Optical Coherence Tomography

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Optical Coherence Tomography
Zhongping Chen, Ph.D. Email zchen_at_bli.uci.edu

• Optical imaging in turbid media
• Coherence and interferometry
• Optical coherence tomography
• Functional Optical Coherence Tomography

Hecht Chapter 7, 9, 12
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Absorption spectra and imaging
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Fluorescence Spectrum and Imaging
Tryptophan
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Optical Imaging

• Microscope
• Fluorescence Imaging
• Confocal Microscopy
• Two/Multi-Photon Fluorescence Microscopy
• Time Domain Optical Imaging
• Polarization Imaging

Surface Imaging
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Cross sectional Imaging and Tomography
BiopsyHistology
Optical Biopsy?Noninvasive cross sectional
imaging
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Optical Tomographic Imaging of Tissue Structure
and Physiology
Challenge Scattering of photon destroy
localization
Mean free scattering path Skin tissue 1/µs 50
µm Blood 1/µs 8 µm
scatterer
scattering media
non-scattering media
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Optical Tomographic Imaging of Tissue Structure
and Physiology
Technology

• Time of flight (only ballistic photons or
  minimally scattered photons are selected)
• Photon migration (amplitude and phase of photon
  density wave are measured)
• Optical coherence tomography (coherence gating
  are used to select minimally scattered photons)

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Optical Coherence Tomography Coherence Gating
Coherence gating

scatterer
Back scattered photons
scattering media
Photon path length
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Optical Coherence Tomography
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Optical Coherence Tomography
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Interference of monochromatic light
Electromagnetic wave EAcos(?t?) A
amplitude ? phase Interference Superposition
of waves E E1 E2 A1 cos(?t?1) A2
cos(?t?2) Phase difference ??? ?2 -
?1 Detection of light waves
I?ltE2gt c 3x108 m/s, n5x1014Hz,
T2x10-15sec, Detector response time 10-9s,-gt
ltsin(wt)gt0
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Interference of monochromatic light
Detection of light waves
I?ltE2gt lt(A1 cos(?t?1) A2 cos(?t?2))2gt
??? ?2 - ?1
If I1I2 I0
In phase ?0, 2?, 4?,..... I
4Io Out of phase ??, 3?, 5?..... I 0
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Coherent Sources

• Monochromatic
• Definite and constant phase relation

E E1 E2 A1 cos(?t?1) A2 cos(?t?2)
Methods to obtain two coherent sources I. Wave
front splitting II. Amplitude
splitting
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Youngs Interference Experiment

• Optical path length difference ?Ldsin?
• Phase difference ??2??L/?
• Constructive interference 2?dsin?/?2m? -gt
  sin?mm?/d m0,1,2,.....
• Destructive interference 2?dsin???(2m1)??
  -gt sin?m(m1/2??/d m0,1,2,.....

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Michelson interferometer
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Michelson interferometer

• Optical path length difference ?L2(L2-L1)
• Phase difference ?????L??
• Detected Light Intensity
• Constructive interference ???L/?2m?
  ?Lm? m0,1,2,.....
• Destructive interference ???L??(2m1)?
  ?L(m1/2)? m0,1,2,3,..

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Photon sources
tc
I
?

• Atoms or molecules radiate wavetrains of finite
  length
• More than one wavelength (spectral bandwidth)
• Fixed phase relation only within individual
  wavetrain

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Coherence
Correlation of light wave at two points in
space-time
??r1,t1r2,t2) ltE(r1,t1)E(r2,t2) gt
Temporal Coherence (longitudinal) GltEa(t)Eb(t)gt

Spatial Coherence (lateral) GltEc(t)Ed(t)gt
Ec
Ea
Eb
k
Ed
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Temporal Coherence
Correlation of light wave along the light
propagation direction GltEa(t)Eb(t)gt
ltE(ttba) E (t) gt
Ea
Eb
k
Lc
Coherence length The length of the wavetrain
where there is definite phase relation.
Coherence time The time for the elementary
wavetrain to pass a single point
tc
Lcc tc
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Temporal Coherence
Temporal coherence is a measure of spectral
bandwidth
A high (good) temporal coherence gives a narrow
spectral bandwidth (pure light of single
wavelength (color))
Fourier transform pair
E(t)
A(?)
tc
D?
t
?
?c_at_1/ D?
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Coherence lengths of light sources
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The effect of finite coherence length
Path length difference r2-r1 ltlt Lc same
wavetrain overlap Interference fringe observable
Path length difference r2-r1 gtgt Lc Different
wavetrain overlap No interference fringe
observable
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Partially Coherent Sources

• Coherent source
• Monochromatic same wavelength
• Constant phase relation

• Incoherent source
• Broad spectrum band P(n)
• Random Phase

• Partially coherent source
• Broad spectrum band (??10100 nm), P(n)
• Definite phase relation within coherence length
  Lc (215 µm)
• If ?LltLc, Interference observed
• If ?LgtgtLc, Interference disappeared

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Interference with Partial Coherence Light Source
I1??1?????????????????2pDL??)
I2??2?????????????????2pDL??)
Laser l2
Laser l1
Interference terms G
Phase change ?????L? ???????????????
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Interference with two light sources of different
frequency
I1??1?
Laser l2
I2??2?
Laser l1
??????1??2?
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Interference with Partial Coherence Light Source
Laser lm
I1??1?????????????????2pDL??)
Laser l3
I2??2?????????????????2pDL??)
Laser l2
Laser l1
I3??3?????????????????2pDL??) ???????
Im??2?????????????????2pDL??)
?????
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Interference with Partial Coherence Light Source
??????1??2?
??????1??2??3?
??????1??2???????7?
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Interference with partial coherence light source
I (??)
For light with discrete wavelengths I(ni)
?
Broad band source
S(?)
For light with continue spectra given by the
spectral density of S(n)
?
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Interference with partial coherence light source
For discrete light with different wavelength
Broad band source
For continuous spectra with spectral density of
S(n)
S(?)
?
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Interference of partially coherent light
Assuming the electrical fields from the partial
coherent source light coupled into the
interferometer is written as an harmonic
superposition
Where E(t) is electrical field amplitude
emitted by a low coherent light source A(?)
is the corresponding spectral amplitude at
optical frequency n. Because phase in each
spectral component are random and independent,
cross spectral density of A(?) satisfies,
Source spectrum
Where So(?) is the source power spectral density
W/Hz ?(n? n) is the Dirac delta function
satisfying and
?
?(n? n)
n
n
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Interference of partially coherent light
A0(n)
A0(n)
Ar(n)
As(n)
Optical path length difference ?L2(L2-L1)
Assume light coupled equally into reference arm
and sample arm with spectral amplitude of Ao(?).
The light coupled back to the detect from the
sample and reference arm is given by
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Interference of partially coherent light
If the time delay (?) between light in reference
and sample paths is changed by translating the
reference mirror, total power detected at the
interferometer output is given by a time-average
of the squared light amplitude
Assuming that there is no spectral modulation in
the reflectivity of both the sample and reference
arms
If the source spectral distribution is a Gaussian
function
Where Lc is the coherence length of the partial
coherence source given by
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Optical Coherence Tomography
S(?)
Dn
Lc
?
Lc?????????
Interference fringes observed only when optical
path lengths are matched within coherence length
of the source
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Optical Coherence Tomography
Michelson interferometer with a broad band
partially coherent source
Axial spatial resolution Lc 0.44l2/Dl
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Interference with Partial Coherence Light Source
Lc?????????
Lc15 µm
Narrow Spectrum
??FWHM 25 nm
Lc5 µm
Broad Spectrum
??FWHM 75 nm
DL
?
Coherence function
Source spectrum
Fourier Transformation
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Optical Coherence Tomography
Michelson interferometer with a broad band
partial coherent source

• Fringe amplitude proportional to backscattered
  light
• Longitudinal (depth) resolution Lc
• Coherence length Lc?????????, (215 µm)
• Lateral resolution by focusing optics (110 µm)
• Probing depth 1/µs 5/µs

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Interference

• Coherence sources

I?ltE2gt

• Partially coherence sources

Lc

• Source power spectrum

• Coherence function

Lc?????????
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Optical Coherence Tomography
Michelson interferometer with a broad band
partial coherent source

• Interference fringes is observed only when
  optical path lengths are matched within the
  coherence length of the source
• Fringe amplitude is proportional to the
  backscattered light     intensity
• Longitudinal (depth) resolution coherence
  length Lc given by
• Lc????????? (215 µm)
• Lateral resolution focusing optics (110 µm)
• Probing depth 1/µs 5/µs

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Operating Principles of OCT
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Operating Principles of OCT Reference Beam Path
Length
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Fiber Based OCT Setup
Michelson Interferometer
Source
Mirror
Detector
A Scan
Pre amp
Band pass Filter
AD Converter
Demodulation
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Optical Biopsy
200 µm
OCT in vivo image of a human hand
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Optical biopsy Speckle averaged OCT image
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Visualization of neonatal freeze lesion
Investigating epilepsy in animal model
Cortex
Cortex
WM
WM
4.7T MRI (1.8 x 1.3 cm)
OCT (2 x 1.8mm)
Histology
R. D. Pearlstein, Z. Chen, et al.
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Optical biopsy OCT image of rat esophagus
Epithelium
Lamina Propria
Muscularis Mucosa
Circular Muscle
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Optical Doppler Tomography
?
?
s
s
f0-?fD
f0?fD
Doppler frequency shift
?
Velocity V?fD?/(2cos(?))
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Optical Doppler Tomography
Combining Doppler velocimetry with optical
sectioning capability of OCT
Lc
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Optical Doppler Tomography