The one-dimensional Dirac dynamical system Sigma is

iu(t) + i sigma(3) u(x) + Vu = 0, x, t > 0; u|(t=0) = 0, x > 0; u(1)|(x=0) = f, t > 0,

where sigma(3) = ((1)(0) (0)(-1)) is the Pauli matrix; V = ((0)(p) (p)(0)) with p = p(x) is a potential; u = ((u2f)(u1f) (x, t)(x, t) is the trajectory in H = L-2(R+; C-2); f is an element of F = L-2(x, t) L-2([0, infinity); C) is a boundary control. System Sigma is not controllable: the total reachable set U = span(t>0){u(f)(center dot, t) | f is an element of F} is not dense in H , but contains a controllable part Sigma(u). We construct a dynamical system Sigma(a), which is con-trollable in L-2(R+; C) and connected with Sigma(u) via a unitary transform. The construction is based on geometrical optics relations: trajectories of Sigma(a) are composed of jump amplitudes that arise as a result of projecting in U onto the reachable sets U-t = {u(f)(center dot, t) | f is an element of F}. System Sigma(a), which we call the am-plitude model of the original sigma, has the same input/output correspondence as system Sigma. As such, Sigma(a) provides a canonical completely reachable realization of the Dirac system.