Aspheric coefficients of deformation for a Cartesian oval surface

Explicit Cartesian oval as a superconic surface for stigmatic imaging optical systems with real or virtual source or image

“…Correcting an aberrated wavefront using equation (2.11), is carried out finding appropriated asphericity coefficients according to the order of the aberrations to be minimized or eliminated. Additionally, these aspheric surfaces are used as approximated stigmatic surfaces, forming an approximated stigmatic image [34].…”

“…An almost standard methodology to correct the effect of aberrations on the image formation is to formulate RSS as a particular case of other ones, capable of being adapted to eliminate or minimize these aberrations, and so achieving an approximately stigmatic image [34]. As we mentioned before, standard aspherical surfaces are written as deformed conics surfaces and are used to correct aberrations.…”

“…The exact mathematical expression of RSS are emphasized in a real point image formation using a real point object, but the cases for virtual object or image have not received the same attention, but in [15], not limited to this configuration, are applied Cartesian surfaces to virtual point objects. Due to the complexity of exact expressions for this kind of optical surfaces, the authors make use of third-party software as OSLO [34,37] to carry out the ray tracing. It is worth to mention that a formulation for ray tracing through funnel concentrator optics as toroids generated from parabolic and elliptical surfaces was proposed [38].…”

“…Additionally, we believe that an explicit expression could be used to design methods to formulate corrective surfaces that compensate aberrations in optical systems composed by RSS, when point object does not lie at the rigorously stigmatic point. Several works have addressed the explicit formulation of an RSS, based on Ferrari's method [30], both exactly [15,[31][32][33] or approximated, using series expansion [32] or using aspherical surfaces [34], some of them listed in table 1. The exact mathematical expression of RSS are emphasized in a real point image formation using a real point object, but the cases for virtual object or image have not received the same attention, but in [15], not limited to this configuration, are applied Cartesian surfaces to virtual point objects.…”