Freeform Elements Research Articles

Design of freeform elements with a large exit pupil for AR display

This work presents an augmented reality display consisting of two freeform lenses. The first lens is composed of two aspherical polished surfaces and one plane surface, while the second lens acts as a compensator to allow distortion-free viewing of the surrounding area. One benefit of this design is the large size of the exit pupil, reaching up to 12mm, and the low distortion value of 1.63%. The optics has a thickness of 22mm and is compatible with 0.49-inch diagonal displays. The field of view is limited to 28◦, which is sufficient for various augmented reality applications.

Wide-field-of-view and high-resolution waveguide display based on the coupling-collimation system

Waveguide display is a common augmented reality (AR) solution. In traditional waveguide display systems, the design of the couplers and the design of the collimators are separated. In order to achieve high imaging resolution under a large field of view, complex collimating lens groups are often required. In this work, a waveguide display scheme based on the coupling-collimation system is proposed. This system consists of a freeform liquid crystal diffractive optical element on the waveguide and a freeform element outside the waveguide, replacing the conventional in-coupler and collimator. Through the overall optimization of the coupling-collimation system, a wide-field-of-view and high-resolution waveguide display can be realized with a simple and compact structure. We demonstrate the effectiveness and superiority of this scheme by exemplifying several design results. The proposed scheme is expected to facilitate the design of waveguide displays with higher performance.

High-efficiency anti-reflective modification of freeform elements and cylindrical lenses for arrayed wide-field astronomical corrector units

High-efficiency anti-reflective modification of freeform elements and cylindrical lenses for arrayed wide-field astronomical corrector units

Calcination-Enhanced Laser-Induced Damage Threshold of 3D Micro-Optics Made with Laser Multi-Photon Lithography

Laser Direct Writing (LDW), also known as 3D multi-photon laser lithography of resins, is a promising technique for fabricating complex free-form elements, including micro-optical functional components. Regular organic or hybrid (organic–inorganic) resins are often used, with the latter exhibiting better optical characteristics, as well as having the option to be heat-treated into inorganic glass-like structures particularly useful for resilient micro-optics. This work is a continuation of our SZ2080™ calcination development of micro-optics, specifically studying the Laser-Induced Damage Threshold (LIDT). Such sol–gel-derived glass 3D micro-structures, particularly those that undergo heat treatment, have not been well-characterized in this respect. In this pilot study, we investigated the LIDT using the Series-on-One (S-on-1) protocol of functional micro-lenses produced via LDW and subsequently calcinated. Our results demonstrate that the LIDT can be significantly increased, even multiple times, by this approach, thus enhancing the resilience and usefulness of these free-form micro-optics. This work represents the first investigation in terms of LIDT into the impact of calcination on LDW-produced, sol–gel-derived glass micro-structures and provides important insights for the development of robust micro-optical devices.

Innovative process for precise grinding of optical free-form elements

The aim of the presented article is to share experience gained throughout the course of two projects focused on precise grinding of a free-form glass optical element with the objective of achieving a surface shape error of less than approximately 10 μm PV before the subsequent polishing phases. Compared to spheres or aspheres machining, it is considerably more demanding, mainly due to the impossibility of using rotationally symmetric shape corrections. The developed and tested process combines a mechanical engineering approach based on the use of the current Computer Aided Design and Computer Aided Manufacturing software with their respective strengths and weaknesses and an optical engineering approach, for which the employment of CNC machines featuring precise control but low flexibility is typical. Therefore, attention is paid mainly to the description of particular process steps like CAD construction and CNC grinding step programming with regard to the necessary software and data handling, as well as the required parametrisation of the used machine equipment.

Freeform based compact receiver front-end for indoor multi-cell VLC system: Fabrication, optical characterization and associated challenges

The prospect of utilizing freeform optics to develop a more compact and smaller VLC receiver front-end is explored in this study for a multi-cell indoor environment. A novel freeform surface element (FSE) has been fabricated by an ultra-precision single-point diamond turning (SPDT) machine and characterized by the mechanical and optical profiler to investigate its potential use inside a freeform diversity receiver. A 9 dB increment in average signal-to-interference-plus-noise-ratio (SINR) is observed after third iteration while the form error reduces to 1.92 µm. The communication functionality of the fabricated FSE is also validated experimentally. The average SINR over the communication floor is computed as 109.29 dB. The fabricated freeform element is further modified to a freeform Fresnel profile for more compactness. The result shows, a substantial decrease in receiver height (2.314 mm) is possible using the proposed approach. Moreover, different fabrication challenges related with freeform Fresnel have been identified and discussed to set the future research pathway.

Analysis of assembly tolerance compensation in microscope objectives with a free-form element at the aperture stop.

We analyze the feasibility of using refractive free-form phase plates at the aperture stop of microscope objectives as an alternative to active alignment to compensate for assembly tolerances. The method involves the determination of misalignment-induced aberrations at the exit pupil, and transferring them to the aperture stop while taking pupil aberrations into consideration. We demonstrate that despite being able to correct only for field-independent aberrations, this method can restore near-diffraction-limited imaging performance of passively aligned systems with practical tolerances, given that the as-designed system is highly corrected. We confirm the results via numerical simulations for two different commercial objective designs.

Synthesis of freeform optical surfaces using neural networks

Subject of study. Developed methods for synthesis of freeform illumination optics (ellipsoid, Monge-Ampere, string, and flow line methods) do not contain a correct description of the transformation of input and output wavefronts determined by the wave aberration function, do not consider the image quality criteria, and are not suitable for the calculation of imaging systems. The most common methods for synthesis of freeform elements of imaging systems (simultaneous multiple surface and ray-mapping methods) are also not ubiquitous because they are aimed at realization of a specific system configuration and, at least, require modification to solve a specific task. The largest complication in the synthesis stages of systems of imaging optics is the determination of the initial system scheme. Design of a method for synthesis of optical systems that does not require a starting point is a highly relevant objective of applied optics. A method allowing the synthesis of freeform optical surfaces for imaging systems using an artificial neural network is presented in this paper. Method. A neural network was built upon radial-basis functions and uses the geometric mapping method to generate the coordinates of the desired optical surface during backward ray tracing. The neural network was trained on different numbers of optical systems, which were automatically generated with variations in structural parameters and positions of the object and image. Main results. The method was demonstrated to operate effectively using more than 17,000 training systems at the ray set dimension of M=4096. The model of a flat-hyperbolic lens calculated using this method has a wave aberration of W<5×10−2 for wavelengths within the diffraction tolerance. Practical significance. The developed method can be used to design high-performance imaging systems.

Cryptographic Strain‐Dependent Light Pattern Generators

AbstractRefractive freeform components are becoming increasingly relevant for generating controlled patterns of light, because of their capability to spatially modulate optical signals with high efficiency and low background. However, the use of these devices is still limited by difficulties in manufacturing macroscopic elements with complex, 3D surface reliefs. Here, 3D‐printed and stretchable magic windows generating light patterns by refraction are introduced. The shape and, consequently, the light texture achieved can be changed through controlled device strain. Cryptographic magic windows are demonstrated through exemplary light patterns, including micro‐QR‐codes, that are correctly projected and recognized upon strain gating while remaining cryptic for as‐produced devices. The light pattern of micro‐QR‐codes can also be projected by two coupled magic windows, with one of them acting as the decryption key. Such novel, freeform elements with 3D shape and tailored functionalities is relevant for applications in illumination design, smart labels, anti‐counterfeiting systems, and cryptographic communication.

Null-screen testing of the complementary freeform surfaces of an adjustable focus lens.

A novel null-screen technique to test freeform optical surfaces for ophthalmic use is presented. We present an off-axis experimental setup to evaluate the surface shape of a two-element commercial adaptable focus lens based on the Alvarez principle. The advantages of the method are that it is fast, easy to implement, and reduces costs. This metrology technique is validated by testing both the convex and the concave complementary freeform elements of the spectacle under test. We also apply two methods to recover the surface shape of both elements: numerical integration and a custom probabilistic algorithm. Results are compared with a reference surface finding that for method 1, the RMS value in sagitta differences is 32.6 microns for the convex surface and 26.5 microns for the concave surface. Meanwhile, for method 2, the RMS value in sagitta differences found is 19.8 microns for the convex surface and 16.9 microns for the concave surface. Results show agreement in RMS in sagitta differences for both surfaces in each of the reconstruction methods employed.

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.

Ultra-precision direct diamond shaping of functional micro features

• Direct Diamond Shaping is presented as a novel machining method, producing unique features using the UPM. • Rotary and linear features can now be machined continuously with a turning tool. • 2D and 3D complex functional micro features can now be realized using the Virtual Rotating Tool Shaping algorithm. • Successfully machined a Bi-focal segmented Fresnel lens by Direct Diamond Shaping without the need for assembly. • Successfully machined a serpentine microfluidic channel with linear and rotary features by Direct Diamond Shaping. • Comprehensive geometrical analysis on tool limitations during shaping of channels is presented. As technological components continue to utilize space effectively within devices without compromise to their operational efficiency, the relevance of accurate and precise parts with good tolerances and surface finishing has shot to prominence. Ultra-Precision Machining (UPM) technology has constantly risen to the challenge by realizing components with superior geometrical accuracies and mirror-like surface finishes, much of which are required in the optical industry. However, conventional diamond shaping processes are usually limited to rotary symmetric components or linear gratings. Thus, the developed Virtual Rotating Tool Shaping (VRTS) addresses these issues by enabling the UPM to fabricate non-rotary symmetric, intricate and freeform elements by Direct Diamond Shaping (DDS). VRTS synchronizes the linear and rotational motions of the ultra-precision machine to constantly align the tool with the cutting direction, while compensating in the linear axes for the run-off. As such, DDS can now achieve a combination of linear and rotary features by planing. In this paper, the developed DDS technique is presented with experimental verifications of the algorithm on a segmented bi-focal Fresnel lens and a serpentine micro-channel, followed by the corresponding analyses.

Freeform axicon with azimuthal variation

An analytical closed-form equation to design a freeform element that replicates an axicon is presented. In this paper, we get the mentioned analytical closed-form equation step by step. The equation comes from applying both the Fermat principle and the Snell's law at the first refractive surface. This Freeform axicon with azimuthal variation can be applied to produce annular conical beams with the possibility to receive wavefronts not necessarily collimated. In the paper, we test the equation in several scenarios to test the design of the Freeform axicon and the results of the performance of the Freeform axicon were as expected.

Compact optical zoom camera module based on Alvarez elements

A compact optical zoom camera module with Alvarez freeform elements is reported. A 3 × magnification in the optical zoom system was achieved by means of lateral shifting two pairs of Alvarez lenses. The optical design performances, profiles of the freeform surfaces, tolerance analysis results, and Monte Carlo yield simulation for mass production of the optical zoom system are presented. The optomechanical structures of the whole camera module including the barrels, actuators, and the slide-guiding systems are also described. The Alvarez elements and aspheric lenses were fabricated by precise injection molding and the movable elements are actuated by voice coil motors with a stroke of 3 mm. A camera module was developed with a size of 25 mm (width) × 25 mm (length) × 6 mm (height). The zooming and imaging capabilities of this Alvarez zoom lens were demonstrated experimentally.

Modeling of a freeform element with a variable light distribution

In this contribution we consider modeling of an optical element with freeform surface. As an example, we synthesize a freeform component, which allows to generate a required image for any object on the basis of Snell’s law and the law of energy conservation. The optical design of the freeform component utilizes ray tracing between the object and image desсribed with complex light distribution patterns.

Remote focusing in confocal microscopy by means of a modified Alvarez lens

Alvarez lenses are actuated lens-pairs which allow one to tune the optical power by mechanical displacement of subelements. Here, we show that a recently realized modified Alvarez lens design which does not require mechanical actuation can be integrated into a confocal microscope. Instead of mechanically moving them, the sublenses are imaged onto each other in a 4f-configuration, where the lateral image shift leading to a change in optical power is created by a galvo-mirror. The avoidance of mechanical lens shifts leads to a large speed gain for axial (and hence also 3D) image scans compared to classical Alvarez lenses. We demonstrate that the suggested operation principle is compatible with confocal microscopy. In order to optimize the system, we have drawn advantage of the flexibility a liquid-crystal spatial light modulator offers for the implementation. For given specifications, dedicated diffractive optical elements or freeform elements can be used in combination with resonant galvo-scanners or acousto-optic beam deflectors, to achieve even faster z-scans than reported here, reaching video rate.

Freeform characterization based on nanostructured diffraction gratings.

The in-line characterization of freeform optical elements during the production cycle is challenging. Recently, we presented a compact sensor setup for the characterization of the wavefront generated by freeform optical elements in transmission. The sensor is based on a common-path interferometer consisting of diffractive components and Fourier filtering being adapted to the subsequent numerical post processing. Additionally, it offers several degrees of freedom for enlarging the measurement range of the wavefront gradients. In this contribution, we propose an advanced sensor setup for the measurement of wavefronts generated by freeform elements in reflection. The main advantage is the uni-axial illumination of the test object and the measuring system without the need for conventional beamsplitters. Due to this uni-axial arrangement, the main challenge is to avoid the effect of stray light and back reflections on the measurement signal-to-noise ratio. This is achieved by implementing a highly absorbing amplitude grating based on nanostructured silicon. We demonstrate the experimentally realized measurement system and compare its performance to a commercial Shack-Hartmann sensor.

Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions.

The application of freeform elements in optical systems increases the number of variables available for correction. This creates the potential to design compact systems with excellent imaging performance. However, it is non-trivial to determine which configuration of the system to choose and where to place the freeform element to obtain the best design. The knowledge of aberration distribution in the system is very helpful in answering these questions. In the following paper, we analyze Zernike surface contributions to the total wave aberration in non-symmetric freeform mirror systems using the method introduced in [J. Opt. Soc. Am. A34, 1856 (2017)JOAOD60740-323210.1364/JOSAA.34.001856]. We demonstrate the benefits of the proposed method in determining effective location of the freeform element and in finding critical differences between possible configurations. By analyzing surface contributions to the total wave aberration characterized by Zernike fringe coefficients, it is possible to find solutions corrected for aberrations of orders higher than the order of coefficients used for freeform sag contribution described with the same Zernike polynomial set.

Freeform additive manufacturing by vari-directional vari-dimensional material deposition

PurposeThe purpose of this paper is to propose and demonstrate a new additive manufacturing approach that breaks the layer-based point scanning limitations to increase fabrication speed, obtain better surface finish, achieve material flexibility and reduce equipment costs.Design/methodology/approachThe freeform additive manufacturing approach conceptually views a 3D article as an assembly of freeform elements distributed spatially following a flexible 3D assembly structure, which conforms to the surface of the article and physically builds the article by sequentially forming the freeform elements by a vari-directional vari-dimensional capable material deposition mechanism. Vari-directional building along tangential directions of part surface gives surface smoothness. Vari-dimensional deposition maximizes material output to increase build rate wherever allowed and minimizes deposition sizes for resolution whenever needed.FindingsProcess steps based on geometric and data processing considerations were described. Dispensing and forming of basic vari-directional and vari-dimensional freeform elements and basic operations of joining them were developed using thermoplastics. Forming of 3D articles at build rates of 2-5 times the fused deposition modeling (FDM) rate was demonstrated and improvement over ten times was shown to be feasible. FDM compatible operations using 0.7 mm wire depositions from a variable exit-dispensing unit were demonstrated. Preliminary tests of a surface finishing process showed a result of 0.8-1.9 um Ra. Initial results of dispensing wax, tin alloy and steel were also shown.Originality/valueThis is the first time that both vari-directional and vari-dimensional material depositions are combined in a new freeform building method, which has potential impact on the FDM and other additive manufacturing methods.

New Process Chain for the Production of Complex Freeforms

AbstractFreeform optics enable completely new solutions in optical design for many different optical applications. Complex optical systems usually need a variety of multiple classic spherical surfaces to fulfill their function. The usage of a freeform surface instead makes it possible to replace some of these spherical surfaces by only one freeform element. Therefore, it is possible to build optical systems that are more compact and lighter than existing ones. However, these new possibilities also lead to new challenges regarding fabrication and assembly of the freeform components. Therefore, an efficient production of such elements needs improvement of existing or development of new manufacturing technologies and process chains. This paper describes a new fabrication approach focused on freeform optics by introducing a process chain consisting of an ultrasonic‐assisted grinding process, an ultrafine grinding method using novel resin bond tools and a CO2 laser polishing process for final surface smoothing.