Download Lecture 25 OCT

EEL6935 Advanced MEMS (Spring 2005)
Instructor: Dr. Huikai Xie
Lecture 25
Optical Coherence Tomography
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Agenda:
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OCT: Introduction
Low-Coherence Interferometry
OCT Detection Electronics
References: Bouma and Tearney, Handbook of Optical Coherence Tomography, Marcel Dekker, Inc, 2002
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4/11/2005
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Echo Time Delay of Sound and Light
100µm
67ns
Electronics: OK
10µm
33fs
Too fast to
electronics
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Measuring Ultrafast Optical Echoes
ƒ Nonlinear optical gating
ƒ Kerr shutter
ƒ Second harmonic generation
o High intensity
o Short pulses
ƒ Interferometric detection
ƒ Low coherence interferometry
ƒ 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
¾ Lack of in vivo intravascular imaging modalities
¾ Lack of high-resolution imaging for early cancer diagnostics
ƒ X-ray (safety, dye, resolution, …)
ƒ Ultrasound (~100µm)
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Optical Coherence Tomography first demonstrated by
Prof. Fujimoto et al. in 1991
Non-invasive or minimal invasive
Based on low coherence interferometry
High Resolution (∝ λ2/∆λ, ~10µm) cross-sectional
images
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Optical Coherence Tomography
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Optical Coherence Tomography
‰ Carl Zeiss Meditec Inc.,
¾ Eye diseases (e.g. glaucoma)
‰ Lightlab Imaging
¾
Cardiovascular imaging
¾
Cancer detection
¾
Dentistry
Zeiss Stratus OCT
‰ Pentax/Lightlab
‰ Olympus
‰ Many universities
Lightlab Imaging
OCT System
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Optical Coherence Tomography
Schematic of a simplified OCT setup
Axial scanning, z
Broadband
source
Reference
mirror
Fiber 1
Transverse
scanning: 1D
or 2D
50:50
Photo
detector
Fiber 2
Beam
splitter
y
x
Electronics
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Computer
z
Sample
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OCT Imaging Catheter
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Low Coherence Interferometry
Michelson Interferometer
Reference
mirror
ER
lR
ES
Light
source
lS
Beam splitter
lD
Photo
detector
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Sample
ES+ ER
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Michelson Interferometer
ER ( t ) = ERm (t )e
ES ( t ) = ESm (t )e
− j [ 2 β R lR −ωt ]
− j [ 2 β S lS −ωt ]
Photocurrent of
the detector:
I=
ηe
E R + ES
2 ω Z0
For monochromatic
light source,
I=
ηe
ω Z0
2
1
2
2
1
* 
 2 ERm + 2 ERS + ℜ ER ES 


{
}
∆l 

ℜ ER ES* = ERm ESm cos  2β ( lR − lS )  = ERm ESm cos  2π

 λ/2
{
}
The interference has a period of λ/2 relative to the length mismatch ∆l.
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Low Coherence Interferometry
For partially coherent light source,
I ∝e
 ∆τ 2 
−
2
 2στ 
Non-dispersive Media
∆l 

cos  2π

 λ/2
∆τ: time delay; στ: standard deviation of the temporal width
which is inversely proportional to the spectral bandwidth
The interference
changes periodically
but the intensity
decays exponentially.
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Low Coherence Interferometry
Full-width at half-maximum (FWHM):
FWHM = 2σ 2 ln 2
where ∆lFWHM and ∆λ are the
full-width at half-maximum
axial resolution and spectral
bandwidth, respectively.
∆lFWHM =
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λ2
2 ln 2 λ02
≈ 0.44 0
π ∆λ
∆λ
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OCT: Detection Electronics
The photocurrent is a sinusoidal signal,
 2∆l 
I ∝ cos (ω0τ ) = cos  ω0


v p 

Assume the reference mirror moves at a constant speed, i.e.,
∆l = vr t
Then
 2v 
I ∝ cos  ω0 r t 

v p 

So, the electrical signal of the detector has a frequency of
fD =
fD
ω
ωD
2v
= 0 2vr = r
λ0
2π 2π v p
For example, vr = 1m/s, λ0 = 1.3µm
Then fD = 1.5MHz
is the Doppler shift due to the moving reference mirror.
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OCT: Detection Electronics
Relations Between Electrical and Optical Frequencies
The electrical signal of the detector has a frequency of
f =
∆f ≈
2vr
λ
2vr
λ02
∆λ
∆f ∆λ
1
≈
→
Q
f D λ0
The equivalent quality factors of both electrical and optical signals are equal.
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OCT: Detection Electronics
Block Diagram of OCT Electronics
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OCT: Detection Electronics
Transimpedance Amplifier
v = iR
C for stability and high-frequency suppression
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OCT: Detection Electronics
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
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OCT: Detection Electronics
Sallen and Key Low-pass Filter
H (s) =
ωn =
H (s) =
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Vo ( s )
Vi ( s )
1
s 2 R1 R2C1C2 + s ( R1 + R2 ) C1 + 1
=
1
R1 R2C1C2
Q=
R1 R2
R1 + R2
C2
C1
ωn2
s 2 + (ωn / Q ) s + ωn2
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OCT: Detection Electronics
Sallen and Key High-pass Filter
H (s) =
ωn =
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ωn2 s 2
s + (ωn / Q ) s + ωn2
2
1
R1 R2C1C2
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Q=
C1C2
C1 + C2
R1
R2
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OCT: Detection Electronics
Passive Network Butterworth Filter
Nth-order low-pass LC ladder network
Nth-order high-pass LC
ladder network
Assume equal source and load resistances (Rs = RL), cutoff frequency ωc and
unity DC gain. The ith L and C .
Li =
2 Rs
ωc
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 ( 2i − 1) π 
sin 

 2N 
Ci =
 ( 2i − 1) π 
sin 

Rsωc
 2N 
2
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OCT: Detection Electronics
Nth-order Butterworth Bandpass Filter
Low-pass to bandpass frequency warping
•
•
•
•
Set ωc = 1 rad/s
Calculate Li and Ci
Transform L to L+C
Transform C to L//C
Bandwidth
B = ω2 − ω1
Midband frequency
ωm = ω2ω1
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OCT: Detection Electronics
Demodulation
• Mixing (multiplier)
∝ cos ( (ωc ± ωs ) t + φs )icos (ωc t + φd )
Phase control
• Envelope detection
~
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OCT: Detection Electronics
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
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