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Method and system for determining projections in non-central catadioptric optical systems

  • US 8,134,786 B2
  • Filed: 06/30/2010
  • Issued: 03/13/2012
  • Est. Priority Date: 06/30/2010
  • Status: Expired due to Fees
First Claim
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1. A method for determining a three-dimensional (3D) location of at least one folding point of a ray between a point in a scene (PS) and a center of projection (COP) of a camera of a catadioptric system, wherein the catadioptric system includes the camera arranged at a distance from a surface of a folding optical element, wherein the folding optical element is selected from a reflector or a refractor, wherein the folding point is on the surface and is caused by a reflection or a refraction of the ray on the surface such that the folding point partitions the ray into an incoming ray and an outgoing ray, and wherein the PS and the COP are identified by 3D locations, comprising steps of:

  • acquiring a configuration of the catadioptric system, wherein the catadioptric system is non central, the surface is a quadric surface rotationally symmetric around an axis of symmetry of the surface, and wherein the COP is arranged on the axis of symmetry;

    mapping the surface, and the 3D locations of the PS and the COP on a two-dimensional (2D) plane defined by the axis of symmetry and the PS to produce a conic and 2D locations of the PS and COP on the 2D plane, wherein the conic is a parameterization of the surface on the 2D plane;

    determining a 2D location of the folding point on the 2D plane based on the conic, the 2D locations of the PS and the COP, and at least one constraint on the incoming ray and the outgoing ray; and

    determining the 3D location of the folding point from the 2D location of the folding point on the 2D plane, wherein the steps of the method are performed by a processor.

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