ipc friedrich-schiller-universität jena 1 tissue is a highly scattering medium (changes of the...
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IPC Friedrich-Schiller-Universität Jena1
Tissue is a highly scattering medium (changes of the refractive)
3. Optical Coherence Tomography (OCT)
Unscattered light ("ballistic photons") shortest pathmaximum information content
Snake photons (forward scattering)time delayedsignificant information content
Diffuse photons: (multiple scattering) diffusion modellittle information to be discriminated
IPC Friedrich-Schiller-Universität Jena2
Identifies scatterers by interference with incoherent reference (Michelson interferometer)
Reference beam interferes with ballistic photons from scattering sample
Fully coherent source no selectivity to photons from a specific depth
White light: Interference only when path difference is within coherence length(a specific depth in sample)
By scanning the reference mirror a depth discrimination is achieved
3. Optical Coherence Tomography (OCT)
IPC Friedrich-Schiller-Universität Jena3
3. Optical Coherence Tomography (OCT)
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The OCT setup
Broadbandsource
Detector
Fiber-opticbeamsplitter
Tissue
Scanningreference mirror
Computer
Amplifier Bandpass filter
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Interference
- 6 - 4 - 2 0 2 4 6Dl@lD1
1.5
2
2.5
3
derusaeM
ytisnetni
- 6 - 4 - 2 0 2 4 6Dl@lD1
1.5
2
2.5
3
derusaeM
ytisnetni
Michelson interferometer
light source
Detector
Coherent source
Partially coherent source
IPC Friedrich-Schiller-Universität Jena6
3. Optical Coherence Tomography (OCT)
1 2
...)()()( 2211 SSSSSSsS zzrzzrzr
zS1zS2
Sample Reflections
2iE
skziss
is ezr
EE 2)(
2
{31 2
...)()()( 2211 SSSSSSsS zzrzzrzr
zS1zS2
Sample Reflections
2iE
skziss
is ezr
EE 2)(
2
{3
Exemplary model for a sample comprising a series of discrete reflectors.
Izatt, Joseph A. Theory of Optical Tomography, 2006Andrew Gomez, Daniel Kim, Jiwon Lee, Kenny Tao
http://www.duke.edu/~yt13/Optical%20Coherence%20Tomography.ppt
IPC Friedrich-Schiller-Universität Jena7
3. Optical Coherence Tomography (OCT)z S
-zR
0
k=2/
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Axial resolution z is determined by coherence length L of the light source i.e. the shorter the coherence length the better the axial resolution
Application of a broad band light source e.g. super-luminescent diode, photonic bandgap fibers
Lateral resolution is determined by the diffraction limited spot size of the focus
A-Scan: assigns every investigated depth point a certain reflectivity
B-Scan: reassembling of multiple A-scans by laterally scanning the light beam along a line
C-Scan: three-dimensional tomography by laterally scanning in two dimensions
0 = center wavelength of the broad band light source = width of the broad band light source (assumption: Gaussian spectrum)
3. Optical Coherence Tomography (OCT)
20
20 44.0
)2ln(2z
IPC Friedrich-Schiller-Universität Jena9
Clinical application of OCT in Ophthalmology
In vivo OCT scan of a retina @ 800 nm (axial resolution = 3 µm)
Cornea OCT image
3. Optical Coherence Tomography (OCT)
Reference beam
Beam splitter
Light source
Detector
Eye
Signal analysis
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1 mm 1 cm 10 cm
Penetration depth (log)
1 m
10 m
100 m
1 mm
Resolution (log)
OCT
Confocalmicroscopy
Ultrasound
Standardclinical
Highfrequency
OCT vs. standard imaging
from: Peter E. Anderson, DTU course 2004
IPC Friedrich-Schiller-Universität Jena11
3. Optical Coherence Tomography (OCT)
•Curvature of OTFs
•Use extended focus techniques?
Problem:•HF information is translated to low frequencies (wrong)
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4. Molecular many electron systems: electronic & nuclear movement
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Hamiltonian for a polyatomic molecule treated as Coulomb system with N nuclei (coordinates {R}) and n electrons (coordinates {ri}) :
In atomic units i.e. ~ = qe = me = 1
Kinetic energy operator for nuclei
Kinetic energy operator for electrons
Nuclei-electron interaction operator
Electron-electron interaction operator
Nuclei-nuclei interaction operator
4. Molecular many electron systems: electronic & nuclear movement
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(3N + 3n)-dimensional problem:
Born-Oppenheimer Approximation: separate treatment of electronic and nuclear
motion allows the total wavefunction of a molecule to be broken into its electronic
and nuclear components:
Decomposition of Hamiltonian:
= adiabatic potential energy surfaces
Schrödinger equation for complete problem:
4. Molecular many electron systems: electronic & nuclear movement
Does not depend on {ri} = constant for given nuclear
geometry