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

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


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



The OCT setup

Broadbandsource

Detector

Fiber-opticbeamsplitter

Tissue

Scanningreference mirror

Computer

Amplifier Bandpass filter


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



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


3. Optical Coherence Tomography (OCT)z S

-zR

0

k=2/


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)


20

20 44.0

)2ln(2z


Clinical application of OCT in Ophthalmology

In vivo OCT scan of a retina @ 800 nm (axial resolution = 3 µm)

Cornea OCT image


Reference beam

Beam splitter

Light source

Detector

Eye

Signal analysis


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



•Curvature of OTFs

•Use extended focus techniques?

Problem:•HF information is translated to low frequencies (wrong)


4. Molecular many electron systems: electronic & nuclear movement


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



(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:


Does not depend on {ri} = constant for given nuclear

geometry