Visualizing N-dimensional spaces proves challenging, even for basic systems with two or three lenses. Such spaces often contain numerous local minima, resulting in a complex landscape characterized by hills and valleys determined by design variables/parameters. There is a risk of drawing too simplified conclusions from these basic cases and just extrapolate to higher dimensions. It is tempting to assume that more complex cases merely feature an extension of the same hill-and-valley merit-function topography into a higher N-dimensional space.

In practical designs, however, the merit function exhibits much greater intricacy compared to basic counterparts. This results in the presence of finer structural details within the parameter landscape, also featuring smaller irregularities. For example, the peak of a mountain might contain locals dip capable of capturing the design and confining it within a highly unfavorable local minimum. Any local or global optimization approach can only attempt to explore parts of this very obscure N-dimensional space in a finite amount of time and at relatively high computational cost. So far, we have not even talked about real-world constraints on top of the nominal optical design parameters. In that sense, ‘First Time Right’ is radically different.

The core concept behind our proprietary ‘First Time Right’ approach is to radically reduce the dimensionality of the parameter space. In a nutshell, our all-analytic calculations provide the surfaces shapes ensuring that all aberrations are simultaneously minimized and balanced per aberration order. This drastic reduction of the initial N parameter space dimensions greatly enhances the speed and efficiency of local and global optimization as well as machine learning-based approaches. Consequently, we can perform an unprecedented in-depth search of this reduced sub-parameter space. Finally, as the design parameters have been largely reduced to a minimum, we can incorporate real-world constraints, tolerances, and costs right from the start.