IPC Friedrich-Schiller-Universität Jena 1 Tissue is a highly scattering medium (changes of the refractive) 3. Optical Coherence Tomography (OCT) Unscattered.

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

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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)

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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

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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

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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

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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