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Lecture 25
Optical Coherence Tomography
Agenda:
OCT: Introduction
Low-Coherence Interferometry
OCT Detection Electronics
4/11/2005
EEL6935 Advanced MEMS (Spring 2005)
Instructor: Dr. Huikai Xie
References: Bouma and Tearney, Handbook of Optical Coherence Tomography, Marcel Dekker, Inc, 2002
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Echo Time Delay of Sound and Light
100m
10m33fs
67ns
Electronics: OK
Too fast to
electronics
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Measuring Ultrafast Optical Echoes
Nonlinear optical gating
Kerr shutter
Second harmonic generation
o High intensity
o Short pulses
Interferometric detection
Low coherence interferometry
White light interferometry
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Michelson Interferometer
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Optical Coherence Tomography
Heart disease and cancer are the top two killers in US
Lack of in vivo intravascular imaging modalities
Lack of high-resolution imaging for early cancer diagnostics X-ray (safety, dye, resolution, )
Ultrasound (~100m)
Optical Coherence Tomography first demonstrated by
Prof. Fujimoto et al. in 1991
Non-invasive or minimal invasive
Based on low coherence interferometry
High Resolution ( 2/, ~10m) cross-sectionalimages
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Optical Coherence Tomography
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Carl Zeiss Meditec Inc.,
Eye diseases (e.g. glaucoma)
Lightlab Imaging
Cardiovascular imaging
Cancer detection
Dentistry
Pentax/Lightlab
Olympus
Many universities
Lightlab Imaging
OCT System
Zeiss Stratus OCT
Optical Coherence Tomography
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Schematic of a simplified OCT setup
50:50Photo
detector
Reference
mirror
Fiber 2
Transverse
scanning: 1Dor 2D
Sample
Beam
splitter
Broadband
source
Electronics Computer
Axial scanning, z
Fiber 1
z
x
y
Optical Coherence Tomography
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OCT Imaging Catheter
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Photo
detector
Reference
mirror
Sample
Michelson Interferometer
Beam splitter
Lightsource
ES
ER
ES+ER
lR
lS
Low Coherence Interferometry
lD
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Photocurrent of
the detector:
( ) [ ]2( ) R Rj l tR RmE t E t e =
( )[ ]2
( )S Sj l t
S SmE t E t e
=2
02R S
eI E E
Z
= +
{ }2 2 *
0
1 1
2 2Rm RS R S
eI E E E E
Z
= + +
{ } ( )* cos 2 cos 2/ 2
R S Rm Sm R S Rm Sm
lE E E E l l E E
= =
For monochromatic
light source,
The interference has a period of/2 relative to the length mismatch l.
Michelson Interferometer
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Non-dispersive Media
2
22cos 2
/ 2
lI e
For partially coherent light source,
: time delay; : standard deviation of the temporal widthwhich is inversely proportional to the spectral bandwidth
The interference
changes periodically
but the intensity
decays exponentially.
Low Coherence Interferometry
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Full-width at half-maximum (FWHM):
2 2ln 2FWHM =
2 2
0 0
2ln20.44FWHMl
=
where lFWHM and are thefull-width at half-maximum
axial resolution and spectral
bandwidth, respectively.
Low Coherence Interferometry
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The photocurrent is a sinusoidal signal,
OCT: Detection Electronics
( )0 02
cos cosp
lI
v
=
Assume the reference mirror moves at a constant speed, i.e.,
0
2cos r
p
vI t
v
rl v t =
Then
So, the electrical signal of the detector has a frequency of
0
0
22
2 2
D rD r
p
vf v
v
= = =
is the Doppler shift due to the moving reference mirror.Df
For example, vr= 1m/s, 0 = 1.3mThen fD = 1.5MHz
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Relations Between Electrical and Optical Frequencies
The electrical signal of the detector has a frequency of
2 rvf
=
The equivalent quality factors of both electrical and optical signals are equal.
2
0
2 rvf
0
1
D
f
Qf
OCT: Detection Electronics
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Block Diagram of OCT Electronics
OCT: Detection Electronics
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Transimpedance Amplifier
C for stability and high-frequency suppression
v iR=
OCT: Detection Electronics
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Bandpass Filters
1. Active Sallen and Key Cascade Filter
Cascading a low-pass S/K filter and a high-pass S/K
filter
2. Passive Network Butterworth Filter
OCT: Detection Electronics
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Sallen and Key Low-pass Filter
( )( )
( ) ( )2 1 2 1 2 1 2 1
1
1
o
i
V sH s
V s s R R C C s R R C = =
+ + +
1 2 1 2
1n
R R C C = 1 2 2
1 2 1
R R CQ
R R C
=
+
( )( )
2
2 2/
n
n n
H ss Q s
=
+ +
OCT: Detection Electronics
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Sallen and Key High-pass Filter
1 2 1 2
1n
R R C C = 1 2 1
1 2 2
C C RQ
C C R=
+
( )( )
2 2
2 2/
n
n n
sH s
s Q s
=
+ +
OCT: Detection Electronics
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Passive Network Butterworth Filter
( )2 12sin
2
si
c
iRL
N
=
( )2 12sin
2i
s c
iC
R N
=
Assume equal source and load resistances (Rs = RL), cutoff frequency c andunity DC gain. The ith L and C .
Nth-orderlow-pass LC ladder network
Nth-orderhigh-pass LC
ladder network
OCT: Detection Electronics
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Nth-order Butterworth Bandpass Filter
Set c = 1 rad/s Calculate Li and Ci Transform L to L+C
Transform C to L//C
Low-pass to bandpass frequency warping
2 1B =
2 1m =
Bandwidth
Midband frequency
OCT: Detection Electronics
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Demodulation
Mixing (multiplier)
Envelope detection
( )( ) ( )cos cosc s s c d t t + +i
OCT: Detection Electronics
~ ~
Phase control
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Noise
Thermal noise
Shot noise
Relative intensity noise
Amplified spontaneous emission (ASE)
Design Issues
Design for shot-noise limited sensitivity
Trade-offs between resolution, power, speed and
sensitivity
OCT: Detection Electronics