Cross-Scale Synergistic Optimization for Miniature Meta-Liquid Hybrid Zoom Imaging

Miniaturized zoom imagers often face a three-way trade-off among tunability, chromatic correction, and optical length. Here, we propose a cross-scale synergistic optimization framework for a metasurface-liquid lens hybrid imager, in which electrowetting actuation, system-level aberration correction, and meta-atom phase, group-delay (GD), and fabrication constraints are optimized in a unified design space. The resulting system uses two liquid lenses, two spherical refractive lenses, and one achromatic metalens to realize 1.5 $\times$ continuous visible-band zoom over a 4-6 mm focal-length range, a 10 $°$ field of view, and a 15.5 mm total optical length. Rather than acting as an isolated focusing element, the metalens serves as a compact dispersion and high-order aberration modulator embedded in the full objective. Full-system wave-optics simulations show that boundary-phase optimization improves multi-wavelength focal consistency while exposing the residual halo imposed by phase folding. Etch-height and system-level tolerance analyses further indicate practical manufacturability margins for the hybrid design.