Abstract
We obtain simple exact formulas for the refracted wavefronts through plano-convex aspheric lenses with arbitrary aspheric terms by considering an incident plane wavefront propagating along the optical axis. We provide formulas for the zero-distance phase front using the Huygens' Principle and the Malus-Dupin theorem. Using the fact that they are equivalent, we have in the second method found a way to use an improper integral, instead of the usual evaluated integral, to arrive at these formulas. As expected, when the condition of total internal reflection is satisfied, there is no contribution to the formation of the refracted wavefront.
Highlights
The aspheric lens can help simplify optical system design by minimizing the number of elements required and yields sharper images than conventional lenses
We have obtained simple formulas for the wavefronts produced by positive convex-plano and plano-convex aspheric lenses having an arbitrary number of aspheric terms, considering a plane wavefront propagating along the optical axis
When the condition of total internal reflexion is satisfied the wavelets do not contribute to the formation of the refracted wavefront, since these wavelets are unlimited they are not perpendicular to the refracted rays
Summary
The aspheric lens can help simplify optical system design by minimizing the number of elements required and yields sharper images than conventional lenses. The caustics and wavefronts either by reflection or refraction are part of a well known subject [3,4,5], the contribution in this work it is to provide simple formulas of the wavefront surfaces caused by refraction on plano-convex aspheric lenses exclusively in a meridional plane by using the Huygens’ principle and the theorem of Malus-Dupin In this manuscript we consider the aspheric equation given according to [5], recently there have been defined new formulas to represent this kind of surface [6, 7]. We assume that a plane wave is incident on the lens parallel to the optical axis, crossing the plane face of the lens without being deflected, and this is propagated to the aspheric surface In this way the Huygens’ principle assumes that a wavefront is the envelope of an aggregate of wavelets centered on a previous wave front in the wave-front train. It is worth stating that the constant of integration omitted in Eq (7) translates the vertex of the zero-distance phase front along the optical axis
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