  Purpose: Despite decades of collective experience, radiofrequency coil
optimization for MR has remained a largely empirical process, with clear
insight into what might constitute truly task-optimal, as opposed to merely
'good,' coil performance being difficult to come by. Here, a new principle, the
Optimality Principle, is introduced, which allows one to predict, rapidly and
intuitively, the form of optimal current patterns on any surface surrounding
any arbitrary body.
  Theory: The Optimality Principle, in its simplest form, states that the
surface current pattern associated with optimal transmit field or receive
sensitivity at a point of interest (per unit current integrated over the
surface) is a precise scaled replica of the tangential electric field pattern
that would be generated on the surface by a precessing spin placed at that
point. A more general perturbative formulation enables efficient calculation of
the pattern modifications required to optimize signal-to-noise ratio in
body-noise-dominated situations.
  Methods and Results: The unperturbed principle is validated numerically, and
convergence of the perturbative formulation is explored in simple geometries.
Current patterns and corresponding field patterns in a variety of concrete
cases are then used to separate signal and noise effects in coil optimization,
to understand the emergence of electric dipoles as strong performers at high
frequency, and to highlight the importance of surface geometry in coil design.
  Conclusion: Like the Principle of Reciprocity from which it is derived, the
Optimality Principle offers both a conceptual and a computational shortcut. In
addition to providing quantitative targets for coil design, the Optimality
Principle affords direct physical insight into the fundamental determinants of
coil performance.
