Structural design of an improved SPIDER optical system based on multimode interference coupler: an update.

The segmented planar imaging detector for electro-optical reconnaissance (SPIDER) enables compact synthetic aperture imaging through photonic integrated circuits (PICs). Our previous work introduced an 8 × 8 multimode interference (MMI) coupler as a three-input front-end primitive that simultaneously extracts mutual intensities for three baselines, replacing the conventional two-aperture one-baseline measurement unit. This paper studies a reduced-output 3 × 6 MMI-SPIDER architecture and characterizes its information structure through a unified design matrix framework: any three-input MMI system with N output ports is formulated as a real-valued linear model M(N)v = y with seven unknowns, and solvability depends on rank(M(N)). For the 8 × 8 system, full-rank port combinations admit closed-form solutions; the 6 × 6 reduction yields a known one-dimensional null space aligned with the real part of a predictable victim mutual-intensity component. The far-field equal-intensity approximation serves as the DC self-intensity anchor, while the null-space structure is governed entirely by the Type-I port geometry. A per-aperture port randomization strategy converts the structured spectral blind zone into a dispersed half-sampling pattern amenable to sparsity-based spectral inpainting. A two-stage reconstruction framework-iterative spectral projection with wavelet sparsity (ISP-WS) followed by deep prior refinement (DPR)-estimates the missing real-part spectral components within strict data-fidelity constraints and suppresses residual artifacts. Representative numerical simulations on three image categories show target-dependent image-quality improvements over the direct-inverse baseline.