Dual-Degree-of-Freedom Continuous Optical Zoom Endoscopic System Based on Liquid Lenses

Endoscopic imaging plays an important role in minimally invasive surgery, clinical diagnosis, and biomedical research. Conventional endoscopic systems with fixed focal lengths are limited in multi-scale observation, while mechanically driven zoom systems often suffer from increased structural complexity and limited stability. In this work, a dual-degree-of-freedom continuous optical zoom endoscopic system based on liquid lenses is proposed. By employing two independently tunable liquid lenses, the system enables simultaneous modulation of optical power and principal plane position, thereby enhancing the flexibility of continuous focusing and magnification control. A Gaussian-bracket-based model is established to describe optical power redistribution and aberration evolution during the zoom process. The proposed system achieves continuous focusing over a wide range from 10 mm to 1000 mm while maintaining imaging performance close to the diffraction limit. In addition, a 1.2× magnified state is realized at a short focusing distance without significant degradation in image quality. The results demonstrate that the proposed dual-degree-of-freedom design provides a compact and effective solution for high-resolution continuous zoom endoscopic imaging.