Design of a curved-target ultrashort throw projector based on predistortion and illumination precorrection.

Ultrashort throw projector (UTP) technology has been a challenging research focus in the fields of large field of view and short-distance projection. In this paper, we propose a design method for a curved-target UTP based on image precorrection. A predistortion method (<1p i x e l) using a radial basis function is presented to effectively correct irregular distortion. A grayscale precorrection method is used to address uneven illumination distribution. We provide a UTP design example and verify the correction methods using two different curved targets (aspherical and freeform), demonstrating effective distortion correction (<1%) and illumination uniformity (>90%). The structure similarity index measure for the projection images shows close or greater than 0.9 correlation.

Automatic control method for freeform surface shapes.

Designing freeform optics with high degrees of freedom can improve their optical performances; however, there are high requirements for controlling the surface shapes of such optics. Optical designers need to add constraints to the optimization process and make repeated adjustments to ensure the manufacturability of these shapes; this process is cumbersome and relies heavily on the experience of the designer. In this study, an automatic control method for freeform surface shapes is proposed. By adding an outer loop to the optimization process, the principal curvature and sag departure of the sampling points are gradually controlled during the optimization cycle based on the system requirements and surface evaluation results. The method was implemented in CODE V and successfully applied to a design example in freeform prism optics.

Design of compact off-axis freeform imaging systems based on optical-digital joint optimization.

Using a freeform optical surface can effectively reduce the imaging system weight and volume while maintaining good performance and advanced system specifications. But it is still very difficult for traditional freeform surface design when ultra-small system volume or ultra-few elements are required. Considering the images generated by the system can be recovered by digital image processing, in this paper, we proposed a design method of compact and simplified off-axis freeform imaging systems using optical-digital joint design process, which fully integrates the design of a geometric freeform system and the image recovery neural network. This design method works for off-axis nonsymmetric system structure and multiple freeform surfaces with complicated surface expression. The overall design framework, ray tracing, image simulation and recovery, and loss function establishment are demonstrated. We use two design examples to show the feasibility and effect of the framework. One is a freeform three-mirror system with a much smaller volume than a traditional freeform three-mirror reference design. The other is a freeform two-mirror system whose element number is reduced compared with the three-mirror system. Ultra-compact and/or simplified freeform system structure as well as good output recovered images can be realized.

Design and fabrication method of holographic waveguide near-eye display with 2D eye box expansion.

Augmented reality near-eye display (AR-NED) technology has attracted enormous interests for its widespread potential applications. In this paper, two-dimensional (2D) holographic waveguide integrated simulation design and analysis, holographic optical elements (HOEs) exposure fabrication, prototype performance evaluation and imaging analysis are completed. In the system design, a 2D holographic waveguide AR-NED integrated with a miniature projection optical system is presented to achieve a larger 2D eye box expansion (EBE). A design method for controlling the luminance uniformity of 2D-EPE holographic waveguide by dividing the two thicknesses of HOEs is proposed, which is easy to fabricate. The optical principle and design method of the HOE-based 2D-EBE holographic waveguide are described in detail. In the system fabrication, laser exposure fabrication method of eliminating stray light for HOEs is proposed, and a prototype system is fabricated and demonstrated. The properties of the fabricated HOEs and the prototype are analyzed in detail. The experimental results verified that the 2D-EBE holographic waveguide has a diagonal field of view (FOV) of 45°, an ultra-thin thickness of 1 mm, and an eye box of 16 mm × 13 mm at an eye relief (ERF) of 18 mm, the MTF values of different FOVs at different 2D-EPE positions can be better than 0.2 at 20 lp/mm, and the whole luminance uniformity is 58%.

Design of an off-axis near-eye AR display system based on a full-color freeform holographic optical element.

In this Letter, we propose a design and fabrication method for a full-color augmented reality (AR) optical system based on a freeform holographic optical element (HOE). A point-by-point design method is proposed to generate the starting point of the system. Based on the preliminarily optimized system, the recording systems of the full-color HOE are designed. A joint optimization is conducted for all the systems, simultaneously considering the overall imaging performance, the diffraction efficiency, the constraints, and fabrication. A prototype is designed and fabricated to validate the feasibility and effectiveness of the proposed method.

Stray light analysis and suppression method of a pancake virtual reality head-mounted display.

Pancake virtual reality head-mounted displays (VR-HMDs) have attracted the attention of researchers in both academia and industry because of the compact size and light weight. However, owing to the use of optical path folding, there exist various stray lights in the optical system, which seriously degrades user experience. In this study, we analyze the causes and effects of multiple types of stray light systematically and design a VR-HMD with low stray light, large exit pupil diameter (EPD), compact form and light weight. Subsequently, several effective stray light suppression solutions are proposed and implemented. Finally, a prototype of a compact pancake VR-HMD system is successfully demonstrated. The prototype has stray light of less than 2.3%, a diagonal field of view (FOV) of 96° and an EPD of 10 mm at an 11 mm eye relief (ERF).

Design method of imaging optical systems using confocal flat phase elements.

Imaging systems consisting of flat phase element such as diffractive optical element, holographic optical element, and metasurface have important applications in many fields. However, there is still a lack of generalized and efficient design methods of these systems, especially for systems with nonsymmetric configurations. We proposed a design method of imaging system consisting of flat phase elements based on confocal properties. The description of the generalized phase function for realizing point-to-point stigmatic imaging is derived. Given the focal length or magnification as well as the locations of the elements based on the design requirements, the phase functions can be calculated very fast and stigmatic imaging of the central field is realized. The systems can be taken as good starting points for further optimization, during which the rotationally symmetric or freeform phase terms can be added. Several design examples are demonstrated to validate the feasibility of the method. The proposed method increases design efficiency while decreasing the dependence on existing systems and skills significantly, and can be easily integrated into optical design software.

Uniformity improvement of two-dimensional surface relief grating waveguide display using particle swarm optimization.

Augmented reality head-mounted displays (AR-HMDs) based on diffractive waveguides have been a challenging and rewarding research topic focusing on near-eye displays. The size of the exit pupil and uniformity of the image illuminance are two important factors that affect the display performance of the diffractive waveguide. In this paper, a novel method for optimizing high uniformity of two-dimensional (2D) diffractive waveguide is proposed. A straight-line 2D surface relief grating (SRG) waveguide with divided grating regions is designed. An illuminance uniformity evaluation model of the energy propagation process is established, and non-sequential ray tracing is utilized to optimize the diffraction efficiency of multi-regions grating to achieve illuminance uniformity distribution. Then, the uniformity distribution of the diffraction efficiency in different fields of view (FOVs) is realized by combining the particle swarm optimization (PSO) algorithm and rigorous couple wave analysis (RCWA) to optimize the grating structural parameters, which further ensures the uniformity of the exit pupil illuminance and angular illuminance. The waveguide with exit pupil expansion (EPE) has exit pupil size of 16 mm × 14 mm at an eye relief (ERF) of 20 mm, exit pupil illuminance uniformity of 91%, and angular uniformity illuminance of 64%.

Design of off-axis reflective imaging systems based on freeform holographic elements.

Holographic optical element (HOE) can be used in many areas in optics due to its characteristics of thin structure, flexible wavefront reconstruction/control ability and angular/wavelength selectivity. In this paper, we propose a design method of off-axis reflective imaging systems based on freeform HOEs, which are fabricated by freeform wavefronts. The freeform HOEs offer many degrees of design freedom and can correct the aberrations in nonsymmetric imaging systems. The initial imaging system with freeform HOEs is generated using a point-by-point design approach, and is used for the preliminary design of the imaging system and the freeform recording system of each HOE. Then a joint optimization is conducted for all the systems, simultaneously considering the imaging performance, the diffraction efficiency, the system constraints and fabrication to get the final design results. To validate the feasibility and effectiveness of the proposed method, an off-axis reflective head-up display system with good performance based on freeform HOEs is designed and fabricated. Detailed procedures of the design and development process of the prototype are demonstrated.

Design method of a wide-angle AR display with a single-layer two-dimensional pupil expansion geometrical waveguide.

Waveguide near-eye displays (NEDs) consist of a planar waveguide combiner and a coupling-in projection system. A two-dimensional geometrical waveguide (TDGW) can achieve an ultra-thin, large exit pupil diameter (XPD), wide-angle NED. The design method of a single-layer TDGW is presented and discussed in detail in this paper. A high-precision processing technology that can effectively guarantee the parallelism accuracy is also presented. A miniature coupling-in projection optics is designed with a catadioptric structure and integrated with the waveguide accordingly. Finally, a TDGW with a thickness of 1.75 mm is designed and analyzed. The results show that the stray light over the normal light is less than 0.5%, and the illuminance uniformity is well optimized. The field of view is up to 55°, and the XPD exceeds 12mm×10mm at an eye relief (ERF) of 18 mm. A proof-of-concept prototype was fabricated and demonstrated.

Designing reflective imaging systems with multiple-surfaces-integrated elements using a Gaussian function freeform surface.

We propose a design scheme and method of a freeform off-axis reflective imaging system with multiple mirrors integrated into one element. The use of a multiple-surfaces-integrated element, described by the Gaussian basis functions freeform surface with local and nonsymmetric properties, significantly decreases the system complexity, as well as reduces the assembly and fabrication difficulty, and achieves high imaging performance. The design theory and process including the initial system design, surface conversion, and system optimization are demonstrated in detail. Three design examples are demonstrated to validate the effect and feasibility of the proposed method, and good imaging performance is obtained.

Design, stray light analysis, and fabrication of a compact head-mounted display using freeform prisms.

It has been a challenge to design an optical see-through head-mounted display that is compact, lightweight, and stray-light-suppressed by using freeform optics. A new type of design based on freeform prisms is presented. The system consists of three optical elements and a micro-display. Two prisms serve as near-eye viewing optics that magnify the image displayed by the micro-display, and the other freeform lens is an auxiliary element attached to the main wedge-shaped prism to provide an undistorted see-through view of a real-world scene. The overall thickness of the optical system does not exceed 9.5 mm, and the weight is less than 9.8 g per eye. The final system is based on a 0.49-inch micro-display and features a diagonal field of view of 38°, an F/number of 1.8, with a 10 mm × 7 mm exit pupil diameter, and a 19 mm eye relief. The causes of stray light in the optical-mechanical system are investigated, and effective solutions or theoretical suppression of stray light are given. The freeform optical elements are successfully fabricated, and the system performance is carefully investigated. The results show that the performance of the optical see-through head-mounted display is adequate for practical applications.

Off-axis reflective imaging system design with a conicoid-based freeform surface.

In this paper, we propose an off-axis reflective system design method based on a non-rotational symmetric conicoid-based freeform (CBF) surface description. The base description avoids complicated calculation of decenter and tilt when using the conventional conic expression, thus simplify the system modeling and optimization process, and it can reduce the number of coefficients that needed to represent mild freeform surfaces. A design method that includes the automatic initial system searching, preliminary optimization with rotationally symmetric surface deviation and fine-tuning with non-symmetric surface deviation is proposed. Two three-mirror systems have been designed to demonstrate the feasibility and conveniences of the proposed method.

Optical design and pupil swim analysis of a compact, large EPD and immersive VR head mounted display.

Virtual reality head-mounted displays (VR-HMDs) are crucial to Metaverse which appears to be one of the most popular terms to have been adopted over the internet recently. It provides basic infrastructure and entrance to cater for the next evolution of social interaction, and it has already been widely used in many fields. The VR-HMDs with traditional aspherical or Fresnel optics are not suitable for long-term usage because of the image quality, system size, and weight. In this study, we designed and developed a large exit pupil diameter (EPD), compact, and lightweight VR-HMD with catadioptric optics. The mathematical formula for designing the catadioptric VR optics is derived. The reason why this kind of immersive VR optics could achieve a compact size and large EPD simultaneously is answered. Various catadioptric forms are systematically proposed and compared. The design can achieve a diagonal field of view (FOV) of 96° at -1 diopter, with an EPD of 10 mm at 11 mm eye relief (ERF). The overall length (OAL) of the system was less than 20 mm. A prototype of a compact catadioptric VR-HMD system was successfully developed.

Ultra-thin multifocal integral LED-projector based on aspherical microlens arrays.

Multifocal imaging has been a challenging and rewarding research focus in the field of imaging optics. In this paper, an ultra-thin multifocal integral LED-projector based on aspherical microlens array (MLA) is presented. A two-layer aspherical sub-lens with NA = 0.3 is proposed as a sub-channel projector and the optimization design ensures high optical integration precision and improves optical efficiency. To avoid the tailoring loss of the projected images between multi-plane projections, the central-projection constraints between size and projection distance for the multifocal projection are defined. The depth of focus (DOF) analysis for MLA and sub-lens is also introduced to proof the sufficiency of realizing multifocal projection. Combined with the radial basis function image warping method, multifocal sub-image arrays were acquired, and three types of multifocal integral projection were realized, breaking through the traditional limitations of the single-focal DOF. A prototype with thickness of less than 4 mm is developed. Substantial simulations and experiments are conducted to verify the effectiveness of the method and the design.

Freeform beam splitting system design for generating an array of identical sub-beams.

Laser beam splitting by freeform optics is promising but less studied. Instead of directly forming a target spot array, we propose to first convert the input beam into a closely connected Gaussian sub-beam array. All the Gaussian sub-beams have the same optical field distributions which thus can produce identical discrete spots on the target plane. Such a design concept is very beneficial to ensure the consistency for laser processing. Importantly, the introduction of an intermediate Gaussian sub-beam array can reduce diffraction effects when the size of each Gaussian sub-beam is sufficiently larger than that of the corresponding sub-area within the input beam. The desired transformation can be achieved by two typical systems. The first system consists of two plano-freeform lenses. The second system is composed of a plano-freeform lens and a lens with an entrance freeform surface and an exit surface of freeform lens array. The two freeform beam splitting systems can be determined based on appropriate ray mappings among the input, intermediate and target irradiance distributions and a subsequent double-surface construction. Geometrical and physical simulations verify the effectivenesses of the two beam splitting systems.

Generating starting points for designing freeform imaging optical systems based on deep learning.

Deep learning is an important aspect of artificial intelligence and has been applied successfully in many optics-related fields. This paper proposes a generalized framework for generation of starting points for freeform imaging optical design based on deep learning. Compared with our previous work, this framework can be used for highly nonrotationally symmetric freeform refractive, reflective, and catadioptric systems. The system parameters can be advanced and the ranges of these system parameters can be wide. Using a special system evolution method and a K-nearest neighbor method, a full dataset consisting of the primary and secondary parts can be generated automatically. The deep neural network can then be trained in a supervised manner and can be used to generate good starting points directly. The convenience and feasibility of the proposed framework are demonstrated by designing a freeform off-axis three-mirror imaging system, a freeform off-axis four-mirror afocal telescope, and a freeform prism for an augmented reality near-eye display. The design framework reduces the designer's time and effort significantly and their dependence on advanced design skills. The framework can also be integrated into optical design software and cloud servers for the convenience of more designers.

Design method of wide field-of-view imaging systems using Gaussian radial basis functions freeform surfaces.

High optical performance systems with wide field-of-view (FOV) have important applications in remote sensing. The radial basis functions, which have a prominent local characteristic in surface description, have attracted much attention in recent years. In this paper, an effective design method for the wide FOV imaging system using Gaussian radial basis function freeform surfaces is proposed. The FOV of the optical system is extended from a relatively small value to a larger one, and the Gaussian radial basis function surfaces are extended stepwise based on certain criteria. A high image quality and small distortion off-axis freeform three-mirror system with a wide FOV (${{60}}^\circ \times {0.6}^\circ$) is designed as an example. Tolerance analysis considering both surface figure error and assembly error is performed. The design results demonstrate the effectiveness of the proposed method.

Designing double freeform surfaces for large ray bending irradiance tailoring of extended LED sources.

Many illumination applications require redistributing the irradiance distributions of LED sources with large ray bending. The problem becomes even more challenging for a compact design where the LED size is no longer ignorable. We tackle this problem by simultaneously designing two freeform optical surfaces. An iterative wavefront tailoring (IWT) method is adapted for obtaining the entrance and exit base freeform surfaces with a predefined ray bending regulation under stereographic coordinates (u, v). The simulated annealing (SA) algorithm is employed for deforming the two base freeform surfaces using the 'uv' polynomials with the purpose of minimizing the relative root-mean-square deviation (RRMSD) between the simulated irradiance distribution and the prescribed one. The optimizations are implemented in an automated workflow which links the optimization engine, 3D modeling software and ray tracing software. The effectiveness of the proposed method is illustrated by designing several double-freeform-surface lenses (central heights: 10 mm) with different ray bending regulated base surfaces and 10-th order uv polynomial departures for generating 500 × 200 mm2 uniform irradiance distributions at a distance of 100 mm from 2 × 2 mm2 and 3 × 3 mm2 sources, respectively.

Compact integrator design for short-distance sharp and unconventional geometric irradiance tailoring.

A compact microlens array (MLA) integral homogenizer composed of a projection MLA, a condenser MLA, and a subimage array mask based on Kohler illumination is presented herein. By adopting the optimal design of an aspheric projection sublens, a short-distance integrator for unconventional geometric irradiance tailoring can be acquired. Compared with the traditional integrator, the integral lens is removed in the proposed integrator. An incident beam with a larger divergence angle is permitted while a sharp illumination performance is maintained. In addition, the illumination distribution with a predefined geometrical profile can be obtained by introducing a subimage array mask without replacing the MLA elements. Through the introduced mask, the illumination attenuation area is cut, the distortion is caused by the large NA, and the peak effect caused by the integral lens of the traditional integrator can be eliminated. The subimage array mask is generated by combining ray tracing and the radial basis function image warping method. By introducing the array mask into the system, an 80% edge relative illumination and an 85% overall illumination uniformity are realized for a compact large-NA integrator with ${\rm NA} = {0.3}$ and thickness of 4.5 mm. An 88% edge relative illumination and a 92% overall illumination uniformity are realized for a small-NA integrator with ${\rm NA} = {0.15}$.