Mathematical modeling and implementation of a panoramic zoom system without central blind area

Abstract

The panoramic annular lens (PAL) is renowned for providing simultaneous vision of the panoramic space. However, its inherent central blind area is a significant drawback. In this study, we aim to harness the benefits of the PAL while mitigating its limitations by proposing a dual-channel panoramic zoom system without a central blind area. The introduction of a positive front lens group for secondary imaging is a critical aspect of our design, which is guided and substantiated by our mathematical imaging model. The results from our design affirm the practicality and effectiveness of the secondary imaging. This design can achieve a zoom ratio of 1.46× and a maximum field of view (FoV) range of 71°∼100°, enabling zooming from front to rear. Exemplifying compactness, our system measures just 60mm in total length, while providing a high-resolution output, as indicated by a modulation transfer function exceeding 0.3 at 200lp/mm. With an F−θ distortion of less than 3.3%, the system maintains low levels of distortion. The analysis is instructive and the design shows potential in situations that necessitate compliance with size and resolution requirements.