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EEL6935 Advanced MEMS 2005 H. Xie 1

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


Echo Time Delay of Sound and Light

100m

10m33fs

67ns

Electronics: OK

Too fast to

electronics


2/12


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


Michelson Interferometer


3/12



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




4/12


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



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



5/12


OCT Imaging Catheter


Photo

detector

Reference

mirror

Sample


Beam splitter

Lightsource

ES

ER

ES+ER

lR

lS

Low Coherence Interferometry

lD


6/12


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.



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.



7/12


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.



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


8/12


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



Block Diagram of OCT Electronics



9/12


Transimpedance Amplifier

C for stability and high-frequency suppression

v iR=



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



10/12


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

=

+ +



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

=

+ +



11/12


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



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



12/12


Demodulation

Mixing (multiplier)

Envelope detection

( )( ) ( )cos cosc s s c d t t + +i


~ ~

Phase control


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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