Computer Generated Holograms CGH

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Computer Generated Holograms (CGH)

• Digital Image Processing III
• 2004
• Leppänen Smolander

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Contents

• Introduction to CGH
• Mathematical Models
• Methods for Encoding and Recording
• Reconstruction

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Introduction to CGH (1)

• Basic stages in the synthesis of CGH
• Find mathematical model for the object and usage
• Compute the mathematical hologram (or amplitude
  and phase distribution)
• Encode samples of the mathematical hologram
• Record the hologram on the physical medium

Computer
Complex amplitude
Computing mathematical hologram
Mathematical model
Usage model
DA conversion
Encoding
Recording
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Introduction to CGH (2)

• Major applications of CGH
• Spatial filters for optical information
  processing
• Optical elements e.g. beam formers, deflectors,
  special diffraction gratings, and information
  display
• Here we focus mainly on display holograms

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Mathematical Models (1)

• To reproduce an object as a hologram we need to
  reproduce the intensities and phases of the light
  waves scattered by the object
• If monochromatic illumination is considered only
  wave amplitude and phase is needed
• Objects ability to reflect and scatter light can
  be described by a radiation reflection factor,
  complex function
• o(x,y,z) o(x,y,z)expiT(x,y,z)
• Light wave field over an object can be described
  by a wave propagation integral over the objects
  surface
• Needed 3D integral can be reduced to 2D by taking
  into consideration natural limitations of visual
  observation
• Integral depends on geometrical dimensions of the
  object and distance of the object from the
  observation plane

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Mathematical Models (2)

• Further simplifications
• Fresnel hologram
• Fourier hologram
• Both can be computed with DFT

Parallel light source
Point light source
Hologram
Hologram
Fresnel hologram
Fourier hologram
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Methods for Encoding and Recording (1)

• Three types of optical media
• Amplitude-only
• Phase-only
• Combined amplitude/phase
• Amplitude-only media
• Controllable parameter is the light intensity
  transmission
• Most common (e.g. silver galid photographic
  emulsion in photography)
• Phase-only
• Controllable parameter is the optical thickness
• E.g. thermoplastic materials, recently micro-lens
  and mirror arrays

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Methods for Encoding and Recording (2)

• Combined amplitude/phase media
• Both parameters, light intensity transmission and
  optical thickness, can be controlled
• Photographic materials with several layers for
  different wavelengths
• No specific recording devices available computer
  printer and display devices are used instead
  which have some drawbacks (binary media)
• Recording methods can be categorized e.g. respect
  to methods of representing complex numbers
  (samples of mathematical hologram)

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Methods for Encoding and Recording (3)
Exponential representation
Combined media
On axis hologram

Phase-only media
Kinoform
Amplitude- only media
Symmetrization
Detour phase
Binary media
Additive representation
Double-phase method
Phase-only media
Multiple phase method
Binary media
Representation by Orthogonal and
bi- orthogonal components
Amplitude- only media
2D-symplex representation
Explicit spatial carrier methods
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Reconstruction

• In the reconstruction CGH (discrete) are
  subjected to analog optical transformation
  (consider as digital to analog conversion)
• Characteristics of a recording device that affect
  the reconstruction
• Type of discretization raster
• Discretization intervals
• Recording aperture
• Physical size of recorded hologram
• An example of symmetrization method on an
  amplitude-only medium given in the book

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Source

• Digital Holography and Digital Image Processing -
  Principles, Methods, Algorithms, Leonid
  Yaroslavsky, Kluwer Academic Publishers 2004