Huygens principle: exact and approximate wavefronts propagated through conic lenses.

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.

Caustics in a meridional plane produced by concave conic mirrors.

We study the formation of caustic surfaces produced by a concave conic mirror considering a point source placed at arbitrary position along the optical axis. Using the caustic formula and a paraxial approximation, we derive analytic expressions to evaluate the spherical aberration at the third order. A formula to reduce this aberration at any order is provided, which gives the condition for stigmatic points. Furthermore, we apply the formulas to evaluate the circle of least confusion for a concave conic mirror as a function of all parameters involved in the process of reflection.