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Computer Generated Holograms CGH

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Compute the mathematical hologram (or amplitude and phase distribution) ... To reproduce an object as a hologram we need to reproduce the intensities and ... – PowerPoint PPT presentation

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Title: Computer Generated Holograms CGH


1
Computer Generated Holograms (CGH)
  • Digital Image Processing III
  • 2004
  • Leppänen Smolander

2
Contents
  • Introduction to CGH
  • Mathematical Models
  • Methods for Encoding and Recording
  • Reconstruction

3
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
4
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

5
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

6
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
7
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

8
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)

9
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
10
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

11
Source
  • Digital Holography and Digital Image Processing -
    Principles, Methods, Algorithms, Leonid
    Yaroslavsky, Kluwer Academic Publishers 2004
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