Light control and optical path design method for stabilized zoom systems based on deformable mirrors

We extend the design methodology for stabilized zoom systems by analyzing the stable convergence of singular points in the solution region for image plane shift compensation and continuous zooming. Using lens group magnification as key parameters, we analyze the stability of singular points related to the descending gradient of the zoom equation and the positions of extremum points within the solution region. These singular points and their solution regions are identified and correspond to solutions of specific optical path structures. With the acquired solution region clusters, we can ensure the performance of stabilized zoom systems and prevent optical performance degradation, especially when a specific zoom ratio is required.