Download Lecture 35: Holography.

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-ofphase – 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
Reference wave plane
x
z
y
Photosensitive plate
1. Records
interference
pattern (linear
response)
2. Emulsion has
small grain
structure ()
Object wave - spherical
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Point object hologram construction:
Intensity distribution on plate

Reference wave
R( x, y, z )  r ( x, y, z )e i ( x , y , z )  re ikz

Object wave
O( x, y, z )  o( x, y, z )ei ( x , y , z )  oe ikr

where
r  x2  y2  z 2
Intensity distribution on plate
I ( x, y )  O  R  OO *  RR *  OR *  O* R
2
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Hologram construction
I ( x, y, z )  r  o  2or cos(   )
2
2
Gabor zone plate
z0
film
plane
I ( x, y )  r  o  2or cos( kr)
2
2
Maxima for kr=2m or r=m
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
t  tb  B( O  O* R  OR * )
2
– backgrond transmittance due to |R|2 term
B – parameter which is a function of the
recording an developing process
 tb

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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,
A( x, y )t p  tb A  BOO * A  BO * RA  BOR * A

i.e. a superposition of 4 waves

If A(x,y)=R(x,y), i.e. reconstruction and reference waves
are identical,
R( x, y )t p  (tb  BOO ) R  BR O  B R O
*
2
*
2
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Hologram reconstruction

Three terms in the reconstructed wave
R( x, y )t p  (tb  BOO ) R  BR O  B R O
*
Direct wave –
identical to
reference wave
except for an
overall change in
amplitude
Conjugate wave
– complex
conjugate of
object wave
displaced by a
phase angle 2 
2
*
2
Object wave –
identical to object
wave except for a
change in intensity
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Hologram reconstruction

Three terms in the reconstructed wave of
the point hologram
R( x, y )t p  (tb  B o )e  Be
2
Direct wave –
identical to
reference wave
(propagates
along z) except
for an overall
change in
amplitude
ikz
i 2 kz  ikr
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
e
 B r eikr
2
Object wave –
Spherical wave
except for a
change in intensity
B|r|2
i.e. reconstructed wavefront
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Direct, object and conjugate waves
Object
wave
Reference wave
Real image
Virtual image
Conjugate
wave
-z
Direct wave
z
z=0
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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
Virtual image
Conjugate
wave
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 >> 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  Δl)
E.g. stress points, wings of fruit fly in motion, compression waves
around a speeding bullet, convection currents around a hot
filament
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