Design Method of Wide Angle Lens Based on Optimization of Local Focal Length through Ray Tracing
The projection model regulates the mapping relationship between the object and image for the imaging system,where they are related by the focal length.The distortion is defined as the departure from the similarity between the object and image,or the departure from the targeted projection model.Thus,the focal length and distortion represent the actual relationship of the optical system.The focal length is the most important and basic parameter of an optical system,which is theoretically defined utilizing the"minor aperture method".According to the regulation of"minor aperture method",the ray close and parallel to the optical axis is traced,and then its angle of convergence after passing through the optical system is recorded for focal length calculation.This regulation is easy to execute during the optical design process but hard to execute for the measurement of the built performance of the optical system.The"minor image height method"is the frequently adopted regulation for focal length measurement,in which ray with minor field of view is traced,and the corresponding image height is recorded for focal length calculation.The"minor image height method"is easy to execute for both design and measurement,and aligns well with the definition of projection.Therefore,if the definition of the focal length is developed from the on axis field of view to the off-axis field of views,then the local focal length which is a field dependent parameter is involuntary generated.And the"minor image height method"is adopted for local focal length definition,in which the image height increment for a minor angle increment is regulated for each field of view.Moreover,the distortion is represented by the variable local focal length for different field of views.And then,the local focal length can be adopted in the process of optical system design for distortion control,for its calculation in the design coincides well with the measurement in the experiment,which is the outstanding priority according to its regulation.A fisheye lens with field of view of 160°,F-number of 4.2,on focal length of 1.61 mm is firstly designed utilizing the local focal lengths for 11 sampled field of views as the target.It is composed of 6 pieces of lenses,in which one aspherical surface is set at a plastic lens,and the equidistant projection is fulfilled.Inspired by the foveated fisheye,the theory of high resolution with rectilinear projection in the central field of view is proposed,and the aforementioned fisheye lens is successfully transformed to the configuration with equidistant projection for the 50%central field of views,adopting the local focal length as the optimization target.Other than objects in the infinity,there are some cases in which the objects is imaged from finite distance,and the object is sometimes even curved.The wide angle lenses with field of view of 120°,F-number of 2.8,on focal length of 1mm are then designed still utilizing the local focal length as the optimization target.The curved objects are 1 000 mm away from the lenses,with the radius of curvature of 800,1 000,1 200,-20 000 mm and infinity,corresponding to convex spherical objects,concave spherical object and plane object respectively.The target local focal length is derived according to the imaging purpose for equal resolution on the curved objects.Diffraction limited imaging quality is achieved,and local focal length relative error is constrained to less than 0.6%with 11 sampled field of views,and the distortion is then less than 0.21%.The generation of local focal length provide a novel parameter for optical system design with complex projections,leveraging its priority of design and measurement coincidence.
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