In general, spherochromatism is denoted as the color variation of spherical aberration in refracting optical systems. If primary axial and lateral color is corrected, in most of the cases spherochromatism is the dominating chromatic aberration. However, in literature only some selected design examples and certain special cases were discussed, but a general analytical 3<sup>rd</sup>-order description based on the chromatic variation of Seidel’s surface contribution for spherical aberration, has not been considered yet. Since furthermore, those selected design examples indicates that spherochromatism is expected to show induced aberration parts, caused by the primary color aberrations of the system, this paper introduces a new description of the 3<sup>rd</sup>-order surface contribution for spherochromatism and gives a discussion on its dependencies on intrinsic and induced aberration parts.
Induced aberrations in general are higher-order aberrations caused by ray perturbations of lower order, picked up surface by surface in the preceding optical system. ,  Therefore, induced aberration coefficients are to some extent depending on the cumulative preexisting aberrations in the system. In the case of color aberrations, induced influences are already observable in the paraxial regime, since even paraxial rays are affected by dispersion. Hence, in every optical system small perturbations in ray heights and ray angles for paraxial rays of different wavelengths are present. These ray perturbations generate induced color aberration effects of higher-order. Here, the different orders refer to the paraxial ray dependency on dispersion. The linear or 1<sup>st</sup>-order terms result in the well-known Seidel contributions of axial and lateral color, where any interaction of dispersion between different lenses is neglected. Starting at 2<sup>nd</sup>-order terms, induced color effects are present. ,  In this contribution, at first an introduction on the basic idea of induced color aberration is given. Following this, a surface resolved analytical description for axial and lateral color, distinguishing between induced and intrinsic parts, will be derived and discussed on a descriptive design example. Here especially the reversibility of raytrace direction is considered.
The design and optimization process of an optical system contains several first order steps. The definition of the appropriate lens type and the fixation of the raytrace direction are some of them. The latter can be understood as a hidden assumption rather than an aware design step. This is usually followed by the determination of the paraxial lens layout calculated for the primary wavelength. It is obvious, that for this primary wavelength the paraxial calculations are independent of raytrace direction. Today, most of the lens designs are specified not to work only for one wavelength, but in a certain wavelength range. Considering such rays of other wavelengths, one can observe that depending on the direction there will already occur differences in the first order chromatic aberrations and additionally in the chromatic variation of the third-order aberrations. The reason for this effect are induced aberrations emerging from one surface to the following surfaces by perturbed ray heights and ray angles. It can be shown, that the total amount of surface-resolved first order chromatic aberrations and the chromatic variation of the five primary aberrations can be split into an intrinsic part and an induced part. The intrinsic part is independent of the raytrace direction whereas the induced part is not.