A calculation model for the collinear holographic systems

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A calculation model for the collinear holographic
systems

• Tsutomu SHIMURA, Shotaro ICHIMURA,
• Ryushi FUJIMURA, and Kazuo KURODA
• IIS, the University of Tokyo
• Xiaodi TAN and Hideyoshi HORIMAI
• OPTWARE Corp

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Collinear Holographic System

• Common objective lens for signal and reference
  beams.
• simple system
• stable
• servo system for conventional optical discs
• Good performance in experiments
• low bit error rate
• high shift selectivity
• large tolerance

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But...

• Theoretical background
• has not been made fully clear yet.
• Especially, why radial, wheel like illumination
  pattern gives good experimental results?
• We present a simple model which gives,
• physical picture of the image formation,
• calculation of pixel spread function,
• a tool to consider the recording density.

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Our Model
Spatial Light Modulator
pixel square aperture
reference pixels
data pixels
f
objective lens
Frounhofer regime
signal
f
reference
recording medium
grating ? coupled mode theory
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Key of our model

• We consider the collinear holographic system can
  as summation of interference of two plane waves.

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Phase mismatch

• Deviation from the Eward sphere
• Existing gratings Kijkl
• all combinations of (i,j), (k,l)
• Diffraction efficiency h, read by (m,n)
• In most cases
• h 0 for (m,n)?(k,l)
• Exception
• Bragg degeneracy

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Diffracted light from one grating Kijkl
illuminated by all reference pixels
calculation 201?201 pixels
just for ONE data pixel
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Integrate all diffracted waves over all gratings

• coherent summation of all diffracted waves to the
  data pixel (i,j) (example)

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Pixel spread function (PxSF)

• has same function as Point Spread Function (PSF)
  in linear imaging system.
• As long as the response of the recording media is
  linear,
• The reconstructed image of the system can be
  calculated by convolution of the PxSF and the
  object.
• Note that PxSF for holographic memory is complex
  function.

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E2 for ring and radial reference pattern
thickness 500 mm
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Ring illumination pattern
Bragg degeneracy
Bragg selectivity
Integration of the diffracted line pattern over
all gratings
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Radial 3 degrees
Integration of the diffracted line pattern over
all gratings
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radial 6 degrees
Integration of the diffracted line pattern over
all gratings
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Thickness
thickness 0.1 mm ? 0.2 mm ? 1.0 mm
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Summary

• Simple model for understanding the image
  formation in Collinear holographic system
• Spread of single point image is determined by
• illumination pattern
• to avoid the effect of Bragg degeneracy
• media thickness
• due to Bragg selectivity
• Recording density
• Media thickness -gt pixel size
• Shift selectivity -gt NA of objective lens