holography

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holography

• DT222/4 S1 2006-7

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l ?/sin? f (spatial frequency) 1/l sin ?/
? f 1/l sin ?/ ? phase 2p sin ?/
?
?
l
?
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Plane wave recording and playback
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laser beam
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Mathematical description of a wave
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acos(kx-wt) acos(kx) at t 0 acos(kx wT/4)
at tT/4 acos(kx-p/2) asinkx acos(kxwt)
acos(kx) at t 0 acos(kxp/2) at t T/4
-asin(kx)
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Coherence problem
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How is light produced? Electronic transitions
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w0 p/T
w
w0
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Light Monochromatic source - bandwidth (in
frequency terms) Dw 2p/T
The electronic transitions in atoms that produce
light last 10-8 to 10-9 sec. a wavetrain length
ranges from 0.3 to 3m But Doppler broadening
increases Dn so do collisions since T gets
broken up in to smaller time intervals and
wavetrain is only mm long in a spectrum lamp.
Q. What is the length of a wavetrain in a
source of white light?
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Coherence
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l
q/2
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plastic

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
photoconductor
charge
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_
_
_ _ _ _ _ _ _ _ _ _ _ _ _
_ _
record
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Ferroelectrics Light frees electrons which drift
until trapped at a crystal defect in a region
where there is no illumination. This creates a
space charge and a spatially varying electric
field which modulates the refractive index
through the electro-optic effect. Hologram can be
erased by heating or uniform illumination.
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Silver halide AgBr Ag
Br- hn Br- Br
e- e- Ag Ag
T Iout/Iin D -log T -log(Iout/Iin)
glogE T E-g t E-g/2
D
logE
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Fixing removes unexposed AgBr amplitude
hologram Bleaching Ag converted to soluble
Ag complex, leaving only never exposed AgBr
(reversal)
shrinkage Ag converted to insoluble Ag complex
no shrinkage (rehalogenation)
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Dichromated gelatin When a dichromate salt is
added to gelatin it becomes light sensitive. The
Cr6ion in (NH4)2Cr2O7 converts to Cr3 which
crosslinks the gelatin. The gelatin which is
remains soft can be washed off in hot water to
make a surface relief hologram (i.e. thickness
depends on original light intensity).
Alternatively it is soaked in water below the
softening temperature and then rapidly dehydrated
in a series of alcohol baths. It is thought that
the rapid dehydration causes the gelatin in the
hardened areas to develop minute voids or cracks
so that there is a lot of empty space (refractive
index of 1.0) in those regions while it the
non-illuminated areas the r.i. remains at around
1.5.
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Photoresist Negative exposed photoresist becomes
insoluble. Unexposed material is washed away in
alkaline developer. Positive, exposed becomes
soft and is removed by developer. Surface relief
in which the optical path of light passing
through the layer at reconstruction depends on
the original recording intensity
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Rainbow holography
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Optical pulse recompression
R
R
O
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IC manufacturing During wafer fabrication,
various layers of substances are formed within
the Si wafer, or deposited on the surface. A thin
film of oxide is formed on the surface of the
wafer by oxidation. Then, a photoengraving
process called photolithography is used to
transfer a desired pattern onto the surface of
the wafer. The oxide surface under the pattern is
then dissolved away by etching. Finally, in a
process called doping, impurities are introduced
into the exposed surface to form device elements
such as the source and drain of a transistor.
Thin films may also be deposited on the wafer to
form additional elements.
mask (image) / expose /dev
O2 photoresist
SiO2 photoresist
Si
doping
bake etch
doped Si
Si
SiO2 photoresist
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This is a delta function at y fsinq
F(y) ejkay/fF(y) e-jkay/f
f(y)
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f(y-p)
F(y) ejkay/fF(y)e-jkay/f
F(y)ejkpy/f
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• Addition and subtraction
• FTd(y-p) d(yp)expjkpy/f exp-jkpy/f
• 2cos(kpy/f)
• Change phase
• expj(kpy/ff) exp-j(kpy/ff)
  1)
• f(yp) and g(y-p)
• F(y)exp -jkpy/fG(y)exp jkpy/f
  2)
• x 2)
• F(y)ejf G(y)e-jf F(y)e-j2kpy/fe-jfG(y)e
  2jky/fejf
• ejfF(y)G(y)e-2jf
  
• ejfF(y) - G(y) f p/2
• ejfF(y) G(y) f p
• Retransform for f -/ g

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multiple imaging
f(x,y)

F(x',y')
?(x - np, y -
mq)
ejknpy'/f ejkmqy'/f
F(x',y')ejknpy'/fejkmqy
'/f
f(x - np, y - mq)
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R
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holographic data storage

• Holographic storage characteristics
• storage capacity - terabytes
• transfer rates - 1 Gbyte/s
• access times - 100 ?s

• volume is used.
• data is stored as 2D arrays
• many pages can be stored in the same
  volume.
• angular/peristrophic

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Phase code multiplexing
0/p
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