Copy of Optical Coherence Tomography

8/14/2019 Copy of Optical Coherence Tomography

1/20

Optical CoherenceTomography

Andrew Gomez

Daniel Kim

Jiwon Lee

Kenny Tao


2/20

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=


3/20

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 =


4/20

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


5/20

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


6/20

Experimental Setup

First Experiment: Low-Coherence

Interferometry

Second Experiment: Optical

Coherence Tomography


7/20

Light Source


8/20

Fiber Coupler (50/50

Beamsplitter)


9/20

Reference Reflector

&

Detector Array

(1-D CCD Camera)


10/20

-Dichroic Mirror

-Sample Stage

Microscope


11/20

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


12/20

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


13/20

Methods Experiment II: Optical CoherenceTomography

Purpose to take two and threedimensional images of internal biologicaltissue microstructure.


14/20

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.


15/20

LCI Results Single

Reflector

1SR zz

k/pixel108.57resolution

pixels33.327periodrwavenumbeaverage

m110

4-

1

=

=

= SRzz


16/20

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

=

=

=


17/20

LCI Results A-scan

m86.7

3.11resolution

6.0

=

=

=

cl

m/pixel

pixelsFWHM


18/20

OCT Results B-scan

0.2mm


19/20

OCT Results B-scan

Sweat glands

Complex conjugate artifacts

0.2mm


20/20

OCT Results 3D Scan

Copy of Optical Coherence Tomography

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