Modal projectors for linear operators in Optics

This paper provides a general framework for calculating modal projectors wi th applications in Optics, Computing the modal expansion coefficients of a given optical magnitude (wavefront phase, refractive index distribution, et c.) expressed as a linear combination of an orthogonal set of basis functio ns 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 fun ction set gives the desired values for the coefficients. Nevertheless, in m ost cases of interest, the magnitude itself is not directly known, but thro ugh observables that can be described as the action of a linear operator ov er the magnitude. in those cases, the computation of the modal coefficients can be also made by a direct projection of the observables, but the origin al basis functions have to be replaced by a new set of functions called mod al projectors. (C) 1999 Elsevier Science B.V. All rights reserved.