Holography

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Holography

• Mon. Dec. 2, 2002

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History of Holography

• Invented in 1948 by Dennis Gabor for use in
  electron microscopy, before the invention of the
  laser
• Leith and Upatnieks (1962) applied laser light to
  holography and introduced an important off-axis
  technique

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Conventional vs. Holographic photography

• Conventional
• 2-d version of a 3-d scene
• Photograph lacks depth perception or parallax
• Film sensitive only to radiant energy
• Phase relation (i.e. interference) are lost

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Conventional vs. Holographic photography

• Hologram
• Freezes the intricate wavefront of light that
  carries all the visual information of the scene
• To view a hologram, the wavefront is
  reconstructed
• View what we would have seen if present at the
  original scene through the window defined by the
  hologram
• Provides depth perception and parallax

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Conventional vs. Holographic photography

• Hologram
• Converts phase information into amplitude
  information (in-phase - maximum amplitude,
  out-of-phase minimum amplitude)
• Interfere wavefront of light from a scene with a
  reference wave
• The hologram is a complex interference pattern of
  microscopically spaced fringes
• holos Greek for whole message

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Hologram of a point source
Construction of the hologram of a point
source Any object can be represented as a
collection of points
Photographic plate

• Photosensitive plate
• Records interference pattern (linear response)
• Emulsion has small grain structure (??)

Reference wave - plane
x
z
Object wave - spherical
y
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Point object hologram construction Intensity
distribution on plate

• Reference wave
• Object wave
• Intensity distribution on plate

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Hologram construction
Gabor zone plate
Maxima for kr2m? or rm? i.e. if the OPL
difference OZ OP is an integral number of
wavelengths, the reference beam arrives at P in
step with the scattered (i.e. object) beam.
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Hologram

• When developed the photographic plate will have a
  transmittance which depends on the intensity
  distribution in the recorded plate
• tb backgrond transmittance due to R2 term
• B parameter which is a function of the
  recording an developing process

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Hologram reconstruction

• When illuminated by a coherent wave, A(x,y),
  known as the reconstruction wave, the optical
  field emerging from the transparency is,
• i.e. a superposition of 4 waves
• If A(x,y)R(x,y), i.e. reconstruction and
  reference waves are identical,

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Hologram reconstruction

• Three terms in the reconstructed wave

Direct wave identical to reference wave except
for an overall change in amplitude
Object wave identical to object wave except for
a change in intensity
Conjugate wave complex conjugate of object wave
displaced by a phase angle 2 ?
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Hologram reconstruction

• Three terms in the reconstructed wave of the
  point hologram

Direct wave identical to reference wave
(propagates along z) except for an overall change
in amplitude

• Conjugate wave spherical wave collapsing to a
  point at a distance z to the right of the
  hologram
• a real image
• displaced by a phase angle 2kz

Object wave Spherical wave except for a change
in intensity Br2 i.e. reconstructed wavefront
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Direct, object and conjugate waves
Object wave
Reference wave
Real image
Virtual image
Direct wave
Conjugate wave
-z
z
z0
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Hologram Direct, object and conjugate waves

• Direct wave corresponds to zeroth order grating
  diffraction pattern
• Object wave gives virtual image of the object
  (reconstructs object wavefront) first order
  diffraction
• Conjugate wave conjugate point, real image (not
  useful since image is inside-out due to negative
  phase angle) first order diffraction
• In general, we wish to view only the object wave
  the other waves just confuse the issue

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Off-axis- Direct, object and conjugate waves
Use an off-axis system to record the hologram,
ensuring separation of the three waves on
reconstruction
Reference wave
Object wave
Direct wave
Conjugate wave
Virtual image
Real image
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Hologram Reflection vs. Transmission

• Transmission hologram reference and object waves
  traverse the film from the same side
• Reflection hologram reference and object waves
  traverse the emulsion from opposite sides

View in Transmission
View in reflection
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Hologram Wavelength

• With a different color, the virtual image will
  appear at a different angle (i.e. as a grating,
  the hologram disperses light of different
  wavelengths at different angles)
• Volume hologram emulsion thickness gtgt fringe
  spacing
• Can be used to reporduce images in their original
  color when illuminated by white light.
• Use multiple exposures of scene in three primary
  colors (R,G,B)

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Hologram Some Applications

• Microscopy M ?r/?s
• Increase magnification by viewing hologram with
  longer wavelength
• Produce hologram with x-ray laser, when viewed
  with visible light M 106
• 3-d images of microscopic objects DNA, viruses
• Interferometry
• Small changes in OPL can be measured by viewing
  the direct image of the object and the
  holographic image (interference pattern produce
  finges ? ?l)
• E.g. stress points, wings of fruit fly in motion,
  compression waves around a speeding bullet,
  convection currents around a hot filament