Transversal aberrations at arbitrary Hartmann-plane distances: application in the least-squares fitting of Hartmann...

In a previous work, we introduced the concept of transversal aberrations {U,V} calculated at arbitrary Hartmann-plane distances z=r [Appl. Opt.55, 2160 (2016)APOPAI1559-128X10.1364/AO.55.002160]. These transversal aberrations can be used to estimate the wave aberration function W, as well as the classical transversal aberrations {X,Y} calculated at a theoretical plane z=f, where f is the radius of a reference semisphere. However, when the ray identification is difficult to achieve at z=f, the use of {U,V} can be of great help. In the context of a least-squares fitting of the Hartmann data, the use of {U,V} is proposed by analyzing some simple examples for the case of a W with aberration terms up to the third order. These examples also consider the hypothesis f≫W, as presented in the majority of the optical applications.