ...
Wigner Distribution Function
             plane wave          spherical wave




             point source        incohere...
Augmented Light Field
             1. free-space propagation
2. virtual light projector with negative radiance
           ...
Free-space propagation
             • In homogeneous medium and the paraxial
               region,
              • LF = A...
Free-space propagation
             • two plane parameterization
                                                         ...
Free-space propagation
             • two plane parameterization
                                                         ...
Free space propagation
             • wave optics: Huygen’s principle
              • point sources on the wavefront
     ...
Free space propagation
             • wave optics: Huygen’s principle
              • point sources on the wavefront
     ...
Free space propagation
             • Mathematical description
                                      j 2π r
              ...
Free space propagation
             • Mathematical description
                                      j 2π r
              ...
Free space propagation
             • with the paraxial approximation
                    spherical
                    wa...
Free space propagation
             • with the paraxial approximation
                    spherical
                    wa...
Fresnel propagation
             • w/ WDF   x                                          x
                              E1 ...
Fresnel propagation
             • w/ WDF   x                                          x
                              E1 ...
Fresnel propagation
             • w/ WDF   x                                                   x
                        ...
Fresnel propagation
             • w/ WDF   x                                                    x
                       ...
Fresnel propagation
             • w/ WDF   x                                                      x
                     ...
diffraction vs. distance


                 single slit
                 a = 64λ




         laser
                      ...
diffraction vs. distance
              Position and Direction
                   in Wave Optics
                 single sl...
diffraction vs. distance
              Position and Direction
                   in Wave Optics
              near zone: f...
diffraction vs. distance
              Position and Direction
                   in Wave Optics
              near zone: f...
Augmented Light Field
             1. free-space propagation
2. virtual light projector with negative radiance
           ...
Virtual light projector
                                WDF
                 Augmented LF

             Traditional
      ...
Young’s experiment
                                  x

                                                    θ             ...
Young’s experiment
                                                     projection                       projection

     ...
Young’s experiment
                                                     projection                       projection

     ...
Virtual light projector
                                                          projection




             real project...
Virtual light projector
                                                                projection




                   ...
Virtual light projector

                                                              first null
             real project...
Virtual light projector

                                                              first null
             real project...
Virtual light projector

                                            hyperbola              first null
                    ...
Virtual light projector
                                                destructive interference
    in high school physic...
Virtual light projector
                                              destructive interference
    in high school physics ...
Question
             • Does a virtual light projector also work for
                incoherent light?




               ...
Question
             • Does a virtual light projector also work for
                incoherent light?
             • Yes!...
Coherence
             • Degree of making interference
              •     coherent                   partially coherent  ...
Coherence
             • throwing stones......




               3D Optical
Se Baek Oh     Systems Group           CVPR 2...
Coherence
             • throwing stones......



                single point source




               3D Optical
Se Bae...
Coherence
             • throwing stones......



                single point source
                               coher...
Coherence
             • throwing stones......



                single point source            many point sources
      ...
Coherence
             • throwing stones......



                single point source            many point sources
      ...
Coherence
             • throwing stones......



                single point source              many point sources
    ...
Coherence
             • Temporal coherence: E(p, t )E (p, t )        1
                                                  ...
Example




             3D Optical
Se Baek Oh   Systems Group       CVPR 2009 - Light Fields: Present and Future   38
Example
       Temporally incoherent;
         spatially coherent




             3D Optical
Se Baek Oh   Systems Group  ...
Example
       Temporally incoherent;
         spatially coherent




             3D Optical
Se Baek Oh   Systems Group  ...
Example
       Temporally incoherent;
                                Temporally & spatially coherent
         spatially c...
Example
       Temporally incoherent;
                                Temporally & spatially coherent
         spatially c...
Example
       Temporally incoherent;
                                       Temporally & spatially coherent
         spat...
Example
       Temporally incoherent;
                                       Temporally & spatially coherent
         spat...
Example
       Temporally incoherent;
                                       Temporally & spatially coherent
         spat...
Temporal coherence
             • Broadband light is incoherent
             • ALF (also LF and WDF) can be defined for
   ...
Young’s Exp. w/ white light

                                         x




                                              ...
Young’s Exp. w/ white light
                                                                  u
                          ...
Young’s Exp. w/ white light
                                                    Red
                                      ...
Young’s Exp. w/ white light
                                                    Red

                                     ...
Spatial coherence
             • ALF w/ virtual light projectors is defined
                for spatially coherent light
  ...
Young’s Exp. w/ spatially
                incoherent light
                                             x




            ...
Young’s Exp. w/ spatially
                incoherent light
                                             x




            ...
Young’s Exp. w/ spatially
                incoherent light
                                             x




            ...
Young’s Exp. w/ spatially
                incoherent light
                                             x




 w/ random p...
Young’s Exp. w/ spatially
                incoherent light
                                                          x



...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Young’s Exp. w/ spatially
                 incoherent light
                                                              ...
Virtual light projectors
             • Very simple modification to the LF
              • interference and diffraction wit...
Augmented Light Field
             1. free-space propagation
2. virtual light projector with negative radiance
           ...
Light Field Transformer

                               WDF
             Augmented LF
         Light
         Field


    ...
Light Field Transformer
                                                                             light field
          ...
Light Field Transformer
             • Q.Virtual light projector for a big aperture?
               •     put the virtual ...
Light Field Transformer
             • Q.Virtual light projector for a big aperture?
               •     put the virtual ...
Light Field Transformer
             • Q.Virtual light projector for a big aperture?
               •     put the virtual ...
Light Field Transformer
             • Q.Virtual light projector for a big aperture?
                 •     put the virtua...
Light Field Transformer
             • Q.Virtual light projector for a big aperture?
                 •     put the virtua...
Light Field Transformer




                                                    Tech report: S. B. Oh et. al
             ...
Light Field Transformer
             • light field interactions w/ optical elements
                               (x1 , θ1...
Light Field Transformer
             • light field interactions w/ optical elements
                                       ...
Light Field Transformer
             • light field interactions w/ optical elements
                                       ...
Light Field Transformer
             • light field interactions w/ optical elements
                                       ...
Light Field Transformer
        Dimension                  Property                             Note
         8D(4D)      ...
8D LF Transformer
             • the most generalized case
                                      (x1 , θ1 )     (x2 , θ2 )...
6D LF Transformer
             • For thin optical elements
                                   x
                          ...
er of times with
ference terms are
tood with the in-
the two pinholes
                     4D LF Transformer
             ...
Light field transformer
             • only amplitude variation (occluders)
                               x
              ...
Applications
                                                                                                             ...
Space of LF representations
Time-frequency representations
Phase space representations
Quasi light field

                 ...
Property of the Representation

                     Constant along                                                    Int...
Benefits & Limitations of the
                        Representation
                                                      ...
Conclusion
             • WDFoptics generalized version of the LF in
               wave
                     is the

    ...
Light Fields in Ray and Wave Optics

Introduction to Light Fields: 
    
      
           
   
     Ramesh Raskar

Wigner...
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Augmenting Light Field

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CVPR 2009 Short Course on Light Field: Present and Future
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  • my background
  • what is the light field?
  • 4D parameterization of plenoptic function, radiance,
  • 4D parameterization of plenoptic function, radiance,
  • 4D parameterization of plenoptic function, radiance,
  • 4D parameterization of plenoptic function, radiance,
  • 4D parameterization of plenoptic function, radiance,
  • in wave optics, WDF exhibit similar property, compare the two,
  • in wave optics, WDF exhibit similar property, compare the two,
  • in wave optics, WDF exhibit similar property, compare the two,
  • in wave optics, WDF exhibit similar property, compare the two,
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • the motivation, to augment lf, model diffraction in light field formulation
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • more specifically, same lf propagation,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • to demonstrate the limitation of LF,
  • in terms of lf,
  • so what is wigner?
  • recall young’s, to make the light field model, we can bring the interference term
  • recall young’s, to make the light field model, we can bring the interference term
  • recall young’s, to make the light field model, we can bring the interference term
  • Augmenting Light Field

    1. 1. Light Fields in Ray and Wave Optics Introduction to Light Fields: Ramesh Raskar Wigner Distribution Function to explain Light Fields: Zhengyun Zhang Break Augmenting LF to explain Wigner Distribution Function: Se Baek Oh Q&A Light Fields with Coherent Light: Anthony Accardi New Opportunities and Applications: Raskar and Oh Q&A: All
    2. 2. 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
    3. 3. Augmenting Light Fields explaining Wigner Distribution Function with LF Se Baek Oh Postdoctoral Associate 3D Optical Systems Group, Dept. of Mechanical Eng. Massachusetts Institute of Technology
    4. 4. Traditional Light Field 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 4
    5. 5. Motivation Traditional Light Field 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 5
    6. 6. Motivation light field direction position (θ, φ) radiance of ray Traditional (x, y) Light Field L(x, y, θ, φ) ref. plane 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 5
    7. 7. Motivation Traditional Light Field http://graphics.stanford.edu 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 5
    8. 8. Motivation Traditional Light Field ray optics based simple and powerful http://graphics.stanford.edu 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 5
    9. 9. Motivation Wigner Distribution Function Traditional Light Field ray optics based simple and powerful 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 6
    10. 10. Motivation rigorous but cumbersome wave optics based Wigner Distribution Function Traditional Light Field ray optics based simple and powerful 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 6
    11. 11. Motivation rigorous but cumbersome wave optics based Wigner Distribution Function holograms beam shaping Traditional Light Field 1µm 1µm ray optics based simple and powerful rotational PSF limited in diffraction & interference 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 6
    12. 12. Augmented LF rigorous but cumbersome wave optics based Wigner Distribution Function Traditional Light Field ray optics based simple and powerful limited in diffraction & interference 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
    13. 13. Augmented LF rigorous but cumbersome wave optics based Wigner WDF Distribution Function Augmented LF Traditional Traditional Light Field Light Field ray optics based simple and powerful limited in diffraction & interference 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
    14. 14. Augmented LF rigorous but cumbersome wave optics based Wigner WDF Distribution Function Augmented LF Traditional Traditional Light Field Light Field ray optics based simple and powerful Interference & Diffraction limited in diffraction & interference Interaction w/ optical elements 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
    15. 15. Augmented LF rigorous but cumbersome wave optics based Wigner WDF Distribution Function Augmented LF Traditional Traditional Light Field Light Field ray optics based simple and powerful Interference & Diffraction limited in diffraction & interference Interaction w/ optical elements Non-paraxial propagation 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 7
    16. 16. Augmented LF • not a new light field • a new methodology/framework to create, modulate, and propagate light fields • stay purely in position-angle space • wave optics phenomena can be understood with the light field 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 8
    17. 17. Augmented LF framework LF (diffractive) optical element 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 9
    18. 18. Augmented LF framework LF LF (diffractive) optical element LF propagation 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 9
    19. 19. Augmented LF framework light field transformer LF LF LF negative radiance (diffractive) optical element LF propagation 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 9
    20. 20. Augmented LF framework light field transformer LF LF LF LF negative radiance (diffractive) optical element LF propagation LF propagation 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 9
    21. 21. Augmented LF framework light field transformer LF LF LF LF negative radiance (diffractive) optical element LF propagation LF propagation 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 9
    22. 22. Augmented LF framework light field transformer LF LF LF LF negative radiance (diffractive) optical element LF propagation LF propagation Diffraction can be included in the light field framework! Tech report, S. B. Oh et al. http://web.media.mit.edu/~raskar/RayWavefront/ 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 9
    23. 23. outline 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 10
    24. 24. outline • Limitations of Light Field analysis 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 10
    25. 25. outline • Limitations of Light Field analysis • Augmented Light Field • free-space propagation u u x x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 10
    26. 26. outline • Limitations of Light Field analysis • Augmented Light Field • free-space propagation • virtual light projector in the ALF • coherence 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 10
    27. 27. outline • Limitations of Light Field analysis • Augmented Light Field • free-space propagation • virtual light projector in the ALF • coherence (x1 , θ1 ) (x2 , θ2 ) • light field transformer L1 (x1 , θ1 ) L2 (x2 , θ2 ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 10
    28. 28. Assumptions • monochromaticinto polychromatic coherent) (= temporally •can be extended • flatland extendedobservation plane) (= 1D • can be to the real world • scalarbefield and into polarized lightone polarization) diffraction (= • can extended • no non-linear effect (two-photon, SHG, loss, absorption, etc) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 11
    29. 29. Young’s experiment screen light from double a laser slit x d I(x) z 2π d I(x) = 1 + cos x λ z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 12
    30. 30. Young’s experiment screen light from double a laser slit x d I(x) z 2π d I(x) = 1 + cos x λ z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 12
    31. 31. Young’s experiment screen light from double a laser slit x d |r1 − r2 | = mλ constructive interference I(x) z 2π d I(x) = 1 + cos x λ z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 12
    32. 32. Young’s experiment screen light from double a laser slit x destructive interference |r1 − r2 | = (m + 1/2)λ d |r1 − r2 | = mλ constructive interference I(x) z 2π d I(x) = 1 + cos x λ z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 12
    33. 33. Young’s experiment x θ+ θ u (= θ/λ) A B A B x A B x θ− Light Field WDF z ref. plane 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 13
    34. 34. Young’s experiment θ+ x θ u (= θ/λ) A B A B x A B x θ− Light Field WDF z ref. plane 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 14
    35. 35. Young’s experiment projection projection θ+ x θ u (= θ/λ) A B A B x A B x θ− Light Field WDF z I(x) I(x) ref. plane 3D Optical x x Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 14
    36. 36. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx 2 2 space local spatial frequency (u = θ/λ) (= fξ in Zhengyun’s slide) • local spatial frequency spectrum (similar as wavelet) • ex) global vs. local frequency in a song global freq. local freq. • complex input g(x), WDF is always real • intensity = projection of WDF along u • WDF can be defined for light (E-field) as well as optical elements (e.g., gratings or apertures) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 15
    37. 37. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx 2 2 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
    38. 38. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx jαx2 2 2 g(x) = e x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
    39. 39. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx jαx2 2 2 g(x) = e “ ”2 x −jα x− x g ∗ x− =e 2 x 2 “ ”2 x x jα x+ 2 g x+ =e jα(2xx ) 2 e x x /2 x /2 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
    40. 40. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx jαx2 2 2 g(x) = e “ ”2 x −jα x− x g ∗ x− =e 2 x 2 “ ”2 x x jα x+ 2 g x+ =e jα(2xx ) 2 e x x x /2 x /2 x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
    41. 41. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx jαx2 2 2 g(x) = e “ ”2 x −jα x− x g ∗ x− =e 2 x 2 “ ”2 x x jα x+ 2 g x+ =e jα(2xx ) 2 e x x . . x /2 x /2 . . . . x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
    42. 42. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx jαx2 2 2 g(x) = e “ ”2 x −jα x− x g ∗ x− =e 2 x 2 “ ”2 x x jα x+ 2 g x+ =e jα(2xx ) 2 e x F x . . x /2 x /2 . . . . x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
    43. 43. Wigner Distribution Function x x Wg (x, u) = g x+ g ∗ x− e−j2πx u dx jαx2 2 2 g(x) = e “ ”2 x −jα x− x g ∗ x− =e 2 x 2 “ ”2 x x jα x+ 2 g x+ =e jα(2xx ) 2 e x F x . . x /2 x /2 . . u Wg (x, u) . . x x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 16
    44. 44. Wigner Distribution Function plane wave spherical wave point source incoherent light 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 17
    45. 45. Augmented Light Field 1. free-space propagation 2. virtual light projector with negative radiance 3. light field transformer
    46. 46. Free-space propagation • In homogeneous medium and the paraxial region, • LF = ALF = WDF WDF Augmented LF Traditional Light Field 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 19
    47. 47. Free-space propagation • two plane parameterization equivalent to θ x x x x d 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 20
    48. 48. Free-space propagation • two plane parameterization equivalent to θ x x x x d 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 21
    49. 49. Free space propagation • wave optics: Huygen’s principle • point sources on the wavefront • coherent superposition of wavelets 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 22
    50. 50. Free space propagation • wave optics: Huygen’s principle • point sources on the wavefront • coherent superposition of wavelets 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 22
    51. 51. Free space propagation • Mathematical description j 2π r e λ r E-field jλr point source j 2π r e λ (x, y) E(x , y ) = E(x, y) ⊗ (x , y ) jλr r= (x − x)2 + (y − y)2 + z 2 z E(x, y) E(x , y ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 23
    52. 52. Free space propagation • Mathematical description j 2π r e λ r E-field jλr point source j 2π r e λ (x, y) E(x , y ) = E(x, y) ⊗ (x , y ) jλr r= (x − x)2 + (y − y)2 + z 2 z E(x, y) E(x , y ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 23
    53. 53. Free space propagation • with the paraxial approximation spherical wavefront 1 quadratic (x − x)2 + (y − y)2 + z2 ≈z+ (x − x)2 + (y − y)2 wavefront 2z z point source exp j 2π λ (x − x)2 + (y − y)2 + z 2 E(x , y ) = E(x, y) dxdy jλ (x − x)2 + (y − y)2 + z 2 j 2π z e λ π ≈ E(x, y) exp j [(x − x)2 + (y − y)2 ] dxdy jλz λz Fresnel diffraction formula 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 24
    54. 54. Free space propagation • with the paraxial approximation spherical wavefront 1 quadratic (x − x)2 + (y − y)2 + z2 ≈z+ (x − x)2 + (y − y)2 wavefront 2z source & aperture size << z z point source exp j 2π λ (x − x)2 + (y − y)2 + z 2 E(x , y ) = E(x, y) dxdy jλ (x − x)2 + (y − y)2 + z 2 j 2π z e λ π ≈ E(x, y) exp j [(x − x)2 + (y − y)2 ] dxdy jλz λz Fresnel diffraction formula 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 24
    55. 55. Fresnel propagation • w/ WDF x x E1 (x) E2 (x ) W1 (x, u) W2 (x , u ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 25
    56. 56. Fresnel propagation • w/ WDF x x E1 (x) E2 (x ) W1 (x, u) W2 (x , u ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 25
    57. 57. Fresnel propagation • w/ WDF x x E1 (x) E2 (x ) W1 (x, u) W2 (x , u ) W2 (x , u ) = W1 (x − λzu , u ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 25
    58. 58. Fresnel propagation • w/ WDF x x E1 (x) E2 (x ) W1 (x, u) W2 (x , u ) W2 (x , u ) = W1 (x − λzu , u ) u x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 25
    59. 59. Fresnel propagation • w/ WDF x x E1 (x) E2 (x ) W1 (x, u) W2 (x , u ) W2 (x , u ) = W1 (x − λzu , u ) u u x-shear transform 1/(λz) x x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 25
    60. 60. diffraction vs. distance single slit a = 64λ laser from Zhengyun’s slide z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 26
    61. 61. diffraction vs. distance Position and Direction in Wave Optics single slit a = 64λ laser from Zhengyun’s slide z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 26
    62. 62. diffraction vs. distance Position and Direction in Wave Optics near zone: few λ (evanescent wave) Fresnel regime Fraunhofer regime (paraxial region) (Far-field) single slit a = 64λ laser from Zhengyun’s slide z 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 26
    63. 63. diffraction vs. distance Position and Direction in Wave Optics near zone: few λ (evanescent wave) 1 FN Fresnel regime FN 1 Fraunhofer regime (paraxial region) (Far-field) non-paraxial single slit region a = 64λ laser from Zhengyun’s slide a2 z rule of thumb: Fresnel number FN = λz 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 26
    64. 64. Augmented Light Field 1. free-space propagation 2. virtual light projector with negative radiance 3. light field transformer
    65. 65. Virtual light projector WDF Augmented LF Traditional Light Field Diffraction and Interference With simple modifications in Light Field - virtual light projector (negative radiance) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 28
    66. 66. Young’s experiment x θ u A B A B x A B x Light Field WDF ref. plane 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 29
    67. 67. Young’s experiment projection projection x θ u A B A B x A B x Light Field WDF I(x) I(x) ref. plane x x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 29
    68. 68. Young’s experiment projection projection x θ u A B A B x A B x Light Field WDF I(x) I(x) ref. plane x x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 29
    69. 69. Virtual light projector projection real projector θ x real projector Augmented LF intensity=0 Not conflict with physics 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 30
    70. 70. Virtual light projector projection 2π real projector cos λ [a − b]θ θ negative virtual light projector positive at the mid point x real projector Augmented LF intensity=0 Not conflict with physics 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 30
    71. 71. Virtual light projector first null real projector (OPD = λ/2) real projector 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 31
    72. 72. Virtual light projector first null real projector (OPD = λ/2) virtual light projector real projector 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 31
    73. 73. Virtual light projector hyperbola first null (OPD = λ/2) asymptote of λ/2 hyperbola valid in Fresnel regime (or paraxial) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 32
    74. 74. Virtual light projector destructive interference in high school physics class, (need negative radiance from virtual light projector) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 33
    75. 75. Virtual light projector destructive interference in high school physics class, (need negative radiance from virtual light projector) m = λ/2 m = 3λ/2 m = 5λ/2 m = 7λ/2 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 33
    76. 76. Question • Does a virtual light projector also work for incoherent light? 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 34
    77. 77. Question • Does a virtual light projector also work for incoherent light? • Yes! 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 34
    78. 78. Coherence • Degree of making interference • coherent partially coherent incoherent • Correlation of two)points on wavefront • E(p , t )E (p , t ∗ 1 1 (≈phase difference) 2 2 p1 Coherent: deterministic phase relation Incoherent: uncorrelated phase relation p2 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 35
    79. 79. Coherence • throwing stones...... 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 36
    80. 80. Coherence • throwing stones...... single point source 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 36
    81. 81. Coherence • throwing stones...... single point source coherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 36
    82. 82. Coherence • throwing stones...... single point source many point sources coherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 36
    83. 83. Coherence • throwing stones...... single point source many point sources coherent if thrown identically, still coherent! 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 36
    84. 84. Coherence • throwing stones...... single point source many point sources coherent if thrown identically, still coherent! if thrown randomly, then incoherent! 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 36
    85. 85. Coherence • Temporal coherence: E(p, t )E (p, t ) 1 ∗ 2 • spectral bandwidth • monochromatic: temporally coherent • broadband (white light): temporally incoherent • Spatial coherence: E(p1 , t)E ∗ (p2 , t) • spatial bandwidth (angular span) • point source: spatially coherent • extended source: spatially incoherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 37
    86. 86. Example 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    87. 87. Example Temporally incoherent; spatially coherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    88. 88. Example Temporally incoherent; spatially coherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    89. 89. Example Temporally incoherent; Temporally & spatially coherent spatially coherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    90. 90. Example Temporally incoherent; Temporally & spatially coherent spatially coherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    91. 91. Example Temporally incoherent; Temporally & spatially coherent spatially coherent Temporally & spatially incoherent 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    92. 92. Example Temporally incoherent; Temporally & spatially coherent spatially coherent Temporally & spatially incoherent Temporally coherent; spatially incoherent ? 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    93. 93. Example Temporally incoherent; Temporally & spatially coherent spatially coherent Temporally & spatially incoherent Temporally coherent; spatially incoherent rotating diffuser laser 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 38
    94. 94. Temporal coherence • Broadband light is incoherent • ALF (also LF and WDF) can be defined for different wavelength and treated independently 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 39
    95. 95. Young’s Exp. w/ white light x I(x) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 40
    96. 96. Young’s Exp. w/ white light u Red x x u Green x u Blue x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 41
    97. 97. Young’s Exp. w/ white light Red I(x) x x Green I(x) x Blue I(x) x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 42
    98. 98. Young’s Exp. w/ white light Red x Green I(x) x Blue 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 42
    99. 99. Spatial coherence • ALF w/ virtual light projectors is defined for spatially coherent light • For partially coherent/incoherent light, adding the defined ALF still gives valid results! 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 43
    100. 100. Young’s Exp. w/ spatially incoherent light x I(x) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 44
    101. 101. Young’s Exp. w/ spatially incoherent light x I(x) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 45
    102. 102. Young’s Exp. w/ spatially incoherent light x I(x) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 46
    103. 103. Young’s Exp. w/ spatially incoherent light x w/ random phase (uncorrelated) I(x) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 47
    104. 104. Young’s Exp. w/ spatially incoherent light x w/ random phase (uncorrelated) I(x) spatially incoherent light: infinite number of waves propagating along all the direction with random phase delay 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 47
    105. 105. Young’s Exp. w/ spatially incoherent light u x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    106. 106. Young’s Exp. w/ spatially incoherent light u x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    107. 107. Young’s Exp. w/ spatially incoherent light u x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    108. 108. Young’s Exp. w/ spatially incoherent light u x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    109. 109. Young’s Exp. w/ spatially incoherent light u x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    110. 110. Young’s Exp. w/ spatially incoherent light u x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    111. 111. Young’s Exp. w/ spatially incoherent light u x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    112. 112. Young’s Exp. w/ spatially incoherent light u x w/ random phase Addition (uncorrelated) u x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 48
    113. 113. Young’s Exp. w/ spatially incoherent light u x x w/ random phase (uncorrelated) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 49
    114. 114. Young’s Exp. w/ spatially incoherent light u x x w/ random phase Addition (uncorrelated) u x 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 49
    115. 115. Virtual light projectors • Very simple modification to the LF • interference and diffraction within light field (geometry based) representation 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 50
    116. 116. Augmented Light Field 1. free-space propagation 2. virtual light projector with negative radiance 3. light field transformer
    117. 117. Light Field Transformer WDF Augmented LF Light Field Interaction at the optical elements 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 52
    118. 118. Light Field Transformer light field transformer WDF LF LF LF LF negative radiance Augmented LF (diffractive) optical element Light Field LF propagation LF propagation Interaction at the optical elements 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 52
    119. 119. Light Field Transformer • Q.Virtual light projector for a big aperture? • put the virtual light projectors for all the possible pairs of two points • WDF of optical elements 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 53
    120. 120. Light Field Transformer • Q.Virtual light projector for a big aperture? • put the virtual light projectors for all the possible pairs of two points • WDF of optical elements 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 53
    121. 121. Light Field Transformer • Q.Virtual light projector for a big aperture? • put the virtual light projectors for all the possible pairs of two points equivalent to compute the WDF mathematically.... 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 53
    122. 122. Light Field Transformer • Q.Virtual light projector for a big aperture? • put the virtual light projectors for all the possible pairs of two points equivalent to compute the WDF mathematically.... • WDF of optical elements 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 53
    123. 123. Light Field Transformer • Q.Virtual light projector for a big aperture? • put the virtual light projectors for all the possible pairs of two points equivalent to compute the WDF mathematically.... • WDF of optical elements representing properties of optical elements 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 53
    124. 124. Light Field Transformer Tech report: S. B. Oh et. al 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 54
    125. 125. Light Field Transformer • light field interactions w/ optical elements (x1 , θ1 ) (x2 , θ2 ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 55
    126. 126. Light Field Transformer • light field interactions w/ optical elements (x1 , θ1 ) (x2 , θ2 ) L1 (x1 , θ1 ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 55
    127. 127. Light Field Transformer • light field interactions w/ optical elements (x1 , θ1 ) (x2 , θ2 ) L1 (x1 , θ1 ) L2 (x2 , θ2 ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 55
    128. 128. Light Field Transformer • light field interactions w/ optical elements (x1 , θ1 ) (x2 , θ2 ) L1 (x1 , θ1 ) L2 (x2 , θ2 ) Light field transformer T (x2 , x1 , θ1 , θ2 ) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 55
    129. 129. Light Field Transformer Dimension Property Note 8D(4D) thick, shift variant, 8D reflectance field, T (x2 , x1 , θ1 , θ2 ) angular variant volume hologram 6D(3D) thin, shift variant, 6D display, T (x, θ1 , θ2 ) angular variant BTF 4D(2D) thin, shift variant, many optical elements T (x, θ) angular invariant 2D(1D) attenuation shield field T (x) 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 56
    130. 130. 8D LF Transformer • the most generalized case (x1 , θ1 ) (x2 , θ2 ) L2 (x2 , θ2 ) L1 (x1 , θ1 ) L2 (x2 , θ2 ) = T (x2 , θ2 , x1 , θ1 )L1 (x1 , θ1 )dx1 dθ1 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 57
    131. 131. 6D LF Transformer • For thin optical elements x 6D Display L2 (x, θ2 ) L1 (x, θ1 ) Courtesy of Martin Fuchs Bidirectional L2 (x, θ2 ) = T (x, θ2 , θ1 )L1 (x, θ1 )dθ1 Texture Function Courtesy of Paul Debevec 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 58
    132. 132. er of times with ference terms are tood with the in- the two pinholes 4D LF Transformer • Figure 7: Concept of virtual light sources for coherent light. w/ anglethe LF representation, no interference is predicted. By In shift invariant elements (in the paraxial region) virtual light sources, the LF propagation still including the n for diffraction • can be used. ould be included. e.g. aperture, lens, thin grating, etc oducing the con- have negative ra- es at a and b as al light source is π[a − b] λ along θ by integrating the l light sources do ne, which agrees Once the virtual L2 (x, θ) = T (x, θ − θ)L1 (x, θ )dθ propagation still Figure 8: Angle shift invariance in a thin transparency. In erly modeled3Dby Group (a) and (b), the output rays rotate in the same fashion 59 Se Baek Oh Optical Systems CVPR 2009 - Light Fields: Present and Future as
    133. 133. Light field transformer • only amplitude variation (occluders) x shield fields for occluders L2 (x, θ) L1 (x, θ) L2 (x, θ) = T (x, θ)L1 (x, θ) Courtesy of D. Lanman 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 60
    134. 134. Applications 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. 61
    135. 135. 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
    136. 136. 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 63
    137. 137. 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 64
    138. 138. Conclusion • WDFoptics generalized version of the LF in wave is the • Augmented Light Field • identicalregion) propagation (in the paraxial free-space • virtual light projectors • light field transformers • Wave opticswith geometrical be based understood phenomena can ray representations 3D Optical Se Baek Oh Systems Group CVPR 2009 - Light Fields: Present and Future 65
    139. 139. 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

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