Free-form surfaces have good aberration correction capability and balance capability for nonrotationally symmetric imaging systems. In this study, we analyzed the quantitative relationship between X–Y polynomial combination and aberration for the efficient design of X–Y free-form optical systems. The purpose of this study was to provide an exhaustive design method for off-axis triple inverse optical systems with X–Y free-form surfaces. Finally, we designed a free-form off-axis optical system with a large field of view (FOV) and low distortion based on the off-axis triple inverse optical system without an intermediate image plane. The primary mirror (PM) of the system adopted an X–Y polynomial free-form surface to correct the aberration of different FOVs of the system and improve the image width and quality. The optical system had a focal length of 1000 mm, an F-value of 9.5, an FOV angle of 23° × 1°, a maximum distortion grid in the FOV less than or equal to −0.05%, and a full-field average wave aberration better than 0.055 λ (λ/18.2, λ = 632.8 nm). The analysis of the design results showed that the system had high-quality imaging and a compact structure. This design method can provide a technical reference for the study of such free-form off-axis systems.

In laser tracking systems, capturing moving targets is a prerequisite to guaranteeing a tracking system’s performance. Previous studies have confirmed that the capture probability of hexagonal spiral scanning is higher than that for other scanning methods, but there is still room for improvement. This article proposes an improved hexagonal honeycomb scanning capture method based on hexagonal spiral scanning for a prior moving target model with a Gaussian distribution positioned within the scanning range of the visual threshold. Through experimental verification, it was found that, within the same scanning field of view, the capture probability can be increased by 3% compared to that in traditional hexagonal spiral scanning, making the capture probability greater than 98%. The improved hexagonal honeycomb structure scanning method proposed in this article provides a new solution for target acquisition problems in fields such as laser communication, laser docking, and airborne radar.