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Optical CoherenceTomography
Andrew Gomez
Daniel Kim
Jiwon Lee
Kenny Tao
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Theory of OCT
Light Source
Reference Reflector
SamplezS1
zS2
zR
Beamsplitter
(50/50)
)(),( tkzii eksE =
Rkzii
R
eE
E 2
2=
Detector
2
SRDEEi +=
Z=0
[ ]skzi
ssi
s ezrEE 2)(2
=
)( sS zr
Light Source
Reference Reflector
SamplezS1
zS2
zR
Beamsplitter
(50/50)
)(),( tkzii eksE =
Rkzii
R
eE
E 2
2=
Detector
2
SRDEEi +=
Z=0
[ ]skzi
ssi
s ezrEE 2)(2
=
)( sS zr
1 2
...)()()( 2211 ++= SSSSSSsS zzrzzrzr
zS1zS2
Sample
Reflections
2
iE
[ ]skzissis ezrE
E2
)(
2
=
{31 2
...)()()( 2211 ++= SSSSSSsS zzrzzrzr
zS1zS2
Sample
Reflections
2
iE
[ ]skzissis ezrE
E2
)(
2
=
{3
Schematic of a Michelson interferometer usedin OCT.
Exemplary model for a sample comprisinga series of discrete reflectors.
Izatt, Joseph A. Theory of Optical Tomography, 200
/2=k
2=
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Discrete ReflectorsRkzi
Ri
R erE
E2
2= ( )...
2
21 2
2
2
1 ++=SS kzi
S
kzi
S
i
s ererE
E
( ) ( ) ++=+= SRSRSRD EEEEEEkI 2
),(
For z=0 at beamsplitter and
( )2
)2(
2
)2(
1
)2(...
2
),(
2
),(),( 21 +++= tkziS
tkzi
S
tkzi
RDSSR erer
kser
kskI
)(),( tkzii eksE =
( )
( ) ( )[ ]
( )[ ] Terms"ncorrelatio-Auto"...2
)(
Terms"ncorrelatio-Cross"...2
)(
Terms"DC"...2
)(
2
)()(
)(2)(2
21
)(2)(2
2
)(2)(2
1
21
2121
2211
+++
+++++
+++=
SSSS
SRSRSRSR
zzkizzki
SS
zzkizzki
SR
zzkizzki
SR
SSRD
eerrkS
eerreerrkS
RRkS
RkS
kI
2
11 SS rR =2
,()( kskS =
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Fourier Domain OCT
F
k0
S(k)(z)
0
lc
0
0.5
1.0
k
0
k
1
F
k0
S(
k)(z)
0
lc
0
0.5
1.0
k
0
k
1
20
22
)(1
)()(
== k
kk
Fkze
kkSez
[ ] 000 cos)()(2
1kzzzzz F++
)()()()( kYkXzyzxF
[ ]
( ) ( )[ ][ ]
( )[ ] nTerms"correlatio-Auto"...))(2(2
)(
2
nTerms"correlatio-Cross"...))(2())(2()(2
Terms"DC"...2
)(
2)(
2121
2211
21
++
+++
+++=
SSSS
SRSRSRSR
SSRD
zzzrrz
zzzrrzzzrrz
RRRz
zi
=
=
2
0)2ln(2)2ln(2
klc
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Results[ ][ ]
( ) ( )[ ]
( )[ ])](2[)](2[4
...)](2[)](2[)](2[)](2[2
...)(4
)(
212121
112111
21
SSSSSS
SRSRSRSRSRSR
SSRD
zzzzrr
zzzzrrzzzzrr
RRRzzi
++
+++++
+++=
zSzS1 zS2
)( sS zr
z-2(zR-zS1)
)(ziD
zR
-2(zR-zS2)2(zR-zS1)2(zR-zS2)
0
0
DC term
Cross-correlation
terms
Auto-
Correlation
terms
Mirror image
artifacts
Delta function reflectors
A-Scan
Example field reflectivity function
zSzS1 zS2
)( sS zr
z-2(zR-zS1)
)(ziD
zR
-2(zR-zS2)2(zR-zS1)2(zR-zS2)
0
0
DC term
Cross-correlation
terms
Auto-
Correlation
terms
Mirror image
artifacts
Delta function reflectors
A-Scan
Example field reflectivity function
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Experimental Setup
First Experiment: Low-Coherence
Interferometry
Second Experiment: Optical
Coherence Tomography
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Light Source
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Fiber Coupler (50/50
Beamsplitter)
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Reference Reflector
&
Detector Array
(1-D CCD Camera)
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-Dichroic Mirror
-Sample Stage
Microscope
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Methods Experiment 1: Low-Coherence
Interferometry Purpose to obtain spectral interferogram
data to measure center wavenumber ko,
standard deviation k and the powerreflectivity of the slide surface
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Low Coherence
Interferometry Procedure
Adjust reference arm micrometersuch that there are no interferencepatterns across the spectrum.
Turn micrometer known distance tilla fringe pattern similar to the oneshown in the theory writeup isobserved (Fig 1).
Calibrate spectrogram plot to be ableto calculate power reflectivity of slidesurface.
Obtain spectrogram (Fig 2) ofreference arm only by blocking lightfrom reaching the microscope. Use tomeasure ko and k. The value of ko iswhere the spectrum is at maximumand k is the difference inwavenumber between maximum and1/e of maximum.
Turn on Fourier processing toobserve A-scan plot.
[ ]2
1 1SR+
0k0
1Sr
Single Reflector Multiple Reflectors
1SR zz
k0
)(kID )(kID
kk
[ ]2
1 1SR+
0k0
1Sr
Single Reflector Multiple Reflectors
1SR zz
k0
)(kID )(kID
kk
F
k0
S(k)(z)
0
lc
0
0.5
1.0
k
0
k
1
F
k0
S(k)(z)
0
lc
0
0.5
1.0
k
0
k
1
Figure 1
Figure 2
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Methods Experiment II: Optical CoherenceTomography
Purpose to take two and threedimensional images of internal biologicaltissue microstructure.
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Optical Coherence
Tomography Procedure
Take B-scan of IR card using DC removaland dual-axis scanning mirror.
Repeat for fingertip. Obtain 3D image bysetting scan pattern to rectangularvolume. This allows 100 sequential B-scansto be taken.
Stop scan and select volume image toobtain 3D rendering of data. Try using with acoin.
Experiment using the 3D rendering program3DView on acquired data.
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LCI Results Single
Reflector
1SR zz
k/pixel108.57resolution
pixels33.327periodrwavenumbeaverage
m110
4-
1
=
=
= SRzz
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LCI Results Reference
Arm
31
0
10481.9
m0.179rad/
m4.799rad/
=
=
=
sR
k
k
3
1
0
10481.9
m0.179rad/
m4.799rad/
=
=
=
sR
k
k
m.l
m.
m.
c 3029
081280
30910
=
=
=
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LCI Results A-scan
m86.7
3.11resolution
6.0
=
=
=
cl
m/pixel
pixelsFWHM
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OCT Results B-scan
0.2mm
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OCT Results B-scan
Sweat glands
Complex conjugate artifacts
0.2mm
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OCT Results 3D Scan