Optical implementation of high-accuracy computing based on interval arithmetic and fixed point theorem
We experimentally implement a new method for high-accuracy optical computing using interval arithmetic and the fixed-point theorem. In the implementation, a fixed point of an affine transformation is calculated by a TV feedback system. Employing interval arithmetic, the errors associated with an optical setup can be ignored. We evaluate two constraints on the optical system that seriously affect computing efficiency. The minimum value of computational accuracy achieved is 10-13, which is determined by the control accuracy of the required affine transformation coefficients.