Using Fermat’s principle for closed-form, real-time tolerancing

We present a rigorous methodology for real-time tolerance and sensitivity analysis applicable to multi-element optical designs. The central novelty is the derivation of exact, closed-form analytical expressions for all relevant optical performance derivatives with respect to manufacturing and alignment parameters. Derived from Fermat’s principle, this approach is universally valid and eliminates computationally expensive iterative ray tracing. These analytical expressions provide immediate sensitivity data for metrics such as RMS spot size and RMS wavefront error (WFE), enabling a true Design-for-Assembly (DFA) assessment. We demonstrate an orders-of-magnitude reduction in computation time compared to traditional Monte Carlo (MC) benchmarks while maintaining accuracy for systems based on Off-the-Shelf (OTS) components.