Step-along power vector method for astigmatic wavefront propagation.

Abstract

To propose both a new algebraic solution and a graphical monitoring method for astigmatic wavefront propagation in the framework provided by power vectors. The generalised propagation equation describing the propagation of astigmatic wavefronts from one plane to another is adapted to the power vectors formalism using a novel algorithm based on a step-along method. The step-along procedure is directly applied to the tuple of power vectors [M, J0 , J45 ] representing an arbitrary astigmatic wavefront and it permits the calculation of the tuple of power vectors [M', J'0 , J'45 ] after a given propagation distance. This is achieved mathematically first by temporarily rotating the astigmatic wavefront so that one of the principal meridians is horizontal, then propagating the wavefront, and finally rotating the propagated wavefront back to its original orientation. A transfer rule for power vectors representing astigmatic wavefronts is analytically obtained. The new algorithm provides an algebraic solution for the propagation of astigmatic wavefronts using power vectors in a homogeneous medium. In addition, the new step-along procedure allows 2D as well as 3D graphical monitoring of the astigmatic wavefront being referred to the X-Y conventional reference framework by virtue of the trajectories of the power vector coordinates. The proposed solution has been validated through several numerical examples. A new step-along method for astigmatic wavefront propagation using power vectors has been presented and validated for classical as well as new numerical examples. The method provides algebraic calculation as well as graphical monitoring of the wavefront vergence during propagation.