Objective The goal of designing the imaging optical system is to image the object to be observed clearly to the image plane, and to realize the mapping relationship between object and image of the observation scene. According to the requirement of similarity between object and image, the pinhole imaging model is generally used, with rectilinear projection, which satisfies the f-tanθ mapping relationship. With the increase of the field of views (FOVs), an equidistant projection is produced, which satisfies the f-θ mapping relationship, and a variety of projections such as stereographic, equisolid, and orthographic are then derived. There are also more complex observation scenarios that generate more personalized mapping relationship requirements. As the scenes for imaging optical system is becoming more complex, the image heights for different FOV need to be carefully constrained when utilizing conventional design method to realize complex mapping relationship between object and image, which requires a large amount of calculations based on ray tracing. Therefore, it is necessary to propose a method that exhibits flexible constrain ability for mapping relationships and satisfies a lot of complex imaging scenes. For this purpose, an optical system design method for complex mapping relationship between object and image based on field-dependent parameters is proposed in this paper.

Methods The essence of the mapping relationship between object and image is to describe the incremental change of image height with the change of the FOV. Due to the multi-type target scene observation requirements, the focusing ability and resolution of the optical system, complex requirements are put forward, and the local parameters related to the FOV can be more intuitive and accurate to characterize these requirements. If the full FOV is divided into multiple sub-fields, and the respective central reference is established in each sub-field of view, then each FOV has its focal length. Like the local focal length, the entrance pupil that changes with the FOV is defined as the local entrance pupil. Further, according to the traditional definition of F-numbers, local F-numbers are generated. Therefore, this paper proposes to use the local focal length and local parameters related to the FOV as the optimization control target to realize the precise control of multi-type mapping relationship and resolution. By assigning different local focal length targets to the center and marginal FOVs, a variety of mappings and a variety of angular resolution distributions are realized. By controlling the same local F-number, a high relative illuminance is achieved.

Results and Discussions Three wide-angle lenses all with 120° FOVs but different mapping relationships by utilizing the proposed design method are presented. The first case provides f-tanθ rectilinear projection in the central −20°-20° FOVs and f-θ equidistant projection in the marginal ±20°-±60° FOVs. The second and third cases both provide uniform distributions of the instantaneous field of view (IFOV) across −16°-16° and ±28°-±60°, and the IFOV in the central is 1.5 and 0.667 times the IFOV in the marginal for the second and third cases respectively.

Conclusions A design method based on field-dependent parameters is proposed in this manuscript, in which the local focal length and local F-number are both utilized for mapping relationship and resolution constraint, and the improvement of relative illumination is simultaneously achieved. The full FOV of the optical system is divided into several sub-fields, and the central reference is found in each sub-field. The first-order parameters such as focal length, entrance pupil and F-numbers, which describe the characteristics of the optical system, can be extended from central FOV to any FOV, and the field-dependent local parameters describing the focusing and resolution characteristics of any FOV of the optical system are formed. Three cases are designed to achieve different mapping relationships and high relative illuminance in the full FOV. The proposed method has the characteristics of flexibility, directness and precision for the regulation of imaging characteristics, and can adapt to the observation requirements of different scenes.