From differentiable modelling to system optimization: The full journey using Geometric Algebra exemplarily applied to improve light sectioning systems

Computer-aided optimization of optical metrology or imaging systems enables faster, more efficient, and often more innovative designs than those created by experts alone. While mastering this may seem challenging, especially for complex systems, the right choice of toolkits makes it far more approachable. This contribution shows how the system behavior can be elegantly modelled using Geometric Algebra, in particular to facilitate the differentiation process for gradient-based optimization. A major challenge is the incorporation of binary constraints (bounds, masks, coverage), which are often crucial for system design, yet implicate non-usable (“flat”) gradients due to their piecewise constant nature. It is shown how these criteria can also be modelled in a differentiable way, and how targeted system modelling allows for simple quality criteria that could hardly be implemented otherwise – exemplarily illustrated by introducing an unconventional ray tracing approach for (specimen) coverage optimization. The proposed methodology is demonstrated for optimizing light sectioning systems but is equally applicable to other optical metrology and imaging systems.