%% ABSTRACT template %% 12th ICCA, Hefei, PRC \documentclass[9pt]{amsart} % \usepackage{amsfonts,amsthm,amssymb,amsmath} \usepackage[scale={0.8,0.9}, a4paper, nofoot, bindingoffset=1cm]{geometry} \parindent0mm \parskip0mm \sloppy % \newtheorem*{theorem}{Theorem} % \newcommand{\ICCAabstract}[5]{{\bf #1}\par\medskip{\sc #2}\\{#4}\\{\tt #3} \par\bigskip {#5}\bigskip\bigskip} % \begin{document} \begin{twocolumn} % % Please do not change ANYTHING outside the following latex command and do NOT use % any hard font commands inside the command options (as \bf, \sf, \large etc.) except \empf{} if % you want to emphasise something. Please do not use labels and reference to formula numbers % in your abstract (as this will cause problems in the production process). You may use the % \begin{theorem} \end{theorem} environment to state theorems, use all font commands and % symbols provided by {amsfonts} and {amssymb} packages INSIDE formulae. % Please do NOT give references in or after your abstract. % % If your abstract exceeds 300 words in length, we will cut it after 300 words and replace % the remainder by \dots % \ICCAabstract% {%Title of Talk Polarimetry, Polarization-sensitive Imaging and Clifford analysis } {% Name BETTINA HEISE1,2; SWANHILD BERNSTEIN 3 } {% Email Address Bettina.Heise@jku.at } {% Address, NO LINE BREAKS 1 Inst. Knowledge-based Mathematical Systems, Johannes-Kepler University, Linz, Austria\\ 2 RECENDT, Linz, Austria\\ 3 Inst. Appl. Analysis, TU Bergakademie Freiberg, Germany } {% Abstract % NOT TO EXCEED 300 WORDS It is always interesting if different disciplines meet and interrogate each other. In optics the field of polarimetry and polarization-sensitive (PS) measurements and imaging are widespread and for a long time in use. Birefringent samples such as mica flakes, stretched polymer films, collagen fibres in bio-imaging or liquid crystal layers can be characterised with such PS imaging techniques. Polarization-sensitive optical coherence tomography (PS-OCT) is one of them. For the mathematical description Stokes vectors or retardation and optical axis approaches are well known and established in the optical community. However, they are also mathematically interesting representations; the representation of polarization on a Poincare sphere is an example; and polarization changes are \textit{walks } on the sphere or rotation on the sphere and lead to geometric or Pancharatnam phase concepts. Cross-linking with quaternions, Clifford analysis and geometric algebra are also discussed here. And although these approaches are classical concepts in both mathematics and physics, they are also important for contemporary optical applications, such as the description of vector vortex beams, vector wave guidance and encoding. } % \end{twocolumn} \end{document}