Digital Hologram Image Processing<br />(DHIP)<br />Conor Mc Elhinney<br />Thursday 29th April<br />Contact: conormce@cs.nu...
Outline<br /><ul><li> Introduction
 Digital Holography
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Outline<br /><ul><li> Introduction
 Overview
 Intro to digital holography
 Digital Holography
 Focus
 Segmentation
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Why digital holography?<br />Yves Gevant Ultimate Hologram<br />http://www.ultimate-holography.com<br />Contact: conormce@...
Why not standard 2D image processing?<br />2D<br />	Standard 2D image processing techniques can be applied to individual d...
Outline<br /><ul><li> Introduction
 Overview
 Intro to digital holography
 Digital Holography
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Black box - reconstructing a digital hologram<br />Digital Hologram<br />Digital Reconstruction<br />Reconstruct<br />Dist...
Black box - Reconstructing a digital hologram<br />Digital Hologram<br />Digital Reconstruction<br />d1<br />Reconstruct<b...
Shallow depth-of-field<br />Reconstructions from digital holograms have a shallow depth of field, sometimes as small as 1m...
Shallow depth-of-field<br />Reconstructions from digital holograms have a shallow depth of field, sometimes as small as 1m...
Focusing a digital hologram<br />Contact: conormce@cs.nuim.ie<br />
Using a window to reconstruct<br />Contact: conormce@cs.nuim.ie<br />
Viewing perspectives<br />Contact: conormce@cs.nuim.ie<br />
What can we do with image processing?<br />Extract shape information<br />Background<br />Segmentation<br />Object <br />S...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Overview
 Maths
 Recording Options
 Error Terms
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent ligh...
Reference <br />Beam<br />Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an o...
Reference <br />Beam<br />Recording a hologram<br /><ul><li> No lens
 Uses coherent light
 Records interference pattern
 Uses a lens
 Uses incoherent light
 Records focused image</li></ul>Holography<br />Photography<br />Sun<br />Laser<br />Object <br />Beam<br />Lens<br />Phot...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
Overview
 Maths
 Error Terms
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
What is in a digital hologram<br />Object wavefront<br />Contact: conormce@cs.nuim.ie<br />
What is in a digital hologram<br />Object wavefront<br />Phase<br />Amplitude<br />Contact: conormce@cs.nuim.ie<br />
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Contact: conormce@cs.nuim.ie<br />
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Contact: conormce...
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Contact: conormce...
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />But a camera reco...
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Int...
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Int...
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Int...
What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Obj...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Overview
 Maths
 Recording Options
 Error Terms
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the se...
In-Line setup<br />This form of holography gets its name from the fact that the reference beam and the object beam are cen...
Off-axis setup<br />In off-axis holography the object beam and reference beam are at a different angle in relation to the ...
Digital hologram recording<br />There are numerous ways of implementing a digital hologram recording setup.<br />There are...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Overview
 DC-term suppression
 Phase shifting digital holography
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />Contact: conormce@cs.nui...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />Contact: conormce@cs.nui...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />Contact: conormce@cs.nui...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three ter...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three ter...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three ter...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three ter...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three ter...
Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three ter...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Overview
 DC-term suppression
 Twin-Image removal
 Phase shifting digital holography
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
DC-term suppression<br />Taking a single hologram prior to any processing, we reconstruct this to demonstrate the corrupti...
DC-term suppression<br />Taking a single hologram prior to any processing, we reconstruct this to demonstrate the corrupti...
DC-term suppression<br />Hologram<br />Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
DC-term suppression<br />Hologram<br />Fourier<br />transform<br />Contact: conormce@cs.nuim.ie<br />
DC-term suppression<br />Hologram<br />Fourier<br />transform<br />High-pass<br />Filter<br />Contact: conormce@cs.nuim.ie...
DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transfo...
DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transfo...
DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transfo...
DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transfo...
DC-term suppression example<br />Contact: conormce@cs.nuim.ie<br />
 Digital Holography
 Error Terms
 Overview
 DC-term suppression
 Twin-Image removal
 Phase shifting digital holography
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Twin-image<br />With the DC-term suppressed we can now view the twin-images.<br />DC-Free Hologram<br />Virtual Image<br /...
Twin-image removal<br />There are different approaches for suppressing or removing the unwanted twin. These are dependent ...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Overview
 DC-term suppression
 Twin-Image removal
 Phase shifting digital holography
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
Phase-shifting digital holography<br />Phase shifting digital holography is a technique which calculates in-line digital h...
Phase-shifting digital holography<br />Notice that the intensity of the virtual image is much lower than the real image. P...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Reconstructing
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Reconstructing
 Overview
 Reconstructing options
 Reconstructing perspectives
 Speckle reduction
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by t...
Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by t...
Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by t...
Reconstructing a digital hologram<br /><ul><li> Focused scene is on film
 The eye can focus on different parts of the scene.</li></ul>Holography<br />Photography<br />Sun<br />Laser<br />Viewer<b...
Outline<br /><ul><li> Introduction
 Digital Holography
 Recording
 Error Terms
 Reconstructing
 Overview
 Reconstructing options
 Reconstructing perspectives
 Speckle reduction
 Focus
 Segmentation
 Extended Focus Image
 Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by a...
Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by a...
The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be...
The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be...
The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be...
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Digital Hologram Image Processing

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Digital Hologram Image Processing

  1. 1. Digital Hologram Image Processing<br />(DHIP)<br />Conor Mc Elhinney<br />Thursday 29th April<br />Contact: conormce@cs.nuim.ie<br />
  2. 2. Outline<br /><ul><li> Introduction
  3. 3. Digital Holography
  4. 4. Focus
  5. 5. Segmentation
  6. 6. Extended Focus Image
  7. 7. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  8. 8. Outline<br /><ul><li> Introduction
  9. 9. Overview
  10. 10. Intro to digital holography
  11. 11. Digital Holography
  12. 12. Focus
  13. 13. Segmentation
  14. 14. Extended Focus Image
  15. 15. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  16. 16. Why digital holography?<br />Using digital holography we can record a scene in a complex valued data structure which retains some of the scene's 3D information. A standard image obtained with a camera records a 2D focused image of the scene from one perspective.<br />Contact: conormce@cs.nuim.ie<br />
  17. 17. Why digital holography?<br />Yves Gevant Ultimate Hologram<br />http://www.ultimate-holography.com<br />Contact: conormce@cs.nuim.ie<br />
  18. 18. Why digital holography?<br />Using digital holography we can record a scene in a complex valued data structure which retains some of the scene's 3D information. A standard image obtained with a camera records a 2D focused image of the scene from one perspective.<br />Reconstructions<br />Why do we need image processing?<br /> However reconstructing a digital hologram returns a 2D image of the scene at a specific depth (300mm from the camera) from an individual perspective (along the optical axis). Algorithms and processing techniques need to be developed to extract the 3D information from digital holograms by processing multiple (volumes of) reconstructions.<br />Image Processing<br />Depth Map<br />Contact: conormce@cs.nuim.ie<br />
  19. 19. Why not standard 2D image processing?<br />2D<br /> Standard 2D image processing techniques can be applied to individual digital holographic reconstructions with varying success.<br />2D<br />Image<br />Processing<br />DHIP<br />Digital Holographic<br />Image<br />Processing<br />Holograms have a shallow depth-of-field, which means that we need to multiple images (reconstructions) over a range of depths and then process this volume of reconstructions to get accurate information back out.<br />Reconstructions<br />Contact: conormce@cs.nuim.ie<br />
  20. 20. Outline<br /><ul><li> Introduction
  21. 21. Overview
  22. 22. Intro to digital holography
  23. 23. Digital Holography
  24. 24. Focus
  25. 25. Segmentation
  26. 26. Extended Focus Image
  27. 27. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  28. 28. Black box - reconstructing a digital hologram<br />Digital Hologram<br />Digital Reconstruction<br />Reconstruct<br />Distance d<br />Contact: conormce@cs.nuim.ie<br />
  29. 29. Black box - Reconstructing a digital hologram<br />Digital Hologram<br />Digital Reconstruction<br />d1<br />Reconstruct<br />d2<br />d3<br />d4<br />d5<br />d6<br />Set of distances {d1,d2,d3,d4,d5,d6}<br />Contact: conormce@cs.nuim.ie<br />
  30. 30. Shallow depth-of-field<br />Reconstructions from digital holograms have a shallow depth of field, sometimes as small as 1mm. This means that processing an individual reconstruction is rarely a good idea. <br />188mm<br />178mm<br />Contact: conormce@cs.nuim.ie<br />
  31. 31. Shallow depth-of-field<br />Reconstructions from digital holograms have a shallow depth of field, sometimes as small as 1mm. This means that processing an individual reconstruction is rarely a good idea. <br />188mm<br />178mm<br />Contact: conormce@cs.nuim.ie<br />
  32. 32. Focusing a digital hologram<br />Contact: conormce@cs.nuim.ie<br />
  33. 33. Using a window to reconstruct<br />Contact: conormce@cs.nuim.ie<br />
  34. 34. Viewing perspectives<br />Contact: conormce@cs.nuim.ie<br />
  35. 35. What can we do with image processing?<br />Extract shape information<br />Background<br />Segmentation<br />Object <br />Segmentation<br />Create Focused<br />Images<br />DHIP<br />DHIP<br />DHIP<br />DHIP<br />Contact: conormce@cs.nuim.ie<br />
  36. 36. Outline<br /><ul><li> Introduction
  37. 37. Digital Holography
  38. 38. Recording
  39. 39. Error Terms
  40. 40. Reconstructing
  41. 41. Focus
  42. 42. Segmentation
  43. 43. Extended Focus Image
  44. 44. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  45. 45. Outline<br /><ul><li> Introduction
  46. 46. Digital Holography
  47. 47. Recording
  48. 48. Overview
  49. 49. Maths
  50. 50. Recording Options
  51. 51. Error Terms
  52. 52. Reconstructing
  53. 53. Focus
  54. 54. Segmentation
  55. 55. Extended Focus Image
  56. 56. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  57. 57. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Contact: conormce@cs.nuim.ie<br />
  58. 58. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Photography<br />Sun<br />Lens<br />Photo Film<br />Contact: conormce@cs.nuim.ie<br />
  59. 59. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Photography<br />Sun<br />Lens<br />Photo Film<br />Contact: conormce@cs.nuim.ie<br />
  60. 60. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Photography<br />Sun<br />Lens<br />Photo Film<br />Contact: conormce@cs.nuim.ie<br />
  61. 61. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Holography<br />Laser<br />Contact: conormce@cs.nuim.ie<br />
  62. 62. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Holography<br />Laser<br />Contact: conormce@cs.nuim.ie<br />
  63. 63. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Holography<br />Laser<br />Contact: conormce@cs.nuim.ie<br />
  64. 64. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Holography<br />Laser<br />Object <br />Beam<br />Holo Film<br />Contact: conormce@cs.nuim.ie<br />
  65. 65. Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Holography<br />Laser<br />Object <br />Beam<br />Holo Film<br />Contact: conormce@cs.nuim.ie<br />
  66. 66. Reference <br />Beam<br />Recording a hologram<br />Recording a hologram is (generally) achieved through illuminating an object with a coherent light source and recording the interference between this beam and a reference beam. It is analogous to recording a photograph.<br />Holography<br />Laser<br />Object <br />Beam<br />Holo Film<br />Contact: conormce@cs.nuim.ie<br />
  67. 67. Reference <br />Beam<br />Recording a hologram<br /><ul><li> No lens
  68. 68. Uses coherent light
  69. 69. Records interference pattern
  70. 70. Uses a lens
  71. 71. Uses incoherent light
  72. 72. Records focused image</li></ul>Holography<br />Photography<br />Sun<br />Laser<br />Object <br />Beam<br />Lens<br />Photo Film<br />Holo Film<br />Contact: conormce@cs.nuim.ie<br />
  73. 73. Outline<br /><ul><li> Introduction
  74. 74. Digital Holography
  75. 75. Recording
  76. 76. Overview
  77. 77. Maths
  78. 78. Recording Options
  79. 79. Error Terms
  80. 80. Reconstructing
  81. 81. Focus
  82. 82. Segmentation
  83. 83. Extended Focus Image
  84. 84. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  85. 85. What is in a digital hologram<br />Object wavefront<br />Contact: conormce@cs.nuim.ie<br />
  86. 86. What is in a digital hologram<br />Object wavefront<br />Phase<br />Amplitude<br />Contact: conormce@cs.nuim.ie<br />
  87. 87. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Contact: conormce@cs.nuim.ie<br />
  88. 88. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Contact: conormce@cs.nuim.ie<br />
  89. 89. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Contact: conormce@cs.nuim.ie<br />
  90. 90. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />But a camera records intensity?<br />Contact: conormce@cs.nuim.ie<br />
  91. 91. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Intensity Only<br />Contact: conormce@cs.nuim.ie<br />
  92. 92. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Intensity Only<br />Contact: conormce@cs.nuim.ie<br />
  93. 93. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Intensity and Phase Information<br />Contact: conormce@cs.nuim.ie<br />
  94. 94. What is in a digital hologram<br />Object wavefront<br />Reference Beam<br />Hologram<br />+<br />=<br />Recorded<br />Objects Amplitude<br />Objects Phase<br />Contact: conormce@cs.nuim.ie<br />
  95. 95. Outline<br /><ul><li> Introduction
  96. 96. Digital Holography
  97. 97. Recording
  98. 98. Overview
  99. 99. Maths
  100. 100. Recording Options
  101. 101. Error Terms
  102. 102. Reconstructing
  103. 103. Focus
  104. 104. Segmentation
  105. 105. Extended Focus Image
  106. 106. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  107. 107. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />Contact: conormce@cs.nuim.ie<br />
  108. 108. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />1) Is your object large or small?<br />Contact: conormce@cs.nuim.ie<br />
  109. 109. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />1) Is your object large or small?<br />This will allow you to choose either a: <br />Macroscopic setup<br />Microscopic setup<br />Contact: conormce@cs.nuim.ie<br />
  110. 110. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />1) Is your object large or small?<br />This will allow you to choose either a: <br />2) Does your object let light through or reflect light?<br />Macroscopic setup<br />Microscopic setup<br />Contact: conormce@cs.nuim.ie<br />
  111. 111. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />1) Is your object large or small?<br />This will allow you to choose either a: <br />2) Does your object let light through or reflect light?<br />This will allow you to make your setup: <br />Macroscopic setup<br />Microscopic setup<br />Reflective mode<br />Transmissive mode<br />Contact: conormce@cs.nuim.ie<br />
  112. 112. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />1) Is your object large or small?<br />This will allow you to choose either a: <br />2) Does your object let light through or reflect light?<br />This will allow you to make your setup: <br /> 3) What are recording architecture do you want?<br />Macroscopic setup<br />Microscopic setup<br />Reflective mode<br />Transmissive mode<br />Contact: conormce@cs.nuim.ie<br />
  113. 113. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />1) Is your object large or small?<br />This will allow you to choose either a: <br />2) Does your object let light through or reflect light?<br />This will allow you to make your setup: <br /> 3) What are recording architecture do you want?<br />The options are:<br />Macroscopic setup<br />Microscopic setup<br />Reflective mode<br />Transmissive mode<br />In-line<br />Off-axis<br />Contact: conormce@cs.nuim.ie<br />
  114. 114. Digital hologram recording options<br />There are (at least) three questions that need to be answered when choosing the setup you want, with the third question the toughest to answer!<br />1) Is your object large or small?<br />This will allow you to choose either a: <br />2) Does your object let light through or reflect light?<br />This will allow you to make your setup: <br /> 3) What are recording architecture do you want?<br />The options are:<br />I will try and cover some of the differences between these two options but that is a topic in itself.<br />Macroscopic setup<br />Microscopic setup<br />Reflective mode<br />Transmissive mode<br />In-line<br />Off-axis<br />Contact: conormce@cs.nuim.ie<br />
  115. 115. In-Line setup<br />This form of holography gets its name from the fact that the reference beam and the object beam are centred on the optical axis. They both are at the same angle in relation to the CCD.<br />Contact: conormce@cs.nuim.ie<br />
  116. 116. Off-axis setup<br />In off-axis holography the object beam and reference beam are at a different angle in relation to the CCD.<br />Contact: conormce@cs.nuim.ie<br />
  117. 117. Digital hologram recording<br />There are numerous ways of implementing a digital hologram recording setup.<br />There are also numerous advantages and disadvantages of using an in-line or off-axis setup. This topic in itself would take a whole talk.<br />For the purposes of this talk all digital holograms were recorded with in-line digital holography.<br />Only <br />Macroscopic<br />Reflective<br />In-line <br />Digital Holograms in this talk<br />Contact: conormce@cs.nuim.ie<br />
  118. 118. Outline<br /><ul><li> Introduction
  119. 119. Digital Holography
  120. 120. Recording
  121. 121. Error Terms
  122. 122. Reconstructing
  123. 123. Focus
  124. 124. Segmentation
  125. 125. Extended Focus Image
  126. 126. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  127. 127. Outline<br /><ul><li> Introduction
  128. 128. Digital Holography
  129. 129. Recording
  130. 130. Error Terms
  131. 131. Overview
  132. 132. DC-term suppression
  133. 133. Twin-Image removal
  134. 134. Phase shifting digital holography
  135. 135. Reconstructing
  136. 136. Focus
  137. 137. Segmentation
  138. 138. Extended Focus Image
  139. 139. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  140. 140. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />Contact: conormce@cs.nuim.ie<br />
  141. 141. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />Contact: conormce@cs.nuim.ie<br />
  142. 142. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />Contact: conormce@cs.nuim.ie<br />
  143. 143. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three terms<br />Contact: conormce@cs.nuim.ie<br />
  144. 144. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three terms<br />The DC-term<br />Contact: conormce@cs.nuim.ie<br />
  145. 145. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three terms<br />The DC-term<br />The virtual image<br />Contact: conormce@cs.nuim.ie<br />
  146. 146. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three terms<br />The DC-term<br />The virtual image<br />The real image<br />Contact: conormce@cs.nuim.ie<br />
  147. 147. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three terms<br />The DC-term<br />The virtual image<br />The real image<br />The DC-term is a term which corrupts any reconstructions of the hologram. It can be removed through spatially filtering the Fourier transform of the hologram.<br />Contact: conormce@cs.nuim.ie<br />
  148. 148. Unwanted terms in a digital hologram<br />The interference pattern recorded is described by:<br />which contains three terms<br />The DC-term<br />The virtual image<br />The real image<br />The DC-term is a term which corrupts any reconstructions of the hologram. It can be removed through spatially filtering the Fourier transform of the hologram.<br />The virtual image and real image are known as the twin-images and are viewed as noise in reconstructions of digital holograms.<br />Contact: conormce@cs.nuim.ie<br />
  149. 149. Outline<br /><ul><li> Introduction
  150. 150. Digital Holography
  151. 151. Recording
  152. 152. Error Terms
  153. 153. Overview
  154. 154. DC-term suppression
  155. 155. Twin-Image removal
  156. 156. Phase shifting digital holography
  157. 157. Reconstructing
  158. 158. Focus
  159. 159. Segmentation
  160. 160. Extended Focus Image
  161. 161. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  162. 162. DC-term suppression<br />Taking a single hologram prior to any processing, we reconstruct this to demonstrate the corruptive effect of the DC-term<br />365 mm<br />Reconstruction plane<br />Hologram<br />Reconstruct<br />Contact: conormce@cs.nuim.ie<br />
  163. 163. DC-term suppression<br />Taking a single hologram prior to any processing, we reconstruct this to demonstrate the corruptive effect of the DC-term<br />365 mm<br />Reconstruction plane<br />Hologram<br />Reconstruct<br />There are many methods for suppressing the DC-term, our twin-image removal algorithm takes as input a DC-term suppressed hologram. For our experiments we apply a high-pass filter in the Fourier domain to suppress the DC-term.<br />Contact: conormce@cs.nuim.ie<br />
  164. 164. DC-term suppression<br />Hologram<br />Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  165. 165. DC-term suppression<br />Hologram<br />Fourier<br />transform<br />Contact: conormce@cs.nuim.ie<br />
  166. 166. DC-term suppression<br />Hologram<br />Fourier<br />transform<br />High-pass<br />Filter<br />Contact: conormce@cs.nuim.ie<br />
  167. 167. DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transform<br />High-pass<br />Filter<br />Contact: conormce@cs.nuim.ie<br />
  168. 168. DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transform<br />High-pass<br />Filter<br />Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  169. 169. DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transform<br />High-pass<br />Filter<br />Reconstruction<br />Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  170. 170. DC-term suppression<br />Hologram<br />DC-Free Hologram<br />Inverse<br />Fourier<br />transform<br />Fourier<br />transform<br />High-pass<br />Filter<br />Reconstruction<br />Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  171. 171. DC-term suppression example<br />Contact: conormce@cs.nuim.ie<br />
  172. 172. Outline<br /><ul><li> Introduction
  173. 173. Digital Holography
  174. 174. Recording
  175. 175. Error Terms
  176. 176. Overview
  177. 177. DC-term suppression
  178. 178. Twin-Image removal
  179. 179. Phase shifting digital holography
  180. 180. Reconstructing
  181. 181. Focus
  182. 182. Segmentation
  183. 183. Extended Focus Image
  184. 184. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  185. 185. Twin-image<br />With the DC-term suppressed we can now view the twin-images.<br />DC-Free Hologram<br />Virtual Image<br />Real Image<br />355 mm<br />-355 mm<br />Contact: conormce@cs.nuim.ie<br />
  186. 186. Twin-image removal<br />There are different approaches for suppressing or removing the unwanted twin. These are dependent on the architecture.<br />We have developed an approach based on image processing for In-Line digital holography.<br />We will discuss this in detail later in the talk<br />Contact: conormce@cs.nuim.ie or tomn@cs.nuim.ie<br />
  187. 187. Outline<br /><ul><li> Introduction
  188. 188. Digital Holography
  189. 189. Recording
  190. 190. Error Terms
  191. 191. Overview
  192. 192. DC-term suppression
  193. 193. Twin-Image removal
  194. 194. Phase shifting digital holography
  195. 195. Reconstructing
  196. 196. Focus
  197. 197. Segmentation
  198. 198. Extended Focus Image
  199. 199. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  200. 200. Phase-shifting digital holography<br />Phase shifting digital holography is a technique which calculates in-line digital holograms which are free of the dc-term and twin-image.<br />This is achieved through recording multiple different holograms where the phase of the reference beam has been modified.<br />By modifying the phase of the reference beam the constant terms in the resulting holograms are the objects amplitude and phase.<br />This allows for the extraction of the object wavefront from multiple holograms.<br />Contact: conormce@cs.nuim.ie<br />
  201. 201. Phase-shifting digital holography<br />Notice that the intensity of the virtual image is much lower than the real image. Phase shifting has suppressed the twin.<br />Virtual Image<br />Real Image<br />Contact: conormce@cs.nuim.ie<br />
  202. 202. Outline<br /><ul><li> Introduction
  203. 203. Digital Holography
  204. 204. Recording
  205. 205. Error Terms
  206. 206. Reconstructing
  207. 207. Focus
  208. 208. Segmentation
  209. 209. Extended Focus Image
  210. 210. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  211. 211. Outline<br /><ul><li> Introduction
  212. 212. Digital Holography
  213. 213. Recording
  214. 214. Error Terms
  215. 215. Reconstructing
  216. 216. Overview
  217. 217. Reconstructing options
  218. 218. Reconstructing perspectives
  219. 219. Speckle reduction
  220. 220. Focus
  221. 221. Segmentation
  222. 222. Extended Focus Image
  223. 223. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  224. 224. Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by the original source, much like in photography.<br />Contact: conormce@cs.nuim.ie<br />
  225. 225. Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by the original source, much like in photography.<br />Photography<br />Sun<br />Viewer<br />PhotoFilm<br />Contact: conormce@cs.nuim.ie<br />
  226. 226. Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by the original source, much like in photography.<br />Holography<br />Laser<br />Viewer<br />Holo Film<br />Contact: conormce@cs.nuim.ie<br />
  227. 227. Reconstructing a digital hologram<br /><ul><li> Focused scene is on film
  228. 228. The eye can focus on different parts of the scene.</li></ul>Holography<br />Photography<br />Sun<br />Laser<br />Viewer<br />Viewer<br />Holo Film<br />PhotoFilm<br />Contact: conormce@cs.nuim.ie<br />
  229. 229. Outline<br /><ul><li> Introduction
  230. 230. Digital Holography
  231. 231. Recording
  232. 232. Error Terms
  233. 233. Reconstructing
  234. 234. Overview
  235. 235. Reconstructing options
  236. 236. Reconstructing perspectives
  237. 237. Speckle reduction
  238. 238. Focus
  239. 239. Segmentation
  240. 240. Extended Focus Image
  241. 241. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  242. 242. Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by a reference beam.<br />In digital holography, numerical reconstruction is achieved through simulating the illumination of the hologram by the reference beam using discrete Fresnel approximations.<br />Contact: conormce@cs.nuim.ie<br />
  243. 243. Reconstructing a digital hologram<br />Reconstructing a hologram is achieved through illuminating the recorded object by a reference beam.<br />In digital holography, numerical reconstruction is achieved through simulating the illumination of the hologram by the reference beam using discrete Fresnel approximations.<br />In this work we employ two approximations<br />Propagation transfer function <br />Discrete Fresnel approximation.<br />Contact: conormce@cs.nuim.ie<br />
  244. 244. The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be thought of as a planar reference beam.<br />Contact: conormce@cs.nuim.ie<br />
  245. 245. The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be thought of as a planar reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is constant for all reconstruction distances.<br />Contact: conormce@cs.nuim.ie<br />
  246. 246. The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be thought of as a planar reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is constant for all reconstruction distances.<br />y<br />x<br />z<br />Hologram<br />Plane<br />Image<br />Plane<br />Contact: conormce@cs.nuim.ie<br />
  247. 247. The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be thought of as a planar reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is constant for all reconstruction distances.<br />This means that field of view is constant irrespective of the propagation distance.<br />Contact: conormce@cs.nuim.ie<br />
  248. 248. The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be thought of as a planar reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is constant for all reconstruction distances.<br />This means that field of view is constant irrespective of the propagation distance.<br />This makes the function reciprocal but also means that if the object recorded is larger than the CCD, to ensure that there is no wrapping in the reconstruction plane sufficient padding needs to be applied at the hologram plane.<br />Contact: conormce@cs.nuim.ie<br />
  249. 249. The propagation transfer function<br />The propagation transfer function illuminates the digital hologram with what can be thought of as a planar reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is constant for all reconstruction distances.<br />This means that field of view is constant irrespective of the propagation distance.<br />This makes the function reciprocal but also means that if the object recorded is larger than the CCD, to ensure that there is no wrapping in the reconstruction plane sufficient padding needs to be applied at the hologram plane.<br />This padding operation can increase computation time.<br />Contact: conormce@cs.nuim.ie<br />
  250. 250. The propagation transfer function<br />Reconstruction plane<br />Hologram plane<br />355 mm<br />2048<br />samples<br />2048<br />samples<br />propagation<br />transfer<br />function<br />Contact: conormce@cs.nuim.ie<br />
  251. 251. The propagation transfer function<br />Reconstruction plane<br />Hologram plane<br />355 mm<br />2048<br />samples<br />2048<br />samples<br />propagation<br />transfer<br />function<br />Aliasing (wrapping of object signal)<br />Contact: conormce@cs.nuim.ie<br />
  252. 252. The propagation transfer function<br />Reconstruction plane<br />Hologram plane<br />355 mm<br />2048<br />samples<br />2048<br />samples<br />propagation<br />transfer<br />function<br />Padding of the hologram plane is required to ensure that the reconstruction is free of wrapping and aliasing.<br />Contact: conormce@cs.nuim.ie<br />
  253. 253. The propagation transfer function<br />Reconstruction plane<br />Hologram plane<br />355 mm<br />2048<br />samples<br />2048<br />samples<br />propagation<br />transfer<br />function<br />4096<br />samples<br />4096<br />samples<br />Contact: conormce@cs.nuim.ie<br />
  254. 254. Discrete Fresnel transform<br />The discrete Fresnel transform illuminates the digital hologram with what can be thought of as a spherical reference beam.<br />Contact: conormce@cs.nuim.ie<br />
  255. 255. Discrete Fresnel transform<br />The discrete Fresnel transform illuminates the digital hologram with what can be thought of as a spherical reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is a function of (primarily) the distance.<br />Contact: conormce@cs.nuim.ie<br />
  256. 256. y<br />x<br />z<br />Discrete Fresnel transform<br />The discrete Fresnel transform illuminates the digital hologram with what can be thought of as a spherical reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is a function of (primarily) the distance.<br />Hologram<br />Plane<br />Image<br />Plane<br />Contact: conormce@cs.nuim.ie<br />
  257. 257. Discrete Fresnel transform<br />The discrete Fresnel transform illuminates the digital hologram with what can be thought of as a spherical reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is a function of (primarily) the distance.<br />This means that as the distance from the digital hologram increases the field of view increases although the number of samples used in the reconstruction process stays the same.<br />Contact: conormce@cs.nuim.ie<br />
  258. 258. Discrete Fresnel transform<br />The discrete Fresnel transform illuminates the digital hologram with what can be thought of as a spherical reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is a function of (primarily) the distance.<br />This means that as the distance from the digital hologram increases the field of view increases although the number of samples used in the reconstruction process stays the same.<br />This also means that the function is not reciprocal.<br />Contact: conormce@cs.nuim.ie<br />
  259. 259. Discrete Fresnel transform<br />The discrete Fresnel transform illuminates the digital hologram with what can be thought of as a spherical reference beam.<br />In this Fresnel approximation the pixel size at the reconstruction plane is a function of (primarily) the distance.<br />This means that as the distance from the digital hologram increases the field of view increases although the number of samples used in the reconstruction process stays the same.<br />This also means that the function is not reciprocal.<br />This allows us to reconstruct objects larger than the CCD with a small number of samples which saves computational time.<br />Contact: conormce@cs.nuim.ie<br />
  260. 260. Discrete Fresnel transform<br />365 mm<br />Reconstruction plane<br />Hologram plane<br />discrete<br />Fresnel<br />transform<br />2048<br />samples<br />2048<br />samples<br />With the discrete Fresnel transform, no padding is required to view this object.<br />Contact: conormce@cs.nuim.ie<br />
  261. 261. Outline<br /><ul><li> Introduction
  262. 262. Digital Holography
  263. 263. Recording
  264. 264. Error Terms
  265. 265. Reconstructing
  266. 266. Overview
  267. 267. Reconstructing options
  268. 268. Reconstructing perspectives
  269. 269. Speckle reduction
  270. 270. Focus
  271. 271. Segmentation
  272. 272. Extended Focus Image
  273. 273. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  274. 274. How do we reconstruct a perspective<br />We select a window size from within the hologram.<br />Win Size<br />Contact: conormce@cs.nuim.ie<br />
  275. 275. How do we reconstruct a perspective<br />We select a window size from within the hologram.<br />There is a trade-off between window size and visual quality.<br />Win Size<br />Contact: conormce@cs.nuim.ie<br />
  276. 276. How do we reconstruct a perspective<br />We select a window size from within the hologram.<br />There is a trade-off between window size and visual quality.<br />We then move the window from the centre of the hologram window.<br />Offset<br />Contact: conormce@cs.nuim.ie<br />
  277. 277. What perspective are we reconstructing<br />Nx<br />y<br />Nx’<br />Ny<br />ay<br />Ny’<br />x<br />ax<br />z<br />d<br />and<br />Contact: conormce@cs.nuim.ie<br />
  278. 278. Perspectives, what we want in the future<br />Nx<br />y<br />Nx’<br />Ny<br />ay<br />Ny’<br />x<br />ax<br />z<br />d<br />We want to move the object closer to the camera<br />We want the size of the camera in mm to stay the same but the pixel size to decrease.<br />Both of these lead to an increase in the range of angles.<br />Contact: conormce@cs.nuim.ie<br />
  279. 279. Outline<br /><ul><li> Introduction
  280. 280. Digital Holography
  281. 281. Recording
  282. 282. Error Terms
  283. 283. Reconstructing
  284. 284. Overview
  285. 285. Reconstructing options
  286. 286. Reconstructing perspectives
  287. 287. Speckle reduction
  288. 288. Focus
  289. 289. Segmentation
  290. 290. Extended Focus Image
  291. 291. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  292. 292. Speckle reduction<br />All coherent imaging systems contain speckle, this is because speckle is created when coherent light illuminates an optically rough surface. <br />The size of speckle increases with the reconstruction distance and exhibits itself as noise in the reconstruction.<br />This is why it is a problem in macroscopic digital holography. The large distance the object needs to be placed away from the camera gives speckle time to evolve and become a corruptive noise in the reconstruction.<br />It is a multiplicative source of noise so standard image processing noise reduction approaches are not always the best option.<br />We apply speckle reduction to reduce noise and improve our image processing algorithms.<br />Contact: conormce@cs.nuim.ie<br />
  293. 293. Speckle reduction<br />Before Speckle reduction<br />After Speckle reduction<br />Contact: conormce@cs.nuim.ie<br />
  294. 294. Speckle reduction<br />Before Speckle reduction<br />After Speckle reduction<br />Contact: conormce@cs.nuim.ie<br />
  295. 295. Outline<br /><ul><li> Introduction
  296. 296. Digital Holography
  297. 297. Focus
  298. 298. Segmentation
  299. 299. Extended Focus Image
  300. 300. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  301. 301. Outline<br /><ul><li> Introduction
  302. 302. Digital Holography
  303. 303. Focus
  304. 304. Focus detection
  305. 305. Autofocus
  306. 306. Depth-from-focus
  307. 307. Segmentation
  308. 308. Extended Focus Image
  309. 309. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  310. 310. Focus Detection<br />Focus detection is based on the application of a focus measure to a set of images or to a region within a set of images.<br />Focus measures are functions which attempt to determine the relative level of focus of sets of images, or regions within sets of images. The accepted image property maximized by these functions is the high spatial frequency energy of the image.<br />Contact: conormce@cs.nuim.ie<br />
  311. 311. High spatial frequency<br />High spatial frequency in images is equivalent to edges, so the more defined an edge is in an image the higher the spatial frequency. <br />Contact: conormce@cs.nuim.ie<br />
  312. 312. High spatial frequency<br />The most accurate way to obtain the spatial frequencies in an image is to use the Fourier transform. The high spatial frequency energy in the Fourier transform is contained in the outer parts of the Fourier transform.<br />Fourier <br />Transform<br />Contact: conormce@cs.nuim.ie<br />
  313. 313. High spatial frequency<br />The most accurate way to obtain the spatial frequencies in an image is to use the Fourier transform. The high spatial frequency energy in the Fourier transform is contained in the outer parts of the Fourier transform.<br />Low Spatial Frequency energy<br />Fourier <br />Transform<br />Contact: conormce@cs.nuim.ie<br />
  314. 314. High spatial frequency<br />The most accurate way to obtain the spatial frequencies in an image is to use the Fourier transform. The high spatial frequency energy in the Fourier transform is contained in the outer parts of the Fourier transform.<br />High Spatial Frequency energy<br />Fourier <br />Transform<br />Contact: conormce@cs.nuim.ie<br />
  315. 315. High spatial frequency<br />So to view the high spatial frequency energy of an image we “block” out the centre pixels from the Fourier transform<br />Fourier <br />Transform<br />X<br />Contact: conormce@cs.nuim.ie<br />
  316. 316. High spatial frequency<br />We then inverse Fourier transform the result and we get a rough edge detected image.<br />Fourier <br />Transform<br />Inverse<br />Fourier <br />Transform<br />X<br />Contact: conormce@cs.nuim.ie<br />
  317. 317. High spatial frequency<br />We then inverse Fourier transform the result and we get a rough edge detected image.<br />Fourier <br />Transform<br />Inverse<br />Fourier <br />Transform<br />X<br />Contact: conormce@cs.nuim.ie<br />
  318. 318. Variance as a focus measure<br />One function which has been shown to be both a sound focus measure and successfully applicable to reconstructions from digital holograms is variance.<br />Image 2<br />Image 4<br />Image 6<br />Image 7<br />Image 10<br />variance<br />Contact: conormce@cs.nuim.ie<br />Image Number<br />
  319. 319. Focus Detection<br />Contact: conormce@cs.nuim.ie<br />
  320. 320. Focus Detection and digital holography<br />We can also reduce the size of the block being focused to detect the focus of smaller image regions.<br />2<br />1<br />4<br />3<br />Contact: conormce@cs.nuim.ie<br />
  321. 321. Outline<br /><ul><li> Introduction
  322. 322. Digital Holography
  323. 323. Focus
  324. 324. Focus detection
  325. 325. Autofocus
  326. 326. Depth-from-focus
  327. 327. Segmentation
  328. 328. Extended Focus Image
  329. 329. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  330. 330. Autofocus - Fibonacci search<br />The Fibonacci search is a modification to the binary search which uses the golden ratio and Fibonacci numbers to speed up the search.<br />Contact: conormce@cs.nuim.ie<br />
  331. 331. Autofocus - Fibonacci search<br />The Fibonacci search is a modification to the binary search which uses the golden ratio and Fibonacci numbers to speed up the search.<br />We use the Fibonacci search and variance, as a focus measure, to create an autofocus algorithm for digital holography. <br />It takes a hologram and a start and end search depth in as input.<br />Contact: conormce@cs.nuim.ie<br />
  332. 332. Autofocus - Fibonacci search<br />The Fibonacci search is a modification to the binary search which uses the golden ratio and Fibonacci numbers to speed up the search.<br />We use the Fibonacci search and variance, as a focus measure, to create an autofocus algorithm for digital holography. <br />It takes a hologram and a start and end search depth in as input.<br />In the first iteration it calculates two depths, reconstructs the hologram and calculates variance on the intensity of the reconstructions.<br />The reconstruction with the highest variance is taken as the best depth estimate. <br />Contact: conormce@cs.nuim.ie<br />
  333. 333. Autofocus - Fibonacci search<br />The Fibonacci search is a modification to the binary search which uses the golden ratio and Fibonacci numbers to speed up the search.<br />We use the Fibonacci search and variance, as a focus measure, to create an autofocus algorithm for digital holography. <br />It takes a hologram and a start and end search depth in as input.<br />In the first iteration it calculates two depths, reconstructs the hologram and calculates variance on the intensity of the reconstructions.<br />The reconstruction with the highest variance is taken as the best depth estimate. <br />At the next iteration a new depth is selected and the focus measure is calculated on the intensity of its reconstruction, it is compared to the previous best focus value and if it is higher, this becomes the new best depth estimate. <br />Contact: conormce@cs.nuim.ie<br />
  334. 334. Autofocus - Fibonacci search<br />The Fibonacci search is a modification to the binary search which uses the golden ratio and Fibonacci numbers to speed up the search.<br />We use the Fibonacci search and variance, as a focus measure, to create an autofocus algorithm for digital holography. <br />It takes a hologram and a start and end search depth in as input.<br />In the first iteration it calculates two depths, reconstructs the hologram and calculates variance on the intensity of the reconstructions.<br />The reconstruction with the highest variance is taken as the best depth estimate. <br />At the next iteration a new depth is selected and the focus measure is calculated on the intensity of its reconstruction, it is compared to the previous best focus value and if it is higher, this becomes the new best depth estimate. <br />This process is continued until the termination condition is met.<br />Contact: conormce@cs.nuim.ie<br />
  335. 335. Fibonacci search – termination condition<br />Typically the Fibonacci search requires a relative definition of accuracy. This is the termination condition as it determines the maximum number of iterations in the Fibonacci search. <br />We have optimized this termination condition for digital holography to take account of the depth-of-focus of the reconstructions.<br />Contact: conormce@cs.nuim.ie<br />
  336. 336. Fibonacci search – termination condition<br />Typically the Fibonacci search requires a relative definition of accuracy. This is the termination condition as it determines the maximum number of iterations in the Fibonacci search. <br />We have optimized this termination condition for digital holography to take account of the depth-of-focus of the reconstructions.<br />Once the depth-of-focus of the two reconstructions being compared by the Fibonacci search overlaps, we stop the search and return the estimated depth. This is because when the depth-of-focus of two reconstructions overlaps we can no longer accurately determine focus.<br />Contact: conormce@cs.nuim.ie<br />
  337. 337. Fibonacci search – termination condition<br />We use the discrete Fresnel transform in our Fibonacci search this is to allow us to compute reconstructions without aliasing faster than if we were using the propagation transfer function.<br />Contact: conormce@cs.nuim.ie<br />
  338. 338. Fibonacci search – termination condition<br />We use the discrete Fresnel transform in our Fibonacci search this is to allow us to compute reconstructions without aliasing faster than if we were using the propagation transfer function.<br />We can calculate the depth-of-focus range [zi,zj] of a reconstruction at distance d using this reconstruction method with:<br />where ΔX is the size of the CCD <br />Contact: conormce@cs.nuim.ie<br />
  339. 339. Fibonacci search – termination condition<br />We use the discrete Fresnel transform in our Fibonacci search this is to allow us to compute reconstructions without aliasing faster than if we were using the propagation transfer function.<br />We can calculate the depth-of-focus range [zi,zj] of a reconstruction at distance d using this reconstruction method with:<br />where ΔX is the size of the CCD <br />The depth-of-focus for reconstructions ranging from 170mm to 1000mm is displayed in this plot.<br />Contact: conormce@cs.nuim.ie<br />
  340. 340. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Contact: conormce@cs.nuim.ie<br />
  341. 341. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Reconstruction distance<br />Contact: conormce@cs.nuim.ie<br />
  342. 342. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Focus value for that distance<br />Contact: conormce@cs.nuim.ie<br />
  343. 343. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Red means current best estimate.<br />Contact: conormce@cs.nuim.ie<br />
  344. 344. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Iteration 2:<br />365.93mm (73.3)<br />Contact: conormce@cs.nuim.ie<br />
  345. 345. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Iteration 2:<br />365.93mm (73.3)<br />Iteration 3:<br />291.1mm (35.9)<br />Contact: conormce@cs.nuim.ie<br />
  346. 346. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Iteration 2:<br />365.93mm (73.3)<br />Iteration 3:<br />291.1mm (35.9)<br />412.20mm (44.8)<br />Iteration 4:<br />Contact: conormce@cs.nuim.ie<br />
  347. 347. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Iteration 2:<br />365.93mm (73.3)<br />Iteration 3:<br />291.1mm (35.9)<br />412.20mm (44.8)<br />Iteration 4:<br />Iteration 5:<br />337.35mm (66.6)<br />Contact: conormce@cs.nuim.ie<br />
  348. 348. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Iteration 2:<br />365.93mm (73.3)<br />Iteration 3:<br />291.1mm (35.9)<br />412.20mm (44.8)<br />Iteration 4:<br />Iteration 5:<br />337.35mm (66.6)<br />Iteration 6:<br />383.6mm (54.3)<br />Contact: conormce@cs.nuim.ie<br />
  349. 349. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Iteration 2:<br />365.93mm (73.3)<br />Iteration 3:<br />291.1mm (35.9)<br />412.20mm (44.8)<br />Iteration 4:<br />Iteration 5:<br />337.35mm (66.6)<br />Iteration 6:<br />383.6mm (54.3)<br />Iteration 7:<br />355.02mm (103.1)<br />Contact: conormce@cs.nuim.ie<br />
  350. 350. Autofocus - Fibonacci search example<br />Search Range: [170mm,............................................................................................., 1000mm]<br />Iteration 1:<br />487.03mm (26.5)<br />682.96mm (22.3)<br />Iteration 2:<br />365.93mm (73.3)<br />Iteration 3:<br />291.1mm (35.9)<br />412.20mm (44.8)<br />Iteration 4:<br />Iteration 5:<br />337.35mm (66.6)<br />Iteration 6:<br />383.6mm (54.3)<br />Iteration 7:<br />355.02mm (103.1)<br />...............<br />Iteration 14:<br />353.42mm (108.0)<br />Contact: conormce@cs.nuim.ie<br />
  351. 351. Autofocus - Fibonacci search example<br />In this example we compare our optimized Fibonacci search with a fixed step size search with a step size of 1mm over a search range between [170mm,1000mm]. <br />We took a Two bolts hologram and computed the fixed step size search and the Fibonacci search. <br />Displayed in the plot is the first 8 estimates output from Fibonacci (both correct and incorrect) overlayed on the focus plot from the fixed step size search.<br />Contact: conormce@cs.nuim.ie<br />
  352. 352. Autofocus<br />Contact: conormce@cs.nuim.ie<br />
  353. 353. Outline<br /><ul><li> Introduction
  354. 354. Digital Holography
  355. 355. Focus
  356. 356. Focus detection
  357. 357. Autofocus
  358. 358. Depth-from-focus
  359. 359. Segmentation
  360. 360. Extended Focus Image
  361. 361. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  362. 362. What is Depth-from focus?<br /> Depth-From-Focus is an image processing technique which is used to determine the depth of a scene or a region within a scene through processing images taken at different focal depths.<br />Why is this applicable to digital holography?<br />Digital Holograms can be numerically reconstructed at an arbitrary depth. <br />These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm.<br />We can then create depth maps of the scene, segment the scene and create extended focused images of the scene.<br />Contact: conormce@cs.nuim.ie<br />
  363. 363. What is Depth-from focus?<br /> Depth-From-Focus is an image processing technique which is used to determine the depth of a scene or a region within a scene through processing images taken at different focal depths.<br />Why is this applicable to digital holography?<br />Digital Holograms can be numerically reconstructed at an arbitrary depth. <br />These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm.<br />We can then create depth maps of the scene, segment the scene and create extended focused images of the scene.<br />Contact: conormce@cs.nuim.ie<br />
  364. 364. What is Depth-from focus?<br /> Depth-From-Focus is an image processing technique which is used to determine the depth of a scene or a region within a scene through processing images taken at different focal depths.<br />Why is this applicable to digital holography?<br />Digital Holograms can be numerically reconstructed at an arbitrary depth. <br />These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm.<br />We can then create depth maps of the scene, segment the scene and create extended focused images of the scene.<br />Contact: conormce@cs.nuim.ie<br />
  365. 365. How to compute a depth map<br />The depth-from-focus process is a three stage process. In the first stage we create a volume of reconstructions over a range of depths. We then apply speckle reduction<br />Stage 1:<br /> At each depth, reconstruct.<br />Focus depthzmax<br />Digital hologram<br />Focus depthzmin<br />Iz(k,l)‏<br />Contact: conormce@cs.nuim.ie<br />
  366. 366. How to compute a depth map<br />In the second stage we calculate what we call focus maps. These are created by computing a focus measure on each overlapping n x n pixel block in a reconstruction.<br />Stage 1:<br /> At each depth, reconstruct and apply speckle reduction.<br />Stage 2:<br /> Calculate focus on each overlapping n x n pixel block of the reconstructions.<br />Focus depthzmax<br />Digital hologram<br />Focus depthzmin<br />Vz(k,l)‏<br />Iz(k,l)‏<br />Contact: conormce@cs.nuim.ie<br />
  367. 367. n<br />n<br />Focus Maps<br />To compute a focus map, we first take a reconstruction and a block size of [n x n]. <br />We then calculate our focus measure on the first block in the top left corner of the reconstruction <br />We then process every block in the reconstruction by raster scanning the reconstruction and processing every block with our focus measure. <br />We store the output value from each block in its corresponding position in a focus map.<br />Contact: conormce@cs.nuim.ie<br />
  368. 368. How to compute a depth map<br />Once we have our focus maps we can continue to our third and final stage which is the computation of the maximum focus map and the depth map.<br />Stage 1:<br /> At each depth, reconstruct and apply speckle reduction.<br />Stage 3: <br />Calculate the maximum focus map and depth map.<br />Stage 2:<br /> Calculate focus on each overlapping n x n pixel block of the reconstructions.<br />Focus depthzmax<br />Max<br />values<br />For each (k,l) find maximum over z<br />Vmax(k,l)‏<br />Digital hologram<br />Depths of max values<br />Focus depthzmin<br />Vz(k,l)‏<br />Iz(k,l)‏<br />D(k,l)‏<br />Contact: conormce@cs.nuim.ie<br />
  369. 369. Depth-from-focus<br />Maximum focus map<br />Depth Map<br />So what are the limiting factors, the factors that affect the quality of depth-from-focus? These are:<br /><ul><li> the block size input to DFF
  370. 370. noise reduction
  371. 371. and the distance between reconstructions</li></ul>Contact: conormce@cs.nuim.ie<br />
  372. 372. Block Size<br /> To determine the depth of a block in an image using a focus measure there needs to be enough object information in the block.<br />Smaller block sizes: finer object features but high error in the estimate of the general shape.<br />Larger block sizes: low error but fine object features lost.<br />Object<br />Contact: conormce@cs.nuim.ie<br />7x7<br />43x43<br />81x81<br />121x121<br />151x151<br />
  373. 373. Speckle reduction<br />Before Speckle reduction<br />After Speckle reduction<br />Contact: conormce@cs.nuim.ie<br />
  374. 374. Speckle reduction<br />Before Speckle reduction<br />After Speckle reduction<br />Contact: conormce@cs.nuim.ie<br />
  375. 375. Distance between reconstructions<br />By changing the distance between reconstructions we affect the quality of the depth maps. The smaller the distance the more features we can detect but at the expense of speed.<br />Contact: conormce@cs.nuim.ie or tomn@cs.nuim.ie<br />
  376. 376. Distance between reconstructions<br />By changing the distance between reconstructions we affect the quality of the depth maps. The smaller the distance the more features we can detect but at the expense of speed.<br />Contact: conormce@cs.nuim.ie or tomn@cs.nuim.ie<br />
  377. 377. Depth map examples<br />Depth map of some hairs recorded by digital holography<br />Reconstruction<br />Depth Map<br />Contact: conormce@cs.nuim.ie<br />
  378. 378. Depth map examples<br />Depth map of a lego block recorded by digital holography<br />Reconstruction<br />Depth Map<br />Contact: conormce@cs.nuim.ie<br />
  379. 379. Outline<br /><ul><li> Introduction
  380. 380. Digital Holography
  381. 381. Focus
  382. 382. Segmentation
  383. 383. Extended Focus Image
  384. 384. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  385. 385. Outline<br /><ul><li> Introduction
  386. 386. Digital Holography
  387. 387. Focus
  388. 388. Segmentation
  389. 389. Background segmentation
  390. 390. Depth segmentation
  391. 391. Extended Focus Image
  392. 392. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  393. 393. What is background segmentation?<br />Background segmentation is the partitioning of a scene into object and background.<br />We have observed that background regions have a lower focus value than object blocks for all depths. We can use this to threshold our maximum focus map into object and background<br />Threshold Line<br />Contact: conormce@cs.nuim.ie<br />
  394. 394. Background segmentation<br />Background segmentation is a simple process, where we take the maximum focus map threshold it and then binarise the result.<br />This is achieved by taking a value A, where everything above A in the maximum focus map is assigned the value 1 and everything below is assigned the value 0.<br />Threshold, binarise<br />and erode<br />Maximum focus map<br />Segmentation mask<br />Contact: conormce@cs.nuim.ie<br />
  395. 395. Thresholding<br />The threshold is manually selected and the effects are shown below.<br />A threshold that is too high does not segment all of the background.<br />A threshold that is too low does not segment all of the object.<br />Reconstruction<br />Segmentation mask<br />Contact: conormce@cs.nuim.ie<br />
  396. 396. Background segmentation<br />Numerical Reconstruction<br />Segmentation Mask<br />Segmented Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  397. 397. Outline<br /><ul><li> Introduction
  398. 398. Digital Holography
  399. 399. Focus
  400. 400. Segmentation
  401. 401. Background segmentation
  402. 402. Depth segmentation
  403. 403. Extended Focus Image
  404. 404. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  405. 405. What is depth segmentation<br />Depth segmentation is the partitioning of a scene into individual objects after the background has been segmented.<br />Why do we want to perform depth segmentation?<br />Again using the example of object recognition, if a scene is complex (containing multiple occluding objects), using depth segmentation we can partition the scene into independent objects for analysis.<br />Reconstruction<br />Depth Map<br />Depth Maps Histogram<br />1<br />2<br />2<br />2<br />1<br />1<br />Contact: conormce@cs.nuim.ie<br />
  406. 406. How do we segment based on depth<br />Select N<br />largest<br />modes from histogram<br />Contact: conormce@cs.nuim.ie<br />
  407. 407. How do we segment based on depth<br />Select N<br />largest<br />modes from histogram<br />1<br />2<br />Contact: conormce@cs.nuim.ie<br />
  408. 408. How do we segment based on depth<br />Select N<br />largest<br />modes from histogram<br />Label all pixels belonging to<br />each mode with the mode index (i.e 1 or 2)<br />1<br />2<br />Contact: conormce@cs.nuim.ie<br />
  409. 409. How do we segment based on depth<br />Extract unlabelled object pixels<br />Select N<br />largest<br />modes from histogram<br />Label all pixels belonging to<br />each mode with the mode index (i.e 1 or 2)<br />1<br />2<br />Contact: conormce@cs.nuim.ie<br />
  410. 410. How do we segment based on depth<br />Extract unlabelled object pixels<br />Select N<br />largest<br />modes from histogram<br />+<br />Label all pixels belonging to<br />each mode with the mode index (i.e 1 or 2)<br />1<br />2<br />Contact: conormce@cs.nuim.ie<br />
  411. 411. How do we segment based on depth<br />Segmentation Image<br />Extract unlabelled object pixels<br />Select N<br />largest<br />modes from histogram<br />+<br />Label all pixels belonging to<br />each mode with the mode index (i.e 1 or 2)<br />1<br />2<br />Contact: conormce@cs.nuim.ie<br />
  412. 412. Processing the segmentation image<br />We have one final step which we use to improve the depth segmentation images. <br />We calculate the area of each of the distinct regions in the segmentation image and remove ones with a relatively small area.<br />We then reassign these pixels to the object with the nearest boundary.<br />Remove small objects from the segmentation image<br /> and resassign these pixels to the nearest object<br />Contact: conormce@cs.nuim.ie<br />
  413. 413. Depth segmentation examples<br />Segmentation Image<br />Region 1<br />Region 2<br />Contact: conormce@cs.nuim.ie<br />
  414. 414. Depth segmentation examples<br />Segmentation Image<br />Region 1<br />Region 2<br />Region 3<br />Region 4<br />Contact: conormce@cs.nuim.ie<br />
  415. 415. Depth segmentation examples<br />Segmentation Image<br />Reconstruction<br />Region 1<br />Region 2<br />Region 3<br />Contact: conormce@cs.nuim.ie<br />
  416. 416. Outline<br /><ul><li> Introduction
  417. 417. Digital Holography
  418. 418. Focus
  419. 419. Segmentation
  420. 420. Extended Focus Image
  421. 421. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  422. 422. What is an Extended Focused image?<br />A disadvantage of holographic reconstructions is the limited depth of field. For a reconstruction at depth d only object points that are located at distance d from the camera are in focus.<br />Why do we want to create an extended focused image?<br />This means that reconstructions can contain large blurry regions. Using our depth maps and the volume of reconstructions used to create them we can create an extended focused image.<br />=<br />+<br />Contact: conormce@cs.nuim.ie<br />Volume of Reconstructions<br />Extended Focused Image<br />Depth Map<br />
  423. 423. Extended focused image creation<br />Contact: conormce@cs.nuim.ie<br />
  424. 424. Extended focused image creation<br />Contact: conormce@cs.nuim.ie<br />
  425. 425. Extended focused image examples<br />Front focal plane<br />Back focal plane<br />1<br />2<br />Extended Focused Image<br />Contact: conormce@cs.nuim.ie<br />
  426. 426. Extended focused image Region 1 <br />Front focal plane<br />Back focal plane<br />Extended Focused Image<br />Contact: conormce@cs.nuim.ie<br />
  427. 427. Extended focused image Region 2<br />Front focal plane<br />Back focal plane<br />Extended Focused Image<br />Contact: conormce@cs.nuim.ie<br />
  428. 428. Extended focused image example<br />Front focal plane<br />Back focal plane<br />Extended Focused Image<br />Contact: conormce@cs.nuim.ie<br />
  429. 429. Outline<br /><ul><li> Introduction
  430. 430. Digital Holography
  431. 431. Focus
  432. 432. Segmentation
  433. 433. Extended Focus Image
  434. 434. Twin-Image removal</li></ul>Contact: conormce@cs.nuim.ie<br />
  435. 435. Twin-image removal algorithm<br />Our twin-image removal algorithm is a three stage process which takes a DC-term suppressed hologram as input. <br />1<br />2<br />3<br />Twin-Image<br />Reconstruction<br />Twin-Image<br />Segmentation<br />Propagation<br />Contact: conormce@cs.nuim.ie<br />
  436. 436. Stage 1: Twin-image Reconstruction<br />The first step of this stage is to determine the focal plane. We have developed a novel fast autofocus algorithm for digital holography.<br />a<br />Automatically detect focal plane<br />Fibonascci<br />focus <br />search<br />d<br />Contact: conormce@cs.nuim.ie<br />
  437. 437. Stage 1: Twin-image Reconstruction<br />a<br />Automatically detect focal plane<br />Fibonascci<br />focus <br />search<br />d<br />Once we have the correct depth we need to calculate the amount of padding required to ensure no aliasing of the wanted object signal.<br />Reconstruct Twin-Image<br />b<br />Twin-Image<br />Hologram Plane<br />Reconstruction<br />Fresnel <br />Transform<br />Fresnel <br />Transform<br />-d<br />d<br />Contact: conormce@cs.nuim.ie<br />
  438. 438. Twin-image Reconstruction<br />We need to pad the hologram to ensure that there is no aliasing. <br />If there is aliasing it means we could remove some of the wanted object in the segmentation process.<br />d mm<br />Twin-Image plane<br />Hologram plane<br />propagation<br />transfer<br />function<br />NH<br />samples<br />NH<br />samples<br />2048<br />samples<br />Contact: conormce@cs.nuim.ie<br />
  439. 439. Stage 2: Twin-image Segmentation<br />The first step in Stage 2 is to calculate a focus map from the intensity of a holograms reconstruction, which will then be used to create a segmentation mask.<br />a<br />Calculate Segmentation Mask<br />Twin-Image Intensity<br />Segmentation Mask<br />Focus Map<br />Calculate<br />Focus Map<br />Threshold<br />and <br />Binarize<br />Contact: conormce@cs.nuim.ie<br />
  440. 440. Background segmentation<br />Simple, accurate background segmentation<br />threshold,<br />erode,<br />binarize<br />Contact: conormce@cs.nuim.ie<br />
  441. 441. Background segmentation<br />Simple, accurate background segmentation<br />threshold,<br />erode,<br />binarize<br />Contact: conormce@cs.nuim.ie<br />
  442. 442. Background segmentation<br />Simple, accurate background segmentation<br />threshold,<br />erode,<br />binarize<br />Contact: conormce@cs.nuim.ie<br />
  443. 443. Stage 2: Twin-image Segmentation<br />Now that we have our reconstruction and our segmentation mask, we apply elementwise multiplication to calculate a wavefront free of the twin-image.<br />a<br />Calculate Segmentation Mask<br />Twin-Image Intensity<br />Segmentation Mask<br />Focus Map<br />Calculate<br />Focus Map<br />Threshold<br />and <br />Binarize<br />b<br />Segment Twin-Image<br />Segmented Twin-Image<br />Segmentation Mask<br />Twin-Image<br />X<br />=<br />Contact: conormce@cs.nuim.ie<br />
  444. 444. Stage 3: Propagation<br />In the third stage we then propagate the twin-image free wavefront back to the hologram plane and remove the centre pixels which relate to the original size of the hologram before padding. <br />Segmented Twin-Image<br />Hologram Plane<br />Fresnel Transform<br />d<br />H(x,y)‏<br />We now have a hologram (H(x,y)) which is free of the twin-image.<br />Contact: conormce@cs.nuim.ie<br />
  445. 445. Implementation<br />We have implemented our algorithm using our framework for digital hologram processing on programmable graphics hardware which has been shown to render images from DHs far more efficiently than traditional CPU-based methods.<br />This stage uses the discrete Fresnel transform and uses holograms of size 2048 x2048<br />Contact: conormce@cs.nuim.ie<br />
  446. 446. Results – Two bolts object<br />DC-term suppressed Hologram Reconstruction<br />Original Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  447. 447. Results – Two bolts object<br />DC-term suppressed Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  448. 448. Results – Two bolts object<br />DC-term suppressed Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  449. 449. Results – Lego block object<br />DC-term suppressed Hologram Reconstruction<br />Original Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  450. 450. Results – Lego block object<br />DC-term suppressed Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  451. 451. Results – Lego block object<br />DC-term suppressed Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  452. 452. Results – Knight object<br />DC-term suppressed Hologram Reconstruction<br />Original Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  453. 453. Results – Knight object<br />DC-term suppressed Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  454. 454. Results – Knight object<br />DC-term suppressed Hologram Reconstruction<br />Twin-image removed Hologram Reconstruction<br />PSI Hologram Reconstruction<br />Contact: conormce@cs.nuim.ie<br />
  455. 455. Results – Rotating object<br />Contact: conormce@cs.nuim.ie<br />
  456. 456. The End – Questions?<br />DC-term suppressed hologram reconstructions<br />Twin-image removed hologram reconstructions<br />Contact: conormce@cs.nuim.ie or tomn@cs.nuim.ie<br />
  457. 457. Contact: conormce@cs.nuim.ie<br />
  458. 458. Contact: conormce@cs.nuim.ie<br />
  459. 459. d<br />Correct object placement<br />To fulfill the sampling theorem an object of size sizeΔO must be placed at least a distance d from the CCD<br />Object<br />plane<br />CCD<br />θ<br />ΔO<br />ΔX<br />d1<br />d2<br />Contact: conormce@cs.nuim.ie<br />
  460. 460. d<br />Correct object placement<br />To fulfill the sampling theorem an object of size sizeΔO must be placed at least a distance d from the CCD<br />This distance d can be calculated with:<br />where δx is the spatial resolution of a pixel on the CCD.<br />Object<br />plane<br />CCD<br />θ<br />ΔO<br />ΔX<br />d1<br />d2<br />Contact: conormce@cs.nuim.ie<br />
  461. 461. d<br />Correct object placement<br />To fulfill the sampling theorem an object of size sizeΔO must be placed at least a distance d from the CCD<br />This distance d can be calculated with:<br />where δx is the spatial resolution of a pixel on the CCD.<br />We can also express the maximum interference angle (theta) as:<br />Object<br />plane<br />CCD<br />θ<br />ΔO<br />ΔX<br />d1<br />d2<br />Contact: conormce@cs.nuim.ie<br />
  462. 462. d<br />Calculating padding<br />If you were to propagate the object signal from the object plane to the Twin-image plane, the object signals spatial extent would have increased significantly.<br />We have worked this out as: <br />Twin-image<br /> plane<br />Object<br />plane<br />Δq<br />CCD<br />θ<br />θ<br />ΔT<br />ΔO<br />ΔX<br />d1<br />d2<br />θ<br />Δq<br />Contact: conormce@cs.nuim.ie<br />
  463. 463. d<br />Calculating padding<br />To calculate the spatial extent of the object signal (ΔT) we need to be able to calculate Δq.<br />Twin-image<br /> plane<br />Object<br />plane<br />Δq<br />CCD<br />θ<br />θ<br />ΔT<br />ΔO<br />ΔX<br />d1<br />d2<br />θ<br />Δq<br />Contact: conormce@cs.nuim.ie<br />
  464. 464. d<br />Calculating padding<br />To calculate the spatial extent of the object signal (ΔT) we need to be able to calculate Δq.<br />It can be seen from the diagram below that Δq can be represented as<br />Twin-image<br /> plane<br />Object<br />plane<br />Δq<br />CCD<br />θ<br />θ<br />ΔT<br />ΔO<br />ΔX<br />d1<br />d2<br />θ<br />Δq<br />Contact: conormce@cs.nuim.ie<br />
  465. 465. d<br />Calculating padding<br />To calculate the spatial extent of the object signal (ΔT) we need to be able to calculate Δq.<br />It can be seen from the diagram below that Δq can be represented as<br />And that d can be expressed as:<br />Twin-image<br /> plane<br />Object<br />plane<br />Δq<br />CCD<br />θ<br />θ<br />ΔT<br />ΔO<br />ΔX<br />d1<br />d2<br />θ<br />Δq<br />Contact: conormce@cs.nuim.ie<br />
  466. 466. Calculating padding<br />To calculate the spatial extent of the object signal (ΔT) we need to be able to calculate Δq.<br />It can be seen from the diagram below that Δq can be represented as<br />And that d can be expressed as:<br />We can then express d1,2 in terms of theta:<br />Contact: conormce@cs.nuim.ie<br />
  467. 467. Calculating padding<br />To calculate the spatial extent of the object signal (ΔT) we need to be able to calculate Δq.<br />It can be seen from the diagram below that Δq can be represented as<br />And that d can be expressed as:<br />We can then express d1,2 in terms of theta:<br />and simplify these to:<br />Contact: conormce@cs.nuim.ie<br />
  468. 468. Calculating padding<br />To calculate the spatial extent of the object signal (ΔT) we need to be able to calculate Δq.<br />It can be seen from the diagram below that Δq can be represented as<br />And that d can be expressed as:<br />and simplify these to:<br />We can then express d as:<br />Contact: conormce@cs.nuim.ie<br />
  469. 469. Calculating padding<br />We can now represent Δq in terms of the object size and CCD size. <br />Contact: conormce@cs.nuim.ie<br />
  470. 470. Calculating padding<br />We can now represent Δq in terms of the object size and CCD size. <br />And ΔT (the spatial extent of the object signal in the twin plane) as: <br />Contact: conormce@cs.nuim.ie<br />
  471. 471. Calculating padding<br />Now that we have the spatial extent of the object signal we can calculate the number of samples required in the hologram plane (NH) with<br />Contact: conormce@cs.nuim.ie<br />
  472. 472. Calculating padding<br />Now that we have the spatial extent of the object signal we can calculate the number of samples required in the hologram plane (NH) with<br />Padding up to this amount guarantees that after propagation to the unwanted twin- image plane the object signal will not be wrapped within the reconstruction window.<br />This equation relies on knowing Δ O which is unknown.<br />Contact: conormce@cs.nuim.ie<br />
  473. 473. Calculating padding<br />Now that we have the spatial extent of the object signal we can calculate the number of samples required in the hologram plane (NH) with<br />Padding up to this amount guarantees that after propagation to the unwanted twin- image plane the object signal will not be wrapped within the reconstruction window.<br />This equation relies on knowing Δ O which is unknown.<br />We take the nearest power of 2 that the is equal to or greater than NH, this is due to the current algorithms use of the fast Fourier transform which is more efficiently computed when a matrix whose size is a power of 2 is input<br />Contact: conormce@cs.nuim.ie<br />
  474. 474. Calculating ΔO<br />But assuming that the hologram was recorded in adherence to the sampling theorem, if we can calculate the distance d the object was positioned away from the CCD we can calculate the maximum size of Δ O at d using<br />(where Nx is the number of samples in the CCD)<br />Contact: conormce@cs.nuim.ie<br />
  475. 475. Calculating ΔO<br />But assuming that the hologram was recorded in adherence to the sampling theorem, if we can calculate the distance d the object was positioned away from the CCD we can calculate the maximum size of ΔO at d using<br />(where Nx is the number of samples in the CCD)<br />Given that we have developed a fast autofocus algorithm, we now have an equation for calculating the number of samples required in the hologram plane to avoid aliasing with no unknowns.<br />Contact: conormce@cs.nuim.ie<br />
  476. 476. Twin-image Reconstruction<br />Now that we have the distance to the in-focus plane of the twin-image and the required amount of padding to ensure no aliasing in the reconstruction plane, we can reconstruct the twin-image with the propagation transfer function.<br />Contact: conormce@cs.nuim.ie<br />

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