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18 December 2012 Single optical surface imaging designs with unconstrained object to image mapping
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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.
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Jiayao Liu, Juan C. Miñano, Pablo Benítez, and Lin Wang "Single optical surface imaging designs with unconstrained object to image mapping", Proc. SPIE 8550, Optical Systems Design 2012, 855011 (18 December 2012);

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