Author:
Tobias Strauß
Affiliation:
Karlsruhe Institute of Technology (KIT), Germany
Keyword(s):
Optical Design, Meridional Focus, Sagittal Focus, Astigmatism, Fermat’S Principle, Differential Geometry.
Related
Ontology
Subjects/Areas/Topics:
Computer Vision, Visualization and Computer Graphics
;
Device Calibration, Characterization and Modeling
;
Image Formation and Preprocessing
;
Image Formation, Acquisition Devices and Sensors
Abstract:
In recent years catadioptric systems, consisting of lenses and mirrors, have gained increasing popularity for
the task of environmental perception. However, focusing of such systems is a common problem as it is often
not considered during the design process of the optical system.
This paper presents a novel approach to address focus in the design of optics with rotational symmetry. The
approach does not only adress the construction of catadioptric systems but can also be used to calculate conventional
optics. The approach is based on the calculation of the first order approximation of meridional and
sagittal focus using differential geometry. Additional conditions like a single-viewpoint can be considered as
well. The derived equations are combined to a set of ordinary differential equations that is used to calculate the
shape of the optical system via numerical integration. The design concept has been verified by multi-chromatic
ray tracing simulations.