Automated design of freeform imaging systems for automotive heads-up display applications.

The freeform imaging system is playing a significant role in developing an optical system for the automotive heads-up display (HUD), which is a typical application of augmented reality (AR) technology. There exists a strong necessity to develop automated design algorithms for automotive HUDs due to its high complexity of multi-configuration caused by movable eyeballs as well as various drivers' heights, correcting additional aberrations introduced by the windshield, variable structure constraints originated from automobile types, which, however, is lacking in current research community. In this paper, we propose an automated design method for the automotive AR-HUD optical systems with two freeform surfaces as well as an arbitrary type of windshield. With optical specifications of sagittal and tangential focal lengths, and required structure constraints, our given design method can generate initial structures with different optical structures with high image quality automatically for adjusting the mechanical constructions of different types of cars. And then the final system can be realized by our proposed iterative optimization algorithms with superior performances due to the extraordinary starting point. We first present the design of a common two-mirror HUD system with longitudinal and lateral structures with high optical performances. Moreover, several typical double mirror off-axis layouts for HUDs were analyzed from the aspects of imaging performances and volumes. The most suitable layout scheme for a future two-mirror HUD is selected. The optical performance of all the proposed AR-HUD designs for an eye-box of 130 mm × 50 mm and a field of view of 13° × 5° is superior, demonstrating the feasibility and superiority of the proposed design framework. The flexibility of the proposed work for generating different optical configurations can largely reduce the efforts for the HUD design of different automotive types.

Freeform illumination optics design for extended LED sources through a localized surface control method.

Freeform illumination optics design with extended light sources to realize an accurate light control is very important, but still remains a challenging issue. Here, we propose a new method to design compact and efficient freeform lenses for extended sources. We employ a localized surface control strategy to directly modify the freeform surface to redistribute the light rays emitted from the extended LED source in a desired manner. By the combination of basic radiometry calculation and backward ray tracing, we obtain the irradiance distribution on the target plane and estimate the localized freeform surface to be modified. The optimization function with a Gaussian form is adopted to modify the localized surface. The smoothness of the freeform surface is taken into account in the optimization process to guarantee the processability of the freeform optics. We demonstrate the effectiveness of the proposed method with three design examples.

Least-squares ray mapping method for freeform illumination optics design: erratum.

We provide corrections of the author list as well as Eq. (12) and (13) in our previous publication [Opt. Express28, 38113811 (2020)10.1364/OE.385254].

Freeform illumination optics for 3D targets through a virtual irradiance transport.

Freeform illumination optics design for 3D target surfaces is a challenging and rewarding issue. The current researches on freeform illumination optics are mostly involved in planar targets, especially for the cases where the targets are perpendicular to the optical axis. Here, we propose a general method to design freeform optics for illuminating 3D target surfaces for zero-étendue sources. In this method, we employ a virtual observation plane which is perpendicular to the optical axis and transfer the irradiance on the 3D target surface to this virtual plane. By designing freeform optics to generate the transferred irradiance distribution, the prescribed irradiance distribution on the 3D target can be realized automatically. The influence of the freeform optics size is considered in the optics design process, which makes it possible to design illumination system for near-field configuration where the influence of the freeform optics size cannot be ignored. We demonstrate the robustness and elegance of the proposed method with three design examples.

Compact freeform illumination optics design by deblurring the response of extended sources.

Freeform illumination design for extended sources is a very challenging but rewarding issue that can benefit a wide range of illumination systems. Here, we propose a method that can achieve compact and highly efficient illumination lenses by deconvolving the blur caused by the extent from light sources. We combine the illumination calculation with the mathematical model of spatially variant convolution and develop a direct computational scheme to calculate the blur kernel without approximations. Two design examples with high optical performances are presented to demonstrate the effectiveness of the proposed method.

Variable-diameter beam-shaping system design with high zoom ratio containing aspheric optical components.

Recently, the optical design of refractive beam-shaping systems has been extensively studied, although such study remains focused on two optical surfaces. Designing a beam-shaping system with variable output beam sizes and prescribed irradiance profiles remains a challenging but rewarding task. Here, we present a design framework, including calculation of the initial system and optimization process, to achieve variable-diameter beam-shaping systems with high zoom ratios. We introduce the whole process of designing a compact 8× zoom system of superior optical performance by transforming a Gaussian beam into flat-top beams with different magnifications. We also present a design of a zoom beam-shaping system transforming a Gaussian beam into variable beams with inverse Gaussian distributions to demonstrate the robustness and efficiency of the proposed method.

Least-squares ray mapping method for freeform illumination optics design.

Computing a source-target map that yields integrable surface normal field is quite challenging for freeform illumination design. Here, we propose a least-squares ray mapping method to calculate a superior ray mapping by iteratively correcting an integrable map to approach the energy conservation and boundary condition. The process is implemented via solving three minimization problems. The first two problems can be figured out pointwise and the third can be converted to two decoupled Poisson equations with Robin boundary conditions. We demonstrate the robustness and high efficiency of the proposed method with several design examples.

Double freeform surfaces design for beam shaping with non-planar wavefront using an integrable ray mapping method.

We propose a method to design double smooth freeform surfaces applied in beam shaping with a ray mapping method in the paper. We couple the calculation of ray mapping and the construction of freeform surfaces to approach the surface normal field integrability condition based on the symplectic flow mapping scheme. In this paper, the incident beam wavefront is not limited to be planar or spherical. Several challenging design examples are presented that include transforming a circular Gaussian beam to an unconventional beam with variously shaped contour, and transforming an elliptic beam to a convergent beam with complex irradiance distribution in non-paraxial regime. The results show the high efficiency and feasibility of the proposed method in designing freeform optics for beam shaping applications.

Globally optimal first-order design of zoom systems with fixed foci as well as high zoom ratio.

In this paper, we propose a systematic approach to automatically retrieve the first-order designs of three-component zoom systems with fixed spacing between focal points based on Particle Swarm Optimization (PSO) algorithm. In this method, equations are derived for the first-order design of a three-component zoom lens system in the framework of geometrical optics to decide its basic optical parameters. To realize the design, we construct the mathematical model of the special zoom system with two fixed foci based on Gaussian reduction. In the optimization phase, we introduce a new merit function as a performance metric to optimize the first-order design, considering maximum zoom ratio, total optical length and aberration term. The optimization is performed by iteratively improving a candidate solution under the specific merit function in the multi-dimensional parametric space. The proposed method is demonstrated through several examples, which cover almost all the common application scenarios. The results show that this method is a practical and powerful tool for automatically retrieving the optimal first-order design for complex optical systems.

Design of a head-up display based on freeform reflective systems for automotive applications.

Automotive head-up display (HUD), a typical application in augmented reality (AR), has gained popularity in recent years. In this paper, we propose a novel design configuration of freeform off-axis three-mirror systems for automotive head-up display (HUD) application. In the configuration, the image source, the flat mirror, and the freeform mirror are allocated on the same horizontal level to guarantee a compact structure as well as to make the optical elements easy to be assembled. The whole design philosophy and procedure, including the analytic method to determine initial structure, structure constraints, and optimization strategy, are demonstrated in detail. Superior optical performance is achieved regardless of the pupil being located at any position inside a rectangular eye box.

Automatically retrieving an initial design of a double-sided telecentric zoom lens based on a particle swarm optimization.

In this paper, we propose an efficient and robust approach to retrieve an optimal first-order design of a double-sided telecentric zoom lens based on the particle swarm optimization (PSO) algorithm. In this method, the design problem is transformed to realize a zoom system with fixed positions of both the front focal point and the rear focal point during zooming. Equations are derived for the paraxial design of the basic parameters of a three-component zoom lens in the framework of geometrical optics. We implement the PSO algorithm in MATLAB to design some test cases to verify the feasibility. As the computational work is completed by the optimization algorithm, instead of the traditional trial-and-error method, our proposed method is efficient and low-threshold. By a simulation result, it is verified that the described method is stable and necessary in finding a proper initial configuration of a zoom lens with two fixed foci as well as a required zoom ratio. Furthermore, a compact initial design of a three-component 2X zoom system with two fixed foci is proposed. Based on the initial design data, a double-sided telecentric zoom system is developed. The result shows the great potential of our proposed method in retrieving proper initial designs of complex optical systems.