Freeform Optics Research Articles

Optical Model of Thermal Radiation Loading System for Turbine Vane Leading Edge

With the increase of combustion temperatures, the thermal radiation effect for hot components in the new generation of aero-engines has become a key factor in the combustion process, cooling structure design, and thermal protection. A radiation loading system can be used as an external heat source to simulate the real thermal environment of hot components in aero-engines. Total receiving power, as well as 3-D heat flux distribution, should better coincide with real conditions. With the aid of freeform optics and the feedback optimization method, the current study develops a concentrating-type radiation heating system fit for the leading-edge surface of a C3X turbine vane. A xenon lamp combined with a freeform reflector was optimized for controllable heat flux. A design method in the area of illumination engineering was innovatively extended for the current model. Considering the effect of polar angular radiative flux distribution of a xenon lamp, a Monte Carlo ray tracing (MCRT) method was adopted to evaluate the optical performance. Feedback modifications based on Bayesian theory were adopted to obtain the optimal shape of the FFS for target heat flux. The current study seeks a feasible way to generate 3-D heat flux distribution for complex curved surfaces, such as turbine vane surfaces, and helps to simulate the real thermal environment of hot components in aero-engines.

Vision ray metrology for freeform optics

Vision ray techniques are known in the optical community to provide low-uncertainty image formation models. In this work, we extend this approach and propose a vision ray metrology system that estimates the geometric wavefront of a measurement sample using the sample-induced deflection in the vision rays. We show the feasibility of this approach using simulations and measurements of spherical and freeform optics. In contrast to the competitive technique deflectometry, this approach relies on differential measurements and, hence, requires no elaborated calibration procedure that uses sophisticated optimization algorithms to estimate geometric constraints. Applications of this work are the metrology and alignment of freeform optics.

A simple design of uniform LED illumination using catadioptric collimator and freeform lenslet array

We introduce a compact lenslet array principle that takes advantage of freeform optics to deploy a light distributor, beneficial for highly efficient, inexpensive, low energy consumption light-emitting diode (LED) lighting system. We outline here a simple strategy for designing the freeform lens that makes use of an array of the identical plano-convex lenslet. The light is redistributed from such lenslet, hinging on the principle of optical path length conservation, and then delivered to the receiver plane. The superimposing of such illumination area from every lenslet occurs on the receiver plane, in which the non-uniform illumination area located in the boundary should have the same dimension as the size of the freeform lenslet array. Such an area, insofar, is negligible due to their small size, which is the crux of our design, representing a large departure from the former implementations. Based on simulations that assess light performance, the proposed design exhibited the compatibility for multiple radiation geometries and off-axis lighting without concern for the initial radiation pattern of the source. As simulated, the LED light source integrated with such proposed freeform lenslet array revealed high luminous efficiency and uniformity within the illumination area of interest were above 70% and 85%, respectively. Such novel design was then experimentally demonstrated to possess a uniformity of 75% at hand, which was close to the simulation results. Also, proposed indoor lighting was implemented in comparison with the commercial LED downlight and LED panel, whereby the energy consumption, number of luminaires and illumination performance were assessed to show the advantage of our simplified model.

Modeling optical emission from a highly multi-mode step-index fiber via ray tracing and the limitations.

Geometric optics is widely applied for diverse optical simulations. In this work, we introduce an incoherent ray model to describe the laser beam radiation emitted from a highly multi-mode step-index fiber, which is frequently applied for industrial laser material processing. First the mathematical validation and the limitation of this model are demonstrated. Then we determine the ray density and the angular spectrum according to measured intensity profiles along the caustic. Furthermore, based on the determined information, we demonstrate the simulation and measurement of the laser beam shaped by an axicon telescope. Not only the reconstruction itself, but also the simulation with free form optics present significant agreements to the measurements. The reasonable modeling of a laser source via geometric optics enables the precise determination of laser radiation and propagation properties with refractive beam shaping technologies.

Freeform and precise irradiance tailoring in arbitrarily oriented planes

Freeform and precise irradiance tailoring in arbitrarily oriented planes is an ultimate goal of nonimaging optics and has not been well addressed. In this paper, we develop a general formulation for arbitrary and precise irradiance tailoring in three-dimensional (3D) space using freeform lenses. This method breaks any symmetric constraints imposed on the geometrical arrangement of conventional beam shaping systems, yielding high-performance beam shaping systems with new functions and flexible geometrical arrangements in 3D space. This method paves a way for the broad application of freeform optics. The robustness and effectiveness of the method is demonstrated by two interesting but challenging designs.

Freeform optics for variable extended depth of field imaging.

Imaging depth of field is shallow in applications with high magnification and high numerical aperture, such as microscopy, resulting in images with in- and out-of-focus regions. Therefore, methods to extend depth of field are of particular interest. Researchers have previously shown the advantages of using freeform components to extend depth of field, with each optical system requiring a specially designed phase plate. In this paper we present a method to enable extended depth-of-field imaging for a range of numerical apertures using freeform phase plates to create variable cubic wavefronts. The concept is similar to an Alvarez lens which creates variable spherical wavefronts through the relative translation of two transmissive elements with XY polynomial surfaces. We discuss design and optimization methods to enable extended depth of field for lenses with different numerical aperture values by considering through-focus variation of the point spread function and compare on- and off-axis performance through multiple metrics.

Fabrication of freeform optical components by fluidic shaping

Freeform optical components enable advanced manipulation of light that is not possible with traditional optical systems. However, their fabrication relies on machining processes that are complex, time-consuming, and require significant infrastructure. Here we present the ability to shape liquid volumes and solidify them into desired freeform components, enabling rapid prototyping of freeform components with high surface quality. The method is based on controlling the minimum energy state of the interface between a curable optical liquid and an immersion liquid, by dictating a geometrical boundary constraint. We provide an analytical solution for the resulting topography given a predefined boundary and demonstrate the fabrication of freeform components with sub-nanometer surface roughness within minutes. Such a fabrication capability, that allows for rapid prototyping of high-quality components, has the potential to answer an unmet need in the optical design industry—allowing researchers and engineers to rapidly test freeform design concepts. It can be further envisioned to be expanded to an industrial scale, allowing for mold-less fabrication of freeform optics.

Freeform gradient-index media: a new frontier in freeform optics.

Freeform optics enable irregular system geometries and high optical performance by leveraging rotational variance. To this point, for both imaging and illumination, freeform optics has largely been synonymous with freeform surfaces. Here a new frontier in freeform optics is surveyed in the form of freeform gradient-index (F-GRIN) media. F-GRIN leverages arbitrary three-dimensional refractive index distributions to impart unique optical influence. When transversely variant, F-GRIN behaves similarly to freeform surfaces. By introducing a longitudinal refractive index variation as well, F-GRIN optical behavior deviates from that of freeform surfaces due to the effect of volume propagation. F-GRIN is a useful design tool that offers vast degrees of freedom and serves as an important complement to freeform surfaces in the design of advanced optical systems for both imaging and illumination.

Surface generation and materials removal mechanism in ultra-precision grinding of biconical optics based on slow tool servo with diamond grinding wheels

Diamond turning, fly-cutting, and milling are the primary manufacturing technologies for generating free-form surfaces; however, they are not sufficiently effective in machining free-form optics on hard and brittle materials. Ultra-precision grinding has been demonstrated to have an outstanding capability in machining difficult-to-cut materials. Therefore, we proposed a novel surface generation technique for free-form optics based on a slow tool servo with diamond grinding wheels (STS-DGW). First, the generation strategies of the wheel path for grinding biconical optics were explored. Subsequently, the generation process of surface topography was theoretically analysed, and the interference between the diamond wheel and biconical optics in the process of surface generation was checked. Eventually, typical biconical free-form optics were fabricated on single-crystal silicon. Submicron profile accuracy and nanometer surface roughness were achieved, and the influence of the processing parameters on the surface topography and material removal mechanism was investigated.

Freeform optical design of beam shaping systems with variable illumination properties.

Freeform optics constitutes a new technology that is currently driving substantial changes in beam shaping. Most of the current beam shaping systems are elaborately tailored for fixed optical properties, which means the output light distribution of a beam shaping system usually cannot be changed. What we present here is a class of beam shaping systems, the optical properties of which can be changed to meet the requirements for different applications. The proposed beam shaping system is composed of a freeform lens and a non-classical zoom system which is designed by ray aiming and the conservation of energy instead of aberration control. The freeform lens includes two elaborately designed freeform optical surfaces, by which both the intensity distribution and wave-front of an incident light beam are manipulated in a desired manner. The light beam after propagating through the non-classical zoom system produces an illumination pattern on a fixed observation plane with a variable pattern size and an unchanged irradiance distribution at different zoom positions. Two design examples are presented to demonstrate the effectiveness of the proposed beam shaping systems.

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.

Reduction of mid-spatial frequency errors on aspheric and freeform optics by circular-random path polishing.

Pseudo-random paths are a useful tool to reduce mid-spatial frequency errors created in the processing of optical surfaces by sub-aperture polishing tools. Several types of patterns have been proposed, including hexagonal, square and circular, but prior literature has largely focused on flat and gently curved surfaces. Here, an extension of the circular-random path to strongly curved aspheric and freeform surfaces is proposed. The main feature of the algorithm is to cover the entire surface to be polished with a uniformly distributed tool path. Aspheric condenser lenses are then polished with a regular raster and circular-random path. Analysis of the optical performance shows that the random path can reduce the amplitude of mid-spatial frequency errors and relative intensity of satellite images. These features are particularly desirable in short wavelength applications, such as mirrors for EUV and X-ray.

Effect of retrace error on stitching coherent scanning interferometry measurements of freeform optics.

We report on the effect of retrace error during measurement of freeform optics using a commercial coherence scanning interferometer (CSI), and its in-built stitching capabilities. It is shown that measuring segments of freeform optics under non-null conditions, results in artifacts on the measured zone, similar to the Seidel aberrations. An experimental approach is used to quantify the induced aberrations based on the local slopes of the surface. Simulation of surfaces containing different order aberrations is shown to have a significant effect on the measurement data. A correction method is proposed that uses experimental measurements to determine the required correction based on local slope and position in the aperture. These corrections reduce the measurement difference from a comparison measurement using a Fizeau interferometer.

Optical elements from 3D printed polymers

Abstract 3D printing belongs to the emerging technologies of our time. Describing diverse specific techniques, 3D printing enables rapid production of individual objects and creating shapes that would not be produced with other techniques. One of the drawbacks of typical 3D printing processes, however, is the layered structure of the created parts. This is especially problematic in the production of optical elements, which in most cases necessitate highly even surfaces. To meet this challenge, advanced 3D printing techniques as well as other sophisticated solutions can be applied. Here, we give an overview of 3D printed optical elements, such as lenses, mirrors, and waveguides, with a focus on freeform optics and other elements for which 3D printing is especially well suited.

Roadmap for the unobscured three-mirror freeform design space.

In rotationally symmetric lens design, there are rule-of-thumb boundaries on field-of-view and aperture for well-known design forms that provide valuable information to the designer prior to starting a design. In the design space of unobscured three-mirror imagers, freeform optics have been shown to provide a significant benefit over conventional surface shapes, but the degree to which they improve the performance for any given combination of field-of-view, entrance pupil diameter, and F-number remains unknown. Thus, designers of these systems are not afforded any pre-design information to inform their specification decisions. Here, we designed over 200 systems to establish a first-of-its-kind roadmap of specification ranges over which an unobscured three-mirror imager using freeform surfaces can achieve diffraction-limited performance in the visible spectrum. The scalability of the findings to the infrared regions of the spectrum is also addressed.

‘First time right’ freeform optics

AbstractToday's design of optical systems relies largely on efficient ray tracing and optimization algorithms. Such a ‘step‐and‐repeat’ approach to optical design typically requires considerable experience, intuition, and trial‐and‐error guesswork. Brussels Photonics (B‐PHOT) researchers have developed a design method that allows highly systematic generation and evaluation of directly calculated freeform design solutions and enables a rigorous, extensive, and real‐time evaluation in solution space. Readers have the opportunity for hands‐on freeform design experience via an open‐access web application.

Analysis of the Advantages of Laser Processing of Aerospace Materials Using Diffractive Optics

We considered possibilities of an application of diffractive free-form optics in laser processing of metallic materials in aerospace production. Based on the solution of the inverse problem of heat conduction, an algorithm was developed that calculates the spatial distribution of the power density of laser irradiation in order to create the required thermal effect in materials. It was found that the use of diffractive optics for the laser beam shaping made it possible to obtain specified properties of processed materials. Laser thermal hardening of parts made of chrome–nickel–molybdenum steel was performed. This allowed us to increase the wear resistance due to the creation in the surface layer of a structure that has an increased hardness. In addition, a method of laser annealing of sheet materials from aluminum–magnesium alloy and low-alloy titanium alloys was developed. Application of this method has opened opportunities for expanding the forming options of these materials and for improving the precision in the manufacturing of aircraft engine parts. It was also shown that welding by a pulsed laser beam with a redistribution of power and energy density makes it possible to increase the strength of the welded joint of a heat-resistant nickel-based superalloy. Increasing the adhesion strength of gas turbine engine parts became possible by laser treatment using diffractive free-form optics.

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

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

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.

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.