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Updated: Jun 3, 2026

Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution
Published on: August 16, 2012
Cartesian oval representation of freeform optics in illumination systems
D Michaelis1, P Schreiber, A Bräuer
1Fraunhofer Institute for Applied Optics and Precision Engineering, Jena, Germany. dirk.michaelis@iof.fraunhofer.de
Abstract:
The geometrical method for constructing optical surfaces for illumination purpose developed by Oliker and co-workers [Trends in Nonlinear Analysis (Springer, 2003)] is generalized in order to obtain freeform designs in arbitrary optical systems. The freeform is created by a set of primitive surface elements, which are generalized Cartesian ovals adapted to the given optical system. Those primitives are determined by Hamiltonian theory of ray optics. The potential of this approach is demonstrated by some examples, e.g., freeform lenses with collimating front elements.
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