Thomas Nobis

Second-order axial color of thin lenses in air

In present research, the influence of higher-order aberrations on the correction of secondary axial color is under investigation. Analytical solutions have so far been restricted to special cases and simple optical systems. Common theories require the tracing of rays of different wavelengths. Such numerical approaches do not support the comprehension of the underlying physical effects. In this paper, a formula for second-order axial color contributions is derived which is based on paraxial ray data for the reference wavelength only. Therefore, it allows the determination of second-order axial color in early paraxial design stages without further numerical ray trace. For systems of thin lenses in air, three second-order effects are identified and discussed using simple examples. A quantitative comparison with intrinsic secondary axial color is given.

A lens-resolved approach for analyzing and correcting secondary color

Secondary color strongly depends on appropriate glass choice during optical design. The specific impact of individual lenses to the overall correction can be revealed by a lens-resolved analysis of secondary color. In this paper, thick-lens contributions to secondary axial and lateral color are presented, utilizing a suitable definition for secondary color when residual primary color is present. Several design examples illustrate the systematic impact of glass choice on the overall color correction.

Chromatic variation of aberration: the role of induced aberrations and raytrace direction

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.

Induced axial and lateral color surface contributions

Induced aberrations in general are higher-order aberrations caused by ray perturbations of lower order, picked up in the preceding optical system. Therefore, in the case of color aberrations, induced influences can already be observed at the second order. They are generated by the preexisting first-order axial and lateral color. The analysis of relevant designs surface by surface to identify performance dominating lenses is a key method for understanding and optimizing those systems. Hence, in this paper a formula for the surface contribution of axial and lateral color including second-order terms is derived and discussed differentiating between intrinsic and induced parts. It is also shown how this can be used to deduce a thick-lens contribution of the second order. All of the approaches are based on the Seidel concept, which characterizes any arbitrary optical system only by the paraxial marginal and chief ray of the primary wavelength.