Freeform Design Research Articles

Design of two-dimensional reflective imaging systems: an approach based on inverse methods

Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional (2D) freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively design reflectors using inverse methods from non-imaging optics and optimize them to obtain a system that produces minimal aberrations. This is done by minimizing a merit function that quantifies aberrations and is dependent on the energy distributions at the source and target of an optical system, which are input parameters essential for inverse freeform design. The proposed method is tested for two configurations: a single-reflector system and a double-reflector system. Classical designs consisting of aspheric elements are well-known for their ability to minimize aberrations. We compare the performance of our freeform optical elements with classical designs. The optimized freeform designs outperform the classical designs in both configurations.

A mathematical model for inverse freeform design of a point-to-point two-reflector system

A mathematical model for inverse freeform design of a point-to-point two-reflector system

Multiwavelength Achromatic Deflector in the Visible Using a Single-Layer Freeform Metasurface.

Deflectors are essential for modulating beam direction in optical systems but often face form factor issues or chromatic aberration with conventional optical elements, such as prisms, mirrors, and diffractive/holographic optical elements. Despite recent efforts to address such issues using metasurfaces, their practicality remains limited due to operation wavelengths in the near-infrared or the fabrication difficulties inherent in the multilayer scheme. Here, we propose a novel single-layer metasurface achieving multiwavelength chromatic aberration-free deflection across the visible spectrum by employing the robust freeform design strategy to simplify the fabrication process. By properly selecting diffraction orders for red, green, and blue wavelengths to achieve identical wavelength-diffraction-order products, the metasurface deflects light at a consistent angle of 41.3° with a high efficiency. The coupled Bloch mode analysis explains the physical properties, and experimental fabrication and characterization confirm its effectiveness. This approach holds potential for various applications such as AR/VR, digital cameras, and high-quality optical systems.

Cassegrain-based concentrator with a high uniformity and acceptance angle

In this study, we improved a Cassegrain concentrator [Appl. Opt. 59, 8603 [2020)APOPAI0003-693510.1364/AO.400756] by redesigning the secondary optical element (SOE) with a freeform design, including geometrically mapped and tilted steps, to replace the design of the primary optical element (POE). This modification increased the acceptance angle and formed a more uniform irradiance distribution in the system without a homogenizer while maintaining the same level of efficiency. The result is a 1236× geometric concentration ratio, 1035× concentration ratio, 83.73% optical efficiency, ±0.40∘ acceptance angle, 8.96 uniformity, and 0.254 aspect ratio.

Micro-optics fabrication using blurred tomography

We demonstrate the fabrication of millimeter-sized optical components using tomographic volumetric additive manufacturing (VAM). By purposely blurring the writing beams through the use of a large etendue source, the layer-like artifacts called striations are eliminated enabling the rapid and direct fabrication of smooth surfaces. We call this method blurred tomography and demonstrate its capability by printing a plano–convex optical lens with comparable imaging performance to that of a commercially available glass lens. Furthermore, due to the intrinsic freeform design nature of VAM, we demonstrate the double-sided fabrication of a biconvex microlens array, and for the first time demonstrate overprinting of a lens onto an optical fiber using this printing modality. This approach to VAM will pave the way for low-cost, rapid prototyping of freeform optical components.

LIFT metallization as an alternative to screen-printing for silicon heterojunction solar cells

The electrical characteristics of solar cells are significantly influenced by the metallization process, making it a crucial step. Screen printing is the standard metallization technique, but there is an increasing interest in the development of methods that allow more versatility, higher process control, and a more efficient use of the expensive metallic pastes used. We focus here on the comparison between the standard screen-printing method, and Light-Induced Forward-Transfer (LIFT), a non-contact, very precise technique, able to transfer volumes down to picolitres. The high flexibility, using free-form designs that do not depend on any mask or physical support, and the efficient use of the metallic paste with almost no waste, are other characteristics that point out LIFT as a very promising alternative. In this paper we include the electric characterization of contacts, and solar silicon heterojunction (SHJ) cells metalized with both techniques. The results show a slightly better efficiency for the screen-printed cells, but good series resistance and fill factor values imply that LIFT is a promising alternative for device metallization.

Diffusion-Based 3D Bioprinting Strategies.

3D bioprinting has enabled the fabrication of tissue-mimetic constructs with freeform designs that include living cells. In the development of new bioprinting techniques, the controlled use of diffusion has become an emerging strategy to tailor the properties and geometry of printed constructs. Specifically, the diffusion of molecules with specialized functions, including crosslinkers, catalysts, growth factors, or viscosity-modulating agents, across the interface of printed constructs will directly affect material properties such as microstructure, stiffness, and biochemistry, all of which can impact cell phenotype. For example, diffusion-induced gelation is employed to generate constructs with multiple materials, dynamic mechanical properties, and perfusable geometries. In general, these diffusion-based bioprinting strategies can be categorized into those based on inward diffusion (i.e., into the printed ink from the surrounding air, solution, or support bath), outward diffusion (i.e., from the printed ink into the surroundings), or diffusion within the printed construct (i.e., from one zone to another). This review provides an overview of recent advances in diffusion-based bioprinting strategies, discusses emerging methods to characterize and predict diffusion in bioprinting, and highlights promising next steps in applying diffusion-based strategies to overcome current limitations in biofabrication.

GarmentCode: Programming Parametric Sewing Patterns

Garment modeling is an essential task of the global apparel industry and a core part of digital human modeling. Realistic representation of garments with valid sewing patterns is key to their accurate digital simulation and eventual fabrication. However, little-to-no computational tools provide support for bridging the gap between high-level construction goals and low-level editing of pattern geometry, e.g., combining or switching garment elements, semantic editing, or design exploration that maintains the validity of a sewing pattern. We suggest the first DSL for garment modeling - GarmentCode - that applies principles of object-oriented programming to garment construction and allows designing sewing patterns in a hierarchical, component-oriented manner. The programming-based paradigm naturally provides unique advantages of component abstraction, algorithmic manipulation, and free-form design parametrization. We additionally support the construction process by automating typical low-level tasks like placing a dart at a desired location. In our prototype garment configurator, users can manipulate meaningful design parameters and body measurements, while the construction of pattern geometry is handled by garment programs implemented with GarmentCode. Our configurator enables the free exploration of rich design spaces and the creation of garments using interchangeable, parameterized components. We showcase our approach by producing a variety of garment designs and retargeting them to different body shapes using our configurator. The library and garment configurator are available at https://github.com/maria-korosteleva/GarmentCode.

Partition of the space of planar quintic Pythagorean-hodograph curves

The quintics are the lowest–order planar Pythagorean–hodograph (PH) curves suitable for free–form design, since they can exhibit inflections. A quintic PH curve r(t) may be constructed from a complex quadratic pre–image polynomial w(t) by integration of r′(t)=w2(t), and it thus incorporates (modulo translations) six real parameters — the real and imaginary parts of the coefficients of w(t). Within this 6–dimensional space of planar PH quintics, a 5–dimensional hypersurface separates the inflectional and non–inflectional curves. Points of the hypersurface identify exceptional curves that possess a tangent–continuous point of infinite curvature, corresponding to the fact that the parabolic locus specified by the quadratic pre–image polynomial w(t) passes through the origin of the complex plane. Correspondingly, extreme curvatures and tight loops on r(t) are incurred by a close proximity of w(t) to the origin of the complex plane. These observations provide useful insight into the disparate shapes of the four distinct PH quintic solutions to the first–order Hermite interpolation problem.

74‐1: Invited Paper: Highly Stretchable and Shrinkable AMOLED for Free Deformation

Flexible display technology has been successfully commercialized with foldable and rollable displays. Because of the limitation of the flexible technology, stretchable displays have attracted great attention which capable of realizing freeform design as a post‐flexible display. However, no technology has yet provided sufficient stretchability and resolution to realize genuine free‐form displays. We report on a highly deformable AMOLED display which capable of elongation over 20%. Moreover, our display is capable of more than 15% shrinkage deformation. We also developed low‐temperature thermal shrink process to make the most of the potential of the display. The fabricated full‐color stretchable AMOLED shows excellent deformability with high pixel density.

PneuPrint: 3D printing on inflatables

This research investigated the feasibility of thermoplastic 3D printing on inflatable membranes. Five experiments were performed in an iterative process through design and manufacture (1), computational simulation and 3D scanning (2), and robotic fabrication on the pneumatic formwork (3). These experiments ranged from small to large-scale 3D printing. Experiment 1 demonstrated the small-scale feasibility of the process and the need to integrate an air-pressure control loop. Experiment 2 investigated the technique transfer from small to large-scale. Experiment 3 analyzed the deviation and shape accuracy of the inflatable membrane. Experiment 4 identified the required fabrication settings and compatibility between the membrane and the 3D printing material. Finally, Experiment 5 demonstrated the design and fabrication potential of large-scale 3D printed elements on pneumatic formworks. The results proved high potential for building freeform design elements for architectural applications on pneumatic formworks.

Worm-like highly deformable Multi-Section B-Spline Offset Feature for topology optimization

This paper presents a highly deformable Multi-Section B-Spline Offset Feature (MS-BSOF) for topology optimization. The MS-BSOF is bio-inspired from the geometric morphology of worms which is modeled with a deformable directrix and deformable cross-sections. The directrix is defined by B-spline curve. The cross-section profile in 3D case is determined by a set of control cross-section profiles, each of which is defined as a closed B-spline (CBS) to ensure high deformability. The implicit representations of the proposed 2D and 3D MS-BSOFs are formulated using the level-set function (LSF). To perform topology optimization, a topology variation modeler (TVM) is constructed with the proposed MS-BSOF within a freeform design domain modeler (FDDM). Several numerical examples are presented to demonstrate the effectiveness and merits of the MS-BSOF.

Free form shape optimization of three dimensional beams using cross section analysis

We introduce an efficient method for shape optimization of three dimensional beams that is based on free-form design of the beam’s cross section. The cross section boundary of each beam segment is parameterized by a closed, unclamped B-spline curve, whose control points’ coordinates serve as design variables. The response of the beam is evaluated globally as a one-dimensional entity using 3D beam finite elements, while each cross section is modeled locally using cross section analysis following anisotropic beam theory. A fully consistent analytical sensitivity analysis is derived to account for the relation between the control points and the beam cross-sectional properties and design updates are performed using gradient-based optimization. The proposed method is applied to several test cases, aiming at minimization of compliance or maximization of the fundamental frequency. The numerical results and a comparison to other methods for beam optimization show that the method can generate highly competitive designs. A consistent quantitative comparison to high resolution continuum topology optimization shows that a performance which is only slightly inferior can be achieved, for only a small fraction of the computational effort.

Multiscale Hybrid Fabrication: Volumetric Printing Meets Two‐Photon Ablation

AbstractMultiscale printing of 3D perfusable geometries holds great potential for a range of applications, from microfluidic systems to organ‐on‐a‐chip. However, the generation of freeform designs spanning from centimeter to micrometer features represents an unmet challenge for a single fabrication method and thus may require the convergence of two or more modalities. Leveraging the great advances in light‐based printing, herein a hybrid strategy is introduced to tackle this challenge. By combining volumetric printing (VP) and high‐resolution two‐photon ablation (2PA), the possibility to create multiscale models with features ranging from mesoscale (VP) to microscale (2PA) is demonstrated. To successfully combine these two methods, micrometer‐size defects generated during the VP process due to optical modulation instability and self‐focusing phenomena are first eliminated. By optical tuning the refractive index of the photoresin, defect‐free VP that can then be combined with 2PA is demonstrated. To facilitate the 2PA process and meet VP requirements, a purely protein‐based photoclick photoresin combining gelatin‐norbornene and gelatin‐thiol is introduced. Finally, the possibility to generate complex organotypic 3D vasculature‐like constructs with features ranging from ≈400 µm of VP to ≈2 µm of 2PA is demonstrated. This hybrid strategy opens new possibilities for multiscale printing, with particular potential for microfluidics and organ/tissue‐on‐a‐chip technologies.

Conformal Volumetric Grayscale Metamaterials.

Conformal artificial electromagnetic media that feature tailorable responses as a function of incidence wavelength and angle represent universal components for optical engineering. Conformal grayscale metamaterials are introduced as a new class of volumetric electromagnetic media capable of supporting highly multiplexed responses and arbitrary, curvilinear form factors. Subwavelength-scale voxels based on irregular shapes are designed to accommodate a continuum of dielectric values, enabling the freeform design process to reliably converge to exceptionally high figures of merit (FOMs) for a given multi-objective design problem. Through additive manufacturing of ceramic-polymer composites, microwave metamaterials, designed for the radio-frequency range of 8-12GHz, are experimentally fabricated and devices with extreme dispersion profiles, an airfoil-shaped beam-steering device, and a broadband, broad-angle conformal carpet cloak, are demonstrated. It is anticipated that conformal volumetric metamaterials will lead to new classes of compact and multifunctional imaging, sensing, and communications systems.

Physical-mechanical behaviors of stainless steel plate-lattice built by material extrusion additive manufacturing

Additive manufacturing (AM) technology has been widely adopted for the fabrication of metal lattices due to its freeform design capability over traditional manufacturing methods. However, the prevalent laser-based AM technologies possess high energy and investment consumption, and relatively low manufacturing speed, hampering their widespread adoption in building metal lattice components. In this study, an integrated approach of material extrusion AM, debinding, and sintering was introduced to produce 17–4 PH stainless steel plate-lattice structures in a time-efficient and cost-effective way. Three types of plate-lattice structures, namely body-centered cubic (BCC), face-centered cubic (FCC) and their combination (BCC-FCC), were successfully fabricated. Physical-mechanical behaviors, including physical deformation and compressive properties, were investigated through modeling, simulation, and experiments. Specifically, the shrinkage of the final sintered parts was predicted by the analytical modeling and characterized by experimental observation, the results of which showed a good consistency. The plate-lattice structure exhibited equiaxed grains on each surface, with a small portion of lath martensite observed at the top surface. Numerical simulation and compression test were conducted to reveal the compressive modulus, yield strength, and the fractural response at large compressive strains. All three types of plate-lattices possessed a lower compressive modulus than the simulated value, but still exhibited extraordinary yield strength under the compressive force compared to the truss-based or triply periodic minimal surface lattices. The successfully built metal plate-lattice structure verifies the great potential of material extrusion AM process, showing a great promise to fabricate complex metal lattice for large scale applications.

Additive manufacturing of silicone-thermoplastic elastomeric composite architectures

Additive manufacturing (AM) methods such as fused filament fabrication (FFF) and direct ink writing (DIW) enable the free-form design and printing of complex architectures using a range of materials. Compared with traditional manufacturing technologies, AM methods are highly automated to reduce waste, assembly costs, and processing errors. By combining different AM deposition methods, we can fabricate composite materials with desired spatial arrangements and anisotropies to meet unique design requirements and to produce integrated multi-material components that are not easily manufactured by traditional strategies. To address a wide variety of mechanical performance requirements, developing hybrid AM technologies into a low-cost, fully-automated manufacturing process can realize a number of new types of elastomer composite architectures. In this work, FFF and DIW methods have been combined to fabricate thermoplastic polyurethane (TPU) reinforced silicone composite materials. Several specimens with different silicone and TPU infill patterns have been designed to characterize the mechanical compression responses of these structures. With 40–80% infill percentages of silicone and 20–60% infill percentages of TPU, composites specimens can be designed to get any specified compression response between 600 N and 9000 N. This TPU-reinforced silicone printing technique can be applied for silicone composite architecture design in a wide range of applications that require tunable elastic responses.

Transfer-Tattoo-Like Cell-Sheet Delivery Induced by Interfacial Cell Migration.

A direct transfer of a cell sheet from a culture surface to a target tissue is introduced. Commercially available, flexible parylene is used as the culture surface, and it is proposed that the UV-treated parylene offers adequate and intermediate levels of cell adhesiveness for both the stable cell attachment during culture and for the efficient cell transfer to a target surface. The versatility of this cell-transfer process is demonstrated with various cell types, including MRC-5, HDFn, HULEC-5a, MC3T3-E1, A549, C2C12 cells, and MDCK-II cells. The novel cell-sheet engineering is based on a mechanism of interfacial cell migration between two surfaces with different adhesion preferences. Monitoring of cytoskeletal dynamics and drug treatments during the cell-transfer process reveals that the interfacial cell migration occurs by utilizing the existing transmembrane proteins on the cell surface to bind to the targeted surface. The re-establishment and reversal of cell polarity after the transfer process are also identified. Its unique capabilities of 3D multilayer stacking, freeform design, and curved surface application are demonstrated. Finally, the therapeutic potential of the cell-sheet delivery system is demonstrated by applying it to cutaneous wound healing and skin-tissue regeneration in mice models.

Automated Posture Positioning for High Precision 3D Scanning of a Freeform Design using Bayesian Optimization

Three-dimensional scanning is widely used for the dimension measurements of physical objects with freeform designs. The output point cloud is flexible enough to provide a detailed geometric description for these objects. However, geometric accuracy and precision are still debatable for this scanning process. Uncertainties are ubiquitous in geometric measurement due to many physical factors. One potential factor is the object’s posture in the scanning region. The posture of target positioning on the scanning platform could influence the normal of the scanning points, which could further affect the measurement variances. This paper first investigates the geometric and spatial factors that could potentially influence scanning variance. This functional relationship is modeled as a Bayesian extreme learning model, which is later utilized to find the object’s optimal posture for variance reduction. A Bayesian optimization approach is proposed to solve this minimization problem. Case studies are presented to validate the proposed methodology.

Investigation on flow mechanism of an advanced transonic centrifugal compressor with free-form impeller at design and off-design speeds

A transonic centrifugal compressor with a ruled-impeller (that is, impeller blades are generated by a set of points swept by a moving straight line) was used as the baseline, and the impeller blades were redesigned using non-ruled surfaces (referred to as the ‘free-form impeller’) in this study to reveal the potential of this design approach to improve the performance of high-pressure-ratio centrifugal compressors. By using the method of Computational Fluid Dynamics (CFD) simulation, the performance characteristic and the flow field inside the impeller and diffuser of the baseline compressor and the free-form one were comparatively analyzed in detail. The results show that the free-form impeller design can improve the performance of the compressor in many aspects no matter at design or off-design speeds. The barreled-sweep inducer can reduce the losses from the shock wave at design speed and extend the compressor stable operating range at off-design speeds. The positive compound-lean impeller blades can suppress the reverse flow at impeller outlet. The flow downstream of the free-form impeller was also improved due to a more uniform outlet flow field provided by it at. This study aims to provide a valuable reference for applying free-form design methods to future advanced centrifugal compressors.