Freeform System Research Articles

LightBot: A Multi-Light Position Robotic Acquisition System for Adaptive Capturing of Cultural Heritage Surfaces.

Multi-light acquisitions and modeling are well-studied techniques for characterizing surface geometry, widely used in the cultural heritage field. Current systems that are used to perform this kind of acquisition are mainly free-form or dome-based. Both of them have constraints in terms of reproducibility, limitations on the size of objects being acquired, speed, and portability. This paper presents a novel robotic arm-based system design, which we call LightBot, as well as its applications in reflectance transformation imaging (RTI) in particular. The proposed model alleviates some of the limitations observed in the case of free-form or dome-based systems. It allows the automation and reproducibility of one or a series of acquisitions adapting to a given surface in two-dimensional space.

Automated design of a slim catadioptric system combining freeform surface and zoom lens.

The development of electronic industry demands miniaturization for zoom lens. Freeform surfaces and catadioptric lens system play important roles in the compactness of optical design. However, the initial structure of the catadioptric system is relatively rare and repeated optimizing in first-order lens design requires advanced knowledge and experiences. That brings challenges for establishing an initial structure for the freeform catadioptric zoom system, which is essential for optical designers. In this work, an automatic design method for the initial structure of a catadioptric system with freeform surface and zoom lens is proposed. As long as the focal length range and total length are determined, the initial structure of the catadioptric zoom lens with arbitrary zoom ratio in a certain range can be obtained for further analysis and optimization. The rapid design method reduces the dependence on experience for catadioptric system design, saves considerable time and can help to ease the difficulty in finding the initial structure of slim zoom lens.

Automatic design method of starting points of freeform off-axis reflective imaging systems of small volume.

For off-axis reflective systems, there is no effective method that can obtain a small-volume starting point automatically. Reducing system volume using the optimization method is usually a difficult and cumbersome process, which usually takes the designer a long time. This paper proposes a method of designing small-volume starting points of freeform off-axis reflective imaging systems, which does not require human involvement after inputting a planar system, specifications and constraints. In the design example presented in this paper, it took only about ten minutes to obtain a small-volume starting point. The starting point obtained by this method makes the optimization process easier, takes less time of designers and more likely to succeed. In the design example, it is also demonstrated that the method has the ability of establishing small-volume starting points with different specifications, which can be used to quickly estimate the minimum volumes that systems with different specifications can achieve and provide guidance for determination of specifications and optimization.

Optical Design at The Age of AI

Data-driven methods to assist lens design have recently begun to emerge; in particular, under the form of lens design extrapolation to find starting points (lenses and freeform reflective system). I proposed a trip over the years to better understand why the AI have been applied first to the starting point problems and where we are going in the future.

Process Development for the Freeform Deposition of a Glass Fiber Reinforced Photopolymer

Continuous fiber additive manufacturing is a rapidly growing field of research and industry. The development of freeform polymer extrusion systems has also seen some interest in the last few years. In this paper, developments to a system combining the concepts of continuous fiber additive manufacturing and freeform extrusion are discussed. The system is able to produce freeform glass fiber reinforced photopolymer extrusions, using 5-axis toolpaths executed by an industrial robot. A simple method of freeform toolpath generation using manual specification of nozzle posture is presented. Process parameters are then identified, and a series of tests to determine suitable values of critical process parameters are described. Results of these tests indicate that, using suitable settings, freeform glass fiber reinforced extrusions can be produced with moderate geometric accuracy, fiber volume fractions in excess of 30 %, and void contents of below 1 %. In addition, using suitable nozzle posture and offset values, fused segments can be extruded in parallel, which will allow for the manufacture of struts comprising multiple joined extrusions.

Design of Freeform Off-Axis Reflective Afocal Systems by Orthogonal Seed Curve Extension Algorithm

Design of Freeform Off-Axis Reflective Afocal Systems by Orthogonal Seed Curve Extension Algorithm

Freeform OST-HMD system with large exit pupil diameter and vision correction capability

Compactness and light weight, large exit pupil diameter and distance, small distortion for virtual image, and see-through light paths are pivotal factors to achieve a better, wearable experience of optical see-through head-mounted displays (OST-HMDs). In addition, light efficiency of the virtual image light path is an important factor for heat dissipation in HMD devices. This paper presents a new type of OST-HMD optical system that includes three wedge-shaped freeform prisms and two symmetric lenses. Based on a 0.71 in. microdisplay, an OST-HMD prototype with a diagonal field of view (FOV) of 45.3°, an F-number (F/#) of 1.8, an exit pupil size of 12 mm × 8 mm , and an eye relief of 18 mm is demonstrated. The maximum value of distortion of the final system is 0.6% and 0.4% for virtual image and see-through light path, respectively. The overall dimension of the optical system per eye is no larger than 30 mm ( width ) × 40 mm ( height ) × 14 mm (thickness), and the weight of the optical module including lenses, holder, and microdisplay is 12.8 g. The light efficiency of the virtual image light path is up to 50% higher than those of other OST-HMD optical solutions.

Engineering Natural Pollen Grains as Multifunctional 3D Printing Materials (Adv. Funct. Mater. 49/2021)

3D Printing Materials The development of 3D printing materials from natural resources is essential in sustainable additive manufacturing. In article number 2106276, Nam-Joon Cho, Juha Song, and co-workers engineer pollen-derived microgel suspension as reinforcements for hydrogel inks and as supporting matrices for freeform 3D printing systems. Pollen grains are attractive candidates to engineer advanced materials for 3D printing applications owing to their natural abundance, renewability, affordability, processibility, monodispersity, and tunable rheological features.

Freeform imaging system with resolution that varies with the field angle in two dimensions.

The human eye's resolution varies with the field angle and has high center resolution and low edge resolution characteristics. In this paper, a freeform imaging system is presented that has resolution distribution characteristics similar to those of the human eye. Field-dependent parameters are used to describe the system's optical properties and a direct design method is proposed to realize the novel functionality. An off-axis reflective freeform imaging system with high center resolution and low edge resolution within a square 30°×30° field of view (FOV) is designed using this method. The maximum instantaneous field of view (IFOV) ratio of center field resolution to edge field resolution is 0.47. Only three freeform surfaces are used to attain good image quality. Simultaneous improvements are observed in both resolution and FOV while the detector remains fixed.

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.

Engineering Natural Pollen Grains as Multifunctional 3D Printing Materials

AbstractThe development of multifunctional 3D printing materials from sustainable natural resources is a high priority in additive manufacturing. Using an eco‐friendly method to transform hard pollen grains into stimulus‐responsive microgel particles, we engineered a pollen‐derived microgel suspension that can serve as a functional reinforcement for composite hydrogel inks and as a supporting matrix for versatile freeform 3D printing systems. The pollen microgel particles enabled the printing of composite inks and improved the mechanical and physiological stabilities of alginate and hyaluronic acid hydrogel scaffolds for 3D cell culture applications. Moreover, the particles endowed the inks with stimulus‐responsive controlled release properties. The suitability of the pollen microgel suspension as a supporting matrix for freeform 3D printing of alginate and silicone rubber inks was demonstrated and optimized by tuning the rheological properties of the microgel. Compared with other classes of natural materials, pollen grains have several compelling features, including natural abundance, renewability, affordability, processing ease, monodispersity, and tunable rheological features, which make them attractive candidates to engineer advanced materials for 3D printing applications.

Aerodynamic Design Optimization of a Transonic Strut-Braced-Wing Regional Aircraft

The aerodynamic design and fuel burn performance of a Mach-0.78 strut-braced-wing regional jet is investigated through aerodynamic shape optimization based on the Reynolds-averaged Navier–Stokes equations. Conceptual-level multidisciplinary design optimization is first performed to size the strut-braced-wing aircraft for a design mission similar to the Embraer E190-E2, with a design range of 3100 nmi at a maximum capacity of 104 passengers, and a maximum payload of 30,200 lb. For direct performance comparisons, a conventional tube-and-wing regional jet is also sized and optimized based on the same reference aircraft. Gradient-based aerodynamic shape optimization is then performed on wing–body–tail models of each aircraft, with the objective of drag minimization at cruise over a 500 nmi nominal mission. Design variables include twist and section shape degrees of freedom, which are realized through a free-form and axial deformation geometry control system, whereas nonlinear constraints include constant lift, zero pitching moment, minimum wing volume, and minimum maximum thickness-to-chord ratios. Results indicate that the optimizer is capable of mitigating shock formation, boundary-layer separation, and other flow interference effects from each wing design, including those within the wing–strut junction of the strut-braced wing. With year 2020 technology levels, the strut-braced-wing regional jet offers a 12.9% improvement in cruise lift-to-drag ratio over an Embraer E190-E2-like conventional tube-and-wing aircraft, which translates to a 7.6% reduction in block fuel for the nominal mission.

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 of a freeform two-reflector system to collimate and shape a point source distribution.

In this paper we propose a method to compute a freeform reflector system for collimating and shaping a beam from a point source. We construct these reflectors such that the radiant intensity of the source is converted into a desired target. An important generalization in our approach compared to previous research is that the output beam can be in an arbitrary direction. The design problem is approached by using a generalized Monge-Ampère equation. This equation is solved using a least-squares algorithm for non-quadratic cost functions. This algorithm calculates the optical map, from which we can then compute the surfaces. We test our algorithm on two cases. First we consider a uniform source and target distribution. Next, we use the model of a laser diode light source and a ring-shaped target distribution.

Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation.

Recently, freeform optics has been widely used due to its unprecedented compactness and high performance, especially in the reflective designs for broad-wavelength imaging applications. Here, we present a generalized differentiable ray tracing approach suitable for most optical surfaces. The established automated freeform design framework simultaneously calculates multi-surface coefficients with merely the system geometry known, very fast for generating abundant feasible starting points. In addition, we provide a "double-pass surface" strategy with desired overlap (not mutually centered) that enables a component reduction for very compact yet high-performing designs. The effectiveness of the method is firstly demonstrated by designing a wide field-of-view, fast f-number, four-mirror freeform telescope. Another example shows a two-freeform, three-mirror, four-reflection design with high compactness and cost-friendly considerations with a double-pass spherical mirror. The present work provides a robust design scheme for reflective freeform imaging systems in general, and it unlocks a series of new 'double-pass surface' designs for very compact, high-performing freeform imaging systems.

Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation

Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation

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.

Freeform imaging systems: Fermat\u2019s principle unlocks \u201cfirst time right\u201d design

For more than 150 years, scientists have advanced aberration theory to describe, analyze and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously, they have developed optical design methods for and manufacturing techniques of imaging systems with ever-increasing complexity and performance up to the point where they are now including optical elements that are unrestricted in their surface shape. These so-called optical freeform elements offer degrees of freedom that can greatly extend the functionalities and further boost the specifications of state-of-the-art imaging systems. However, the drastically increased number of surface coefficients of these freeform surfaces poses severe challenges for the optical design process, such that the deployment of freeform optics remained limited until today. In this paper, we present a deterministic direct optical design method for freeform imaging systems based on differential equations derived from Fermat’s principle and solved using power series. The method allows calculating the optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic, deterministic, scalable, and holistic character of our method with catoptric and catadioptric design examples. As such we introduce a disruptive methodology to design optical imaging systems from scratch, we largely reduce the “trial-and-error” approach in present-day optical design, and we pave the way to a fast-track uptake of freeform elements to create the next-generation high-end optics. We include a user application that allows users to experience this unique design method hands-on.

Towards automatic freeform optics design: coarse and fine search of the three-mirror solution space

Design of an optical system, whether classic or novel, in the past or the present, requires significant effort from the designer. In addition to design methods and theories, the designer’s skills and experience in optical system design are particularly important, which may require years of practice to learn. The diversity and variety of results are limited because of the difficulty, time, and labor costs required. In this article, we propose an automatic design method for freeform optics that can achieve a diverse range of three-mirror designs. The optical specifications and the design constraints are the only inputs required, and a variety of results can be obtained automatically. The output results have various structures and various optical power distributions with high imaging qualities. By implementing the design method, designers can not only realize an overview of the solution space of the three-mirror freeform system, but can also focus on specific designs.

Freeform optical surface design in an off-axis reflective imaging system by a double seed curve extension algorithm.

A double seed curve extension (DSCE) method is proposed to design a freeform surface directly in an off-axis reflective imaging system. Compared with the basic seed curve extension (SCE) method, the DSCE can effectively reduce the error of freeform surface construction and improve the imaging quality of the off-axis reflective imaging system. In addition, the method can be employed to design an off-axis reflective imaging system consisting of multiple freeform surfaces with several virtual image points set in advance. In order to verify the DSCE method, three examples are given. One is the off-axis freeform one-mirror system, one is a compact off-axis three-mirror imaging system with two freeform surfaces, and the other is an off-axis reflective system with three freeform surfaces. The modulation transfer function (MTF) of the one-mirror system is greater than 0.9 at 20 lp/mm, which is close to the diffraction limit. The average of the sagittal and tangential MTFs of the second system designed by the SCE and DSCE methods are 0.26 and 0.74 at spatial frequency of 20 lp/mm, respectively. And the MTF of the last system designed by the DSCE method is greater than 0.9 at 20 lp/mm, which is better than that of the SCE method.