Ray and Wave Aberrations Revisited: A Huygens-Like Construction Yields Exact Relations

John Restrepo 1, 2 Pawel Stoerck 3 Ivo Ihrke 1, 2
1 MANAO - Melting the frontiers between Light, Shape and Matter
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest, LP2N - Laboratoire Photonique, Numérique et Nanosciences
Abstract : The aberrations of an optical system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersections measured in the image plane. The classical connection between the two descriptions is an approximation, the error of which has, so far, not been quantified analytically. We derive exact analytical equations for computing the wavefront surface, the aberrated ray directions, and the transverse ray aberrations in terms of the wave aberrations (OPD) and the reference sphere. We introduce precise conditions for a function to be an OPD function, show that every such function has an associated wavefront, and study the error arising from the classical approximation. We establish strict conditions for the error to be small. We illustrate our results with numerical simulations. Our results show that large numerical apertures and OPD functions with strong gradients yield larger approximation errors.
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https://hal.inria.fr/hal-01240231
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Submitted on : Tuesday, December 8, 2015 - 7:36:34 PM
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John Restrepo, Pawel Stoerck, Ivo Ihrke. Ray and Wave Aberrations Revisited: A Huygens-Like Construction Yields Exact Relations. Journal of the Optical Society of America, Optical Society of America, 2015. ⟨hal-01240231⟩

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