Abstract

Exact and approximate formulae for refracted wavefronts through singlet lenses are obtained by considering an incident plane wavefront propagating along the optical axis. We provide two different approaches for the wavefronts approximated at the second order based on the Huygens principle and the Malus–Dupin theorem. We have in the first method found a way to use iterative wavelets instead of the usual evaluated integral to arrive at these formulae, showing a physical and mathematical correspondence between both methods. Finally, we introduce a parabolic wavefront into the irradiance transport equation in order to provide an analytical solution for the distribution of illumination.

© 2019 Optical Society of America

Huygens’ Principle: Exact wavefronts produced by aspheric lenses

Maximino Avendaño-Alejo, Luis Castañeda, Arturo Maldonado, and Naser Qureshi
Opt. Express 21(24) 29874-29884 (2013)

Sagittal and tangential foci produced by tilted plane wavefronts refracted through simple lenses

Maximino Avendaño-Alejo, Edwin Román-Hernández, Gabriel Castillo-Santiago, Jesús DelOlmo-Márquez, and Luis Castañeda
Appl. Opt. 58(22) 5959-5967 (2019)

Exact wavefronts and caustic surfaces produced by planar ripple lenses

Maximino Avendaño-Alejo, Luis Castañeda, and Iván Moreno
Opt. Express 23(17) 21637-21649 (2015)

Analytic conic constants to reduce the spherical aberration of a single lens used in collimated light

Maximino Avendaño-Alejo, Edwin Román-Hernández, Luis Castañeda, and Victor Ivan Moreno-Oliva
Appl. Opt. 56(22) 6244-6254 (2017)

Caustics in a meridional plane produced by plano-convex conic lenses

Maximino Avendaño-Alejo, Dulce González-Utrera, and Luis Castañeda
J. Opt. Soc. Am. A 28(12) 2619-2628 (2011)