Dynamic Programming Applications in Optics

The term dynamic programming (DP) is not applied exclusively to optical systems but, rather, to physical systems, in general. All physical processes taking place in natural phenomena are intrinsically deterministic sequential ones (Schrödinger 1944). By a deterministic sequential process, we understand the following: let f be an arbitrary quantity having an initial value f 0 at time t 0, 54 f 1 at time t 1,…, fn at time tn with: t 0 < t 1 … < tn. Then, we state that (f 0, f 1,…, fN) constitutes a sequential process. Moreover, and by hypothesis, fr is a functional of f r-1 only (r = 1, 2,…, n). Therefore, the analysis of the process can be reduced to that of a subprocess. The functional relation: fr = fr (f r-1) can be used to solve complex problems.