Student Seminar - Optimizing Aperture Configurations in Sparse Segmented Imaging Systems Using Physics-Inspired Computational Methods

The configuration of sub-aperture elements in sparse, segmented imaging systems has long presented a nontrivial optimization problem characterized by competing requirements related to spatial-frequency coverage, redundancy minimization, and compactness. Conventional layout schemes typically necessitate undesirable compromises: high-density packing schemes introduce significant baseline degeneracy, complicating segment-specific diagnostics, whereas overly sparse distributions induce pronounced attenuation in mid-range spatial frequencies, thereby reducing the modulation transfer function (MTF) characteristics of the system. In this work, we introduce a physics-motivated modeling approach in which the aperture coordinates are treated as interacting particles evolving under an analogy to a nonlinear Schrödinger-type system. Several computational optimization strategies were examined within this framework; a simulated-annealing-based search was identified as the most suitable. The system MTF is mapped to a Schrödinger-based cost functional, constructed to identify optimal configurations, characterized by a frequency-domain uniformity under the prescribed constraints. The search converges to configurations exhibiting overall spatial-frequency homogeneity while preserving compactness. The approach is applicable to any aperture shape and provides a systematic procedure for finding optimal segmented arrangements across various design requirements.