Freeform Optical Surfaces Research Articles

Design and fabrication of computer-generated holograms for testing optical freeform surfaces

Freeform optical surfaces (FOSs) will be the best elements in the design of compact optical systems in the future. However, it is extremely difficult to measure freeform surface with sufficient accuracy, which impedes the development of the freeform surface. The design and fabrication of computer-generated hologram (CGH), which has been successfully applied to the tests for aspheric surfaces, cannot be directly adopted to test FOSs due to their non-rotational asymmetry. A novel ray tracing planning method combined with successively optimizing even and odd power coefficients of phase polynomials in turn is proposed, which can successfully design a non-rotational asymmetry CGH for the tests of FOSs with an F-θ lens. A new eight-step fabrication process is also presented aiming to solve the problem that the linewidth on the same circle of the CGH for testing freeform surface is not uniform. This problem cannot be solved in the original procedure of CGH fabrication. The test results of the step profiler show that the CGH fabricated in the new procedure meets the requirements.

Lightweight spatial-multiplexed dual focal-plane head-mounted display using two freeform prisms

Accommodation and convergence play critical roles in the natural viewing of three-dimensional (3D) scenes, and these must be accurately matched to avoid visual fatigue. However, conventional stereoscopic head-mounted displays lack the ability to adjust accommodation cues. This is because they only have a single, fixed image plane, but the 3D virtual objects generated by a pair of stereoscopic images are displayed at different depths, either in front or behind the focal plane. Therefore, in order to view objects clearly, the eyes are forced to converge on those objects while maintaining accommodation fixed on the image plane. By employing freeform optical surfaces, we design a lightweight and wearable spatial-multiplexed dual focal-plane head-mounted display. This display can adjust the accommodation cue in accordance with the convergence cue as well as generate the retinal blur cue. The system has great potential applications in both scientific research and commercial market.

The Effect of Vibration on the Surface Topography in Micro-Milling

Optical freeform surfaces have a strict request on surface quality, but the vibration of tool , which is often ignored in previous studies, have a great influence on surface topography in micro-milling. This paper constructs a micro-milling motion model concerned with tool vibration, and the impact of tool vibration on feed-interval scallop in micro-milling is analyzed. The results show that tool vibration always lead to an increment of surface roughness; and vibration amplitude and feed per tooth are the major factors that have an effect on feed-interval scallop form and surface quality.

Integrated optofluidic system for monitoring particle mass concentrations based on planar emitter–receiver units

We demonstrate an integrated optofluidic system for monitoring the particle mass concentration and the Sauter mean diameter of polydisperse flowing suspensions of water and standardized test dust. For optimum integration, a planar emitter-receiver unit is developed and fabricated on Si technology. A vertical cavity surface emitting laser at 850 nm serves as light source, and monolithically integrated segmented photodiodes detect both the attenuation of the primary light beam and the scattered light. The optical system is integrated into a planar transparent polymethylmethacrylate substrate by micromilling of an optical freeform surface and electron beam evaporation of reflective layers following the concept of planar integrated free-space optical systems. We are able to detect 1 mg/L of the standards ISO 12103-A2 (fine test dust), -A3 (medium test dust), and -A4 (coarse test dust) and to determine the Sauter mean diameter of the particle size distribution.

Development of a large-range atomic force microscope measuring system for optical free form surface characterization

In this paper, a large-range atomic force microscope (AFM) measuring system is developed for optical free form surface characterization. Based on the self-sensing tuning fork probe, a compact AFM head is developed, which is easy to combine with a scanning stage. Depending on the probe's unique structure and the usage of dynamic working mode, the tip–sample interaction force is reduced, improving the system's dynamic response performance. A two-platform structure is applied in the system, which combines a PZT stage with a motor driving platform. A dual feedback strategy is applied to ensure a measuring range up to 25 mm × 25 mm × 5 mm. The system includes three laser interferometers to make the measuring data traced to the ‘meter’ definition. A standard one-dimensional grating is tested to show the performance of the system. A millimeter scale optical free form surface with a sinusoidal structure array is measured relying on the two-platform structure implemented. The high frequency information and low frequency information of the sample are separated automatically, which represent the profile and roughness, respectively.

Comparative assessment of freeform polynomials as optical surface descriptions

Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enables the fabrication of freeform optics, or more specifically, optical surfaces for imaging applications that are not rotationally symmetric. Various forms of polynomials for describing freeform optical surfaces exist in optical design and to support fabrication. A popular method is to add orthogonal polynomials onto a conic section. In this paper, recently introduced gradient-orthogonal polynomials are investigated in a comparative manner with the widely known Zernike polynomials. In order to achieve numerical robustness when higher-order polynomials are required to describe freeform surfaces, recurrence relations are a key enabler. Results in this paper establish the equivalence of both polynomial sets in accurately describing freeform surfaces under stringent conditions. Quantifying the accuracy of these two freeform surface descriptions is a critical step in the future application of these tools in both advanced optical system design and optical fabrication.

Freeform Optical Surfaces: Report from OSA’s First Incubator Meeting

Just as business incubator programs are designed to support the development of fledgling companies, OSA’s new incubator meeting series is structured to encourage the growth of exciting new areas within optics. The first one was devoted to the topic of freeform optics-a field that is actively evolving due to recent technological advances.

Extending Nodal Aberration Theory to include mount-induced aberrations with application to freeform surfaces

This paper introduces the path forward for the integration of freeform optical surfaces, particularly those related to φ-polynomial surfaces, including Zernike polynomial surfaces, with nodal aberration theory. With this formalism, the performance of an optical system throughout the field of view can be anticipated analytically accounting for figure error, mount-induced errors, and misalignment. Previously, only misalignments had been described by nodal aberration theory, with the exception of one special case for figure error. As an example of these new results, three point mounting error that results in a Zernike trefoil deformation is studied for the secondary mirror of a two mirror and three mirror telescope. It is demonstrated that for the case of trefoil deformation applied to a surface not at the stop, there is the anticipated field constant contribution to elliptical coma (also called trefoil) as well as a newly identified field dependent contribution to astigmatism: field linear, field conjugate astigmatism. The magnitude of this astigmatic contribution varies linearly with the field of view; however, it has a unique variation in orientation with field that is described mathematically by a concept that is unique to nodal aberration theory known as the field conjugate vector.

초정밀 기상측정용 다이아프램 타입 접촉식 프로브의 개발

The diaphragm-type stylus probe was developed for ultra-precision on-machine measurement (OMM) application. This probe is equipped with two diaphragms which are parallel and one capacitive sensor is used for detecting the vertical motion of end tip in the stylus when it is contacted to the optical freeform surface. For better performance of proposed probes, several design parameters such as axial stiffness and the lateral deformations were investigated with finite element analysis techniques. To verify the feasibility, the profiles of the master sphere ball were measured on the ultra-precision milling machine. The measurement results show that the proposed probe can calculate the radius of the circle within the accuracy of 0.1 for the ultraprecision optical surface.

Algorithm for irradiance tailoring using multiple freeform optical surfaces

The design of freeform lenses and reflectors allows to achieve non-radially symmetric irradiance distributions whilst keeping the optical system compact. In the case of a point-like source, such as an LED, it is often desired to capture a wide angle of source light in order to increase optical efficiency. This generally results in strongly curved optics, requiring both lens surfaces to contribute to the total ray refraction, and thereby minimising Fresnel losses. In this article, we report on a new design algorithm for multiple freeform optical surfaces based on the theory of optimal mass transport that adresses these requirements and give an example of its application to a problem in general lighting.

Freeform Optical Surfaces: A Revolution in Imaging Optical Design

A revolutionary optical surface is the result of developments in the theory of aberrations, techniques in optical system optimization, computation speed, precision fabrication of surfaces without symmetry, and extensions to the range of the surface slopes allowed in optical testing.

Injection molded high precision freeform optics for high volume applications

Abstract Injection molding offers a cost-efficient method for manufacturing high precision plastic optics for high-volume applications. Optical surfaces such as flats, spheres and also aspheres are meanwhile state-of-the-art in the field of plastic optics. The demand for surfaces without symmetric properties, commonly referred to as freeform surfaces, continues to rise. Currently, new mathematical approaches are under consideration which allow for new complex optical designs. Such novel optical designs strongly encourage development of new manufacturing methods. Specifically, new surface descriptions without an axis of symmetry, new ultra precision machining methods and non-symmetrical shrinkage compensation strategies have to be developed to produce freeform optical surfaces with high precision for high-volume applications. This paper will illustrate a deterministic and efficient way for the manufacturing of ultra precision injection molding tool inserts with submicron precision and show the manufacturing of replicated freeform surfaces with micrometer range shape accuracy at diameters up to 40 mm with a surface roughness of approximately 2 nm.

Computer generated hologram null test of a freeform optical surface with rectangular aperture

In null computed generated hologram (CGH) test of optical elements, fitting method is needed in null CGH design to generate continuous phase function from the ray-traced discrete phase data. The null CGH for freeform testing usually has a deformed aperture and a high order phase function, because of the aberrations introduced by freeform wavefront propagation. With traditional Zernike polynomial fitting method, selection of an orthogonal basis set and choosing number of terms are needed before fitting. Zernike polynomial fitting method is not suitable in null CGH design for freeform testing; a novel CGH design method with cubic B-spline interpolation is developed. For a freeform surface with 18×18 mm2 rectangular aperture and 630 μm peak-to-valley undulation, the null CGH with a curved rectangular aperture is designed by using the method proposed. Simulation and experimental results proved the feasibility of the novel CGH design method.

Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description

This paper focuses on the design, fabrication, and metrology technologies of the ultra-precision optical freeform surface for progressive addition lens (PAL). The PAL, which has a front surface with far-view zone, near-view zone, and intermediate zone, was used to remedy presbyopia by distributing optical powers of the three zones. The PAL surface is a freeform surface because of its non-symmetrical power distribution. We introduce the PAL freeform surface design methodologies, including B-spline description and its optimization. After optimization of B-spline parameters of the PAL surface, we demonstrate the fabrication and measurement technologies of the mold for PAL surface by using ultra-precision freeform machining machine with slow tool servo function and ultra-precision 3D metrology system with user-defined function.

Optimized free-form optical trapping systems

We report a comprehensive process for designing and prototyping new and optimized optical trapping systems. A combination of traditional lens design strategies, simulation of optical forces, and high-end ultraprecision machining of optical free-form surfaces is applied to the realization of a highly specialized optical trapping system. The resulting compact and lightweight optical modules potentially open new classes of applications for optical manipulation. As an example we present a customized 3D trapping module made of a single piece of polymethylmethacrylate, with a large working distance of 650 μm.

Edge clustered fitting grids for φ-polynomial characterization of freeform optical surfaces

With the recent emergence of slow-servo diamond turning, optical designs with surfaces that are not intrinsically rotationally symmetric can be manufactured. In this paper, we demonstrate some important limitations to Zernike polynomial representation of optical surfaces in describing the evolving freeform surface descriptions that are effective for optical design and encountered during optical fabrication. Specifically, we show that the ray grids commonly used in sampling a freeform surface to form a database from which to perform a φ-polynomial fit is limiting the efficacy of computation. We show an edge-clustered fitting grid that effectively suppresses the edge ringing that arises as the polynomial adapts to the fully nonsymmetric features of the surface.

Prediction of surface generation in ultra-precision raster milling of optical freeform surfaces using an Integrated Kinematics Error Model

Due to the geometrical complexity of optical freeform surfaces, it is still difficult to predict the form errors for ultra-precision multi-axis raster milling of these surfaces with sub-micrometer form accuracy. This paper presents an Integrated Kinematics Error Model (IKEM) for the analysis of form error for ultra-precision raster milling of optical freeform surfaces. It attempts to address the challenges of previous kinematics models which are either too conceptual or too theoretical in which the error components are difficult to determine. As an alternate approach, the components of the machine motion errors are analyzed and the homogenous transformation matrix is employed to build a kinematic machining error model step by step. Considering the difficulties and inconveniences of measuring separate error components, IKEM is proposed on the theory of multi-body kinematics and the surface generation mechanism in ultra-precision machining. A series of experiments have been conducted to further validate the proposed model. The successful development of IKEM makes it more convenient for machining error budgets, and can also be generalized and applicable for other multi-axis machining systems.

Variable-diameter refractive beam shaping with freeform optical surfaces

We propose a refractive two-element system that converts the gaussian irradiance of an incident laser beam into a nominally flat-top output spot at a given distance with the capability to vary the spot diameter. The elements are high-order freeform surfaces that, when laterally translated, form a variable composite beam shaper. The general approach for determining the required freeform surfaces is discussed, and example design results are presented.

A New 2-DOF Fast Tool Servo for Diamond Turning of Freeform Optical Surface

This paper discusses the design of a new type fast tool servo (FTS) for precision diamond turning. The FTS has two degrees. One of them is transversal along the Z axis of lathe and the other is rotation around the Y axis. Both of the two movements are driven by electromagnetic force. The moving assembly is designed to be parallel structure for guarantying both of the two movements has similar response frequency and maximum stroke. The output force of normal electromagnetic force generated by magnetic flux bias motor has been calculated. The design of transmission mechanism has been presented. The result of acceleration calculation shows that the FTS achieves acceleration up to about 650G in both directions of movement.

Constructing optical freeform surfaces using unit tangent vectors of feature data points

A method for generating smooth freeform optical surfaces from B-spline is proposed. In this method, the unit tangent vectors of feature data points are employed as constraints. Based on design methods of freeform surface, both feature data points and unit tangent vectors are obtained, and control points and knot vectors of the freeform surface are computed by the interpolation theory. The freeform surfaces are constructed with the control points and knot vectors to ensure the desired normal at each feature data point. Freeform surfaces are constructed by this method and compared with the traditional method. The results show that beams are controlled well by this method with a maximum uniformity more than 99%, and better results can be obtained with fewer feature data points for this method.