Abstract

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) [CrossRef]  ]. 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 $f\gg W$, as presented in the majority of the optical applications.

© 2017 Optical Society of America

Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances

Alejandro Téllez-Quiñones, Daniel Malacara-Doblado, Ricardo Flores-Hernández, David A. Gutiérrez-Hernández, and Miguel León-Rodríguez
Appl. Opt. 55(9) 2160-2168 (2016)

Modal processing of Hartmann and Shack–Hartmann patterns by means of a least squares fitting of the transverse aberrations

Geovanni Hernández-Gómez, Daniel Malacara-Doblado, Zacarías Malacara-Hernández, and Daniel Malacara-Hernández
Appl. Opt. 53(31) 7422-7434 (2014)

Least-squares fitting of Hartmann or Shack–Hartmann data with a circular array of sampling points

Zacarías Malacara-Hernández, Daniel Malacara-Doblado, and Daniel Malacara-Hernández
Appl. Opt. 54(28) E113-E122 (2015)

Modal processing of Hartmann and Shack–Hartmann patterns by means of a least squares fitting of the transverse aberrations: erratum

Geovanni Hernández-Gómez, Daniel Malacara-Doblado, Zacarías Malacara-Hernández, and Daniel Malacara-Hernández
Appl. Opt. 54(8) 1870-1871 (2015)

Least-squares fitting of orthogonal polynomials to the wave-aberration function

J. L. Rayces
Appl. Opt. 31(13) 2223-2228 (1992)