3rd-order spherochromatism surface contribution and its intrinsic and induced aberration parts

An investigation of the chromatic effects in refracting optical systems naturally shows that all five Seidel aberrations vary in wavelength because they are all dependent on the refractive index. In general, the color variation of spherical aberration is denoted as spherochromatism. Besides the chromatic variation of 1st-order paraxial parameters, e.g., focal length and magnification, described by axial and lateral color, spherochromatism can also strongly affect the color correction of an optical system. However, to the best of our knowledge, the literature shows no exact analytical formula available, specifying this effect. Actually, a general 3rd-order description based on the chromatic variation of Seidel's surface contribution for spherical aberration has not yet been considered. Therefore, this paper deals with this mentioned analytical gap and provides a description of a 3rd-order surface contribution for spherochromatism. Based on this, the result is analyzed and discussed concerning the differentiating between intrinsic and induced aberration parts. In the case of spherochromatism, its 3rd-order contribution shows induced effects caused by prior summed-up primary color aberrations of the system.