On the focussing of light, as limited by the uncertainty principle

Abstract

Equations indicating the minimum size of the focal spot in an optical system appear in various forms. Many of these are approximations to special cases, such as the size of the Airy ring pattern produced by a circular lens as a function of its aperture size, wavenumber, k 0, and focal length, f. Various forms of focal point engineering enable arbitrarily narrow central maxima. However, a simple application of the uncertainty principle suggests an underlying limit to the spread of the intensity distribution in the focal plane that cannot be bettered. For cylindrically symmetric focussing elements and intensity distributions, the root mean square radius, r rms, in the lens plane is related to that in the focal plane, R rms, by r rms R rms ≥ f/k 0.