Today’s optical design of imaging systems relies mostly on efficient ray tracing and (local or global) optimization algorithms. Such a traditional 'step-and-repeat' approach to optical design typically requires considerable experience, intuition, and sometimes trial-and-error guesswork. Such a time-consuming design process applies especially, but not only, to freeform optical systems. In particular, the identification of a suitable initial design to then adapt and further optimize has often proven to be a laborious process.

We present our developed 'first time right' design method that allows a highly systematic generation and evaluation of directly calculated imaging optics design solutions and thus enables a rigorous, extensive, and real-time evaluation in solution space. The method is based on differential equations derived from Fermat’s principle that can be solved effectively by using a power series method. This approach allows calculating all optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. Such directly calculated optical design solutions can be readily used as starting point for further and final optimization. We demonstrate the deterministic and holistic nature of our method and the streamlined design process for various real-world examples ranging from spherical lens designs to freeform imaging systems. The method allows calculating all optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic, deterministic, scalable, and holistic character of our method for various design examples ranging from spherical lens designs to freeform imaging systems.