Design of Freeform Surface Low-Distortion Automotive Lens Based on Point-by-Point Construction
Objective Currently,automotive lenses are advancing towards high resolution,wide viewing field,and low distortion.High resolution and wide viewing fields enable automotive lenses to capture clearer and broader images.However,these advancements often lead to increased optical distortion within the system.Given the critical role of autonomous driving in personal safety,addressing distortion issues is paramount as they can compromise image quality and thereby affect the safety of autonomous driving.Moreover,existing real-time correction algorithms for image distortion are not fully developed.Therefore,addressing this issue at the hardware level presents a more stable solution.Currently,the automotive lenses available on the market primarily employ aspherical designs for distortion correction.However,the ability of aspherical lenses to handle distortion still lags behind that of freeform surfaces.Aspherical lenses require more complex element arrangements and pose challenges in determining optimal positions,leading to increased manufacturing and design complexities.In contrast,freeform surfaces offer greater design flexibility,making them more effective in correcting aberrations and controlling distortion.Within coaxial optical systems,two primary design methods exist for the initial structure of freeform surfaces.One method involves progressive optimization,which imposes stricter requirements on surface shapes and offers limited distortion correction capabilities.The other method involves deflecting chief rays emitted from the exit pupil,while this approach compromises image quality and fails to meet high-resolution demands.Therefore,based on the theory of point-by-point construction,we propose a freeform surface design method that deflects both chief rays and various aperture rays to address distortion in automotive lenses while meeting high-resolution requirements.This approach enables the design of automotive lenses with higher resolution,wider viewing fields,and low distortion suitable for autonomous driving applications.Methods Correction of distortion in an optical system involves redirecting the light rays to focus on the ideal image point position rather than the actual image point position on the image plane.The process of determining the freeform surface profile revolves around solving discrete points.The solving process is divided into three main phases.Firstly,the image plane is sampled to collect coordinates of ideal and real image points across different viewing fields,grouped by polar coordinates θ.Secondly,the starting points of the light rays are sampled,with particular emphasis on the principal ray and other edge rays based on exit pupil size.Thirdly,corresponding rays are computed,originating from sampled exit pupil coordinates.This establishes the positions and directions of the incident rays.Subsequently,the front surface of the freeform surface lens is defined as flat,with the back surface determined as the freeform surface to be optimized.After two reflections,light rays reach the ideal image point position.The first reflection computes outgoing rays using the vector refraction law,with these rays then serving as incident rays for the second reflection.Leveraging the vector refraction law and point-by-point construction method,discrete points are calculated sequentially to define the freeform surface profile.Once discrete points are obtained,the profile undergoes fitting and is imported into optical design software for verification.Results and Discussions The verification of the optical layout using this design method,upon integrating the freeform surface lens into the original automotive lens,effectively corrects distortion while marginally reducing imaging quality,yet maintaining modulation transfer function(MTF)thresholds(Fig.11).Subsequent optimization yields optical layouts for both freeform surface automotive lenses(Fig.12)and aspherical automotive lenses(Fig.13).Various parameters are evaluated for original automotive lens,the addition of freeform surface lenses,and the addition of aspherical lenses.Regarding MTF,the freeform surface automotive lens exhibits a 0.064 improvement over the original automotive lens and a 0.073 improvement over the aspherical automotive lens(Fig.14).Optical distortion decreases from-10.00％to 0.68％(Fig.15),with TV distortion dropping from-6.58％to below 0.01％.Furthermore,the freeform surface lens demonstrates superior advantages in optical and TV distortion compared to the aspherical lens at the same positions.The reduction in distortion corresponds to an approximate 11 percentage point decrease in illuminance between the freeform surface and aspherical automotive lenses(Fig.16).Tolerance analysis is conducted on the freeform surface automotive lens introduced various methods for different surface profiles,with Monte Carlo analysis revealing a 90％probability that average diffraction MTF exceeds 0.55 at 59.5 lp/mm(Table 6).These results indicate ease of manufacture and adjustment,meeting requirements for batch production of automotive lenses.Conclusions To address distortion issues in automotive lenses,we advocate employing freeform surfaces for correction.During the freeform surface design process,careful consideration is given to principal rays influencing distortion and edge rays of various apertures affecting imaging quality.This approach not only corrects distortion across diverse viewing fields but also ensures high resolution in automotive lenses.Compared to alternative design methods,this approach accommodates less stringent surface representation requirements and exhibits a slower resolution degradation.It aligns closely with final design objectives and is more accessible for researchers with limited software optimization expertise.We present a comprehensive design of automotive lenses using freeform surfaces in this paper.Following the lens design,our optical system evaluation confirms that integrating freeform surface lenses into the automotive lenses enhances MTF by 0.064,reduces optical distortion by 9.32 percentage points,and diminishes TV distortion by over 6.57 percentage points.This underscores the efficacy of our design approach in addressing system distortion during later stages of optical design.Comparative analysis with aspherical surfaces at the same positions further highlights the superior performance of freeform surfaces in MTF and distortion reduction.Compared to conventional automotive lenses,freeform surface lenses offer higher resolution,broader viewing fields,and smaller distortion,in keeping with trends in automotive lens development.To ensure manufacturing performance,tolerance,and yield analyses confirm ease of manufacture and adjustment,meeting requirements for automotive lens batch production.
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