Shedding new light on ray tracing for optical metrology systems by using Geometric Algebra

Camera-based optical metrology systems can be described well with geometric optics by tracing chief rays. To do this, geometric objects alongside operations and transformations have to be modelled. Although this problem is long-solved by using linear algebra and vector analysis, cumbersome case differentiations for different object types and tedious, usually coordinate-dependent exception handling (e.g. to avoid gimbal lock) are required. Useful concepts such as homogeneous coordinates or quaternions have been introduced to overcome this, which as a whole can become extensive quickly. Recently the use of geometric algebras was suggested in computer science as a unifying approach. As both objects and transformations are represented by elements of the algebra, operations can be implemented elegantly in a unified way. Concepts like homogeneous coordinates, Plücker coordinates, and (bi-)quaternions are inherently incorporated. In this contribution we will show how the powerful combination of geometric optics and geometric algebra can be used for ray tracing camera-based optical metrology and imaging systems, and how this approach allows for a more concise and realistic modelling.