Understanding third-order aberrations of zoom lenses using a modernized Hopkins method

Complex zoom lenses with a large number of elements can often be analyzed more efficiently by reducing the design to its constituent lens groups (e.g., fixed and moving). In the early stages of the zoom lens design process, each lens group can be modeled as a single paraxial lens to improve the analysis of lens motions, packaging, and other first-order properties. Given a zoom lens’ paraxial layout, an aberration design method can be used to determine ideal third-order monochromatic aberration contributions of the lens groups. However, it is not clear if the aberration design directly leads to an optimal final design that accounts for chromatic aberrations, higher order aberrations, and tolerance sensitivity. We used H. H. Hopkins’ method of aberration design to analyze the third-order aberration balances from a diverse set of patented modern photography zoom lenses. We provide three examples that show that the optimal third-order aberration balance of a zoom lens is primarily determined by the paraxial layout and can be found using Hopkins’ method. We propose a heuristic explanation for this idea using a new interpretation of Wynne’s relations, which we call the natural aberrations. This enables lens designers to more easily understand third-order aberration balancing principles of zoom lenses and can enable further study of optimal paraxial layouts, a priori zoom lens tolerancing, and design automation techniques.