3 Optical Coherence Tomography OCT Tissue is a

3. Optical Coherence Tomography (OCT) Tissue is a highly scattering medium (changes of the refractive) Unscattered light ("ballistic photons") shortest path maximum information content Snake photons (forward scattering) time delayed significant information content Diffuse photons: (multiple scattering) diffusion model little information to be discriminated 1 IPC Friedrich-Schiller-Universität Jena

3. Optical Coherence Tomography (OCT) 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 2 IPC Friedrich-Schiller-Universität Jena

3. Optical Coherence Tomography (OCT) 3 IPC Friedrich-Schiller-Universität Jena

The OCT setup Broadband source Fiber-optic beamsplitter Tissue Scanning reference mirror Detector Computer Amplifier 4 Bandpass filter IPC Friedrich-Schiller-Universität Jena

Interference Coherent source Michelson interferometer light source Detector Partially coherent source 5 IPC Friedrich-Schiller-Universität Jena

3. Optical Coherence Tomography (OCT) Exemplary model for a sample comprising a series of discrete reflectors. Andrew Gomez, Daniel Kim, Jiwon Lee, Kenny Tao http: //www. duke. edu/~yt 13/Optical%20 Coherence%20 Tomography. ppt 6 Izatt, Joseph A. Theory of Optical Tomography, 2006 IPC Friedrich-Schiller-Universität Jena

3. Optical Coherence Tomography (OCT) k=2 p/l z. S-z. R 0 7 IPC Friedrich-Schiller-Universität Jena

3. Optical Coherence Tomography (OCT) Axial resolution Dz is determined by coherence length DL of the light source i. e. the shorter the coherence length the better the axial resolution l 0 = center wavelength of the broad band light source Dl = width of the broad band light source (assumption: Gaussian spectrum) 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 8 IPC Friedrich-Schiller-Universität Jena

3. Optical Coherence Tomography (OCT) Clinical application of OCT in Ophthalmology Reference beam Eye Beam splitter In vivo OCT scan of a retina @ 800 nm (axial resolution = 3 µm) Light source Signal analysis Detector Cornea OCT image 9 IPC Friedrich-Schiller-Universität Jena

OCT vs. standard imaging Resolution (log) Standard clinical 1 mm Ultrasound 100 mm 10 mm High frequency Confocal microscopy OCT 1 mm Penetration depth (log) 10 1 mm from: Peter E. Anderson, DTU course 2004 1 cm 10 cm IPC Friedrich-Schiller-Universität Jena

3. Optical Coherence Tomography (OCT) • Curvature of OTFs • Use extended focus techniques? Problem: • HF information is translated to low frequencies (wrong) 11 IPC Friedrich-Schiller-Universität Jena

4. Molecular many electron systems: electronic & nuclear movement 12 IPC Friedrich-Schiller-Universität Jena

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 13 IPC Friedrich-Schiller-Universität Jena

4. Molecular many electron systems: electronic & nuclear movement (3 N + 3 n)-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: Does not depend on {ri} = constant for given nuclear geometry Decomposition of Hamiltonian: = adiabatic potential energy surfaces Schrödinger equation for complete problem: 14 IPC Friedrich-Schiller-Universität Jena