Achromatic stigmatism: achromatic Cartesian ovoid

Abstract

Monochromatic and chromatic aberrations are imaging defects mainly studied from a geometrical optics point of view. These defects are treated through optimization and minimization methods to achieve acceptable performance in optical imaging systems, where the correct choice of glass materials is one of the main challenges. The selection of glass materials is a complex issue that requires a large amount of computing power within sophisticated computational algorithms and enough professional experience in the area. However, in this work, we propose a new methodology to treat the chromatic and geometrical aberrations simultaneously by taking advantage of the relationship between form parameters of Cartesian surfaces and wavelength in the material. From this relationship, we obtain an achromatism principle that establishes the conditions for refracting systems to present a strictly achromatic stigmatism.

Primary aberrations theory in optical systems composed of Cartesian refracting surfaces

“…Accordingly, the imaging systems derived from these families of surfaces present rigorous aplanatism, which increases the interest of these surfaces to be applied in the design of optical instruments with the highest demanding requirements, just as for spherical surfaces at their Young points in microscopy [26,27]. And there is a recent study about chromatism in systems composed of Descartes’s ovoids, concluding that using these optical surfaces can result in achromatic imaging systems [28]. The above motivates us to study the intrinsic optical aberrations in Descartes’s ovoids, and especially primary optical aberrations, whose general formulation must contain the particular cases of primary optical aberrations formulated for conic section of revolution surfaces, including the formulation for a spherical surface, especially leading to an explicit characterization of optical aberrations on aspheric surfaces.…”