ABSTRACT
The concept of weak solutions was introduced in a geometric framework which allows a rigorous formulation of and solution to the FFR problem and many other optical design problems. The reader will see that this framework is highly versatile as, in combination with the concept of weak solutions, it can be used to formulate, analyze, and solve a large variety of optical design problems concerned with the redirecting and redistribution of light. Moreover, the solutions obtained with the supporting quadric method (SQM) are freeform surfaces, that is, surfaces determined by the goals and constraints of the design without any a priori assumptions on their shape. The concept of weak solutions was introduced in a geometric framework which allows a rigorous formulation of and solution to the FFR problem and many other optical design problems.
