Modal projectors for linear operators in Optics

摘要

This paper provides a general framework for calculating modal projectors with applications in Optics. Computing the modal expansion coefficients of a given optical magnitude (wavefront phase, refractive index distribution, etc.) expressed as a linear combination of an orthogonal set of basis functions is a straightforward task when the magnitude is known in all the points of its domain of definition. A simple projection operation on the basis function set gives the desired values for the coefficients. Nevertheless, in most cases of interest, the magnitude itself is not directly known, but through observables that can be described as the action of a linear operator over the magnitude. In those cases, the computation of the modal coefficients can be also made by a direct projection of the observables, but the original basis functions have to be replaced by a new set of functions called modal projectors.