Symmetry studies of refraction data
Abstract
In this paper we describe the additive and multiplicative decomposition of refraction matrices with respect to a dihedral basis and show the effectiveness of that basis in developing new statistical summaries of refraction data. We also show that under certain projective restrictions the refraction matrices are homeomorphic to an open solid torus and discuss the many potential data-analytic consequences of that representation. A local analysis based on a class of Möbius transformations is introduced leading to a set of new summary statistics of potential use in comparative and correlational studies of refraction data.
- Publication:
-
Journal of Modern Optics
- Pub Date:
- January 2014
- DOI:
- 10.1080/09500340.2013.871587
- Bibcode:
- 2014JMOp...61..138V
- Keywords:
-
- dihedral fourier analysis;
- group theory;
- cornea;
- refraction matrices;
- mathematical methods;
- visual optics