Proceedings Article | 18 December 2012
Proc. SPIE. 8550, Optical Systems Design 2012
KEYWORDS: Reflectivity, Singular optics, Optical design, Differential equations, Monochromatic aberrations, 3D image processing, Geometrical optics, Wavefronts, Eye, Optical imaging
In this work, novel imaging designs with a single optical surface (either refractive or reflective) are presented. In some of
these designs, both object and image shapes are given but mapping from object to image is obtained as a result of the
design. In other designs, not only the mapping is obtained in the design process, but also the shape of the object is found.
In the examples considered, the image is virtual and located at infinity and is seen from known pupil, which can emulate
a human eye.
In the first introductory part, 2D designs have been done using three different design methods: a SMS design, a
compound Cartesian oval surface, and a differential equation method for the limit case of small pupil. At the point-size
pupil limit, it is proven that these three methods coincide.
In the second part, previous 2D designs are extended to 3D by rotation and the astigmatism of the image has been
studied. As an advanced variation, the differential equation method is used to provide the freedom to control the
tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a
curved object surface have been obtained. Finally, this anastigmatic differential equation method has been extended to
3D for the general case, in which freeform surfaces are designed.
