Decoupling Design for Freeform Multiple-Mirror-Integrated Reflective Cameras for Vision-Based Measurement

Freeform multiple-mirror-integrated reflective cameras with multiple mirrors have emerged as crucial observation instruments in the field of vision- based measurement. However, the design of these cameras often involves complex multi-parameter coupling problems, leading to significant computational burdens, reduced design flexibility, and compromised performance, especially when additional manufacturing constraints are imposed. To address these challenges, this study introduces a novel method that decouples the multi-parameter optimization problem into two distinct mathematical models: parameter calculation and surface optimization. First, a comprehensive mathematical model is established, taking into account both signal acquisition and manufacturing limitations to enable the rapid and accurate calculation of the position and angle parameters of each mirror in a multiple-mirror-integrated reflective camera. Second, based on the parameters related to the mirrors obtained from the first model, the coordinates of discrete points on the mirror surfaces are determined, and the freeform mirror surfaces are refined using surface fitting techniques. Third, two cameras with different optical path designs are created and tested, with both qualitative and quantitative results confirming that the cameras meet the requirements for high signal acquisition. Finally, the designed cameras are applied for object detection with their generated images, and the results prove the effectiveness and practicality of our designed cameras.