Freeform Optics Research Articles

Hybrid fiber–solid-state laser with 3D-printed intracavity lenses

Microscale 3D-printing has revolutionized micro-optical applications ranging from endoscopy, imaging, to quantum technologies. In all these applications, miniaturization is key, and in combination with the nearly unlimited design space, it is opening novel, to the best of our knowledge, avenues. Here, we push the limits of miniaturization and durability by realizing the first fiber laser system with intra-cavity on-fiber 3D-printed optics. We demonstrate stable laser operation at over 20 mW output power at 1063.4 nm with a full width half maximum (FWHM) bandwidth of 0.11 nm and a maximum output power of 37 mW. Furthermore, we investigate the power stability and degradation of 3D-printed optics at Watt power levels. The intriguing possibilities afforded by free-form microscale 3D-printed optics allow us to combine the gain in a solid-state crystal with fiber guidance in a hybrid laser concept. Therefore, our novel ansatz enables the compact integration of a bulk active media in fiber platforms at substantial power levels.

Efficient and compact freeform optics design for customized LED lighting

Efficient and compact freeform optics design for customized LED lighting

Optical design mode based on fast automatic design process for freeform reflective imaging systems with modest FOV.

Traditional optical design methods require designer intervention in the system's evolution from the starting point to the final design. Trial-and-error during design optimization improves system performance step by step but requires much time and effort. A new optical design framework, end-to-end fast automatic design, is proposed and achieved for the freeform reflective optics in this paper, which promotes a new optical design mode. Compared with the traditional mode through improving performance after each trial, an optical system with good image quality can be directly obtained in the end-to-end design process with simple input and no human involvement within a short time. If there is still the possibility for performance improvement of the obtained system, the designer can vary the input parameters repeatedly to obtain multiple systems with good image quality. Finally, the desired system is selected from these systems. Compared with the step-by-step trials in traditional optimization, this new optical design mode involves high-speed trials of the end-to-end automatic design process, reducing the dependence on experience and skill. In this paper, an end-to-end fast automatic design method for freeform imaging systems is developed based on a new design route. Using an initial plane system as an input, a freeform system with excellent image quality can be designed automatically within 1-2 min. After several trials of the end-to-end fast design process, three high-performance freeform systems are designed successfully that consider volume control, beam obscuration, and mirror interference.

Feature-adaptive toolpath planning with enhanced surface texture uniformity for ultra-precision diamond milling of freeform optics

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Interferometric metrology probe for highly sloped freeform optics.

A wide variety of systems are employed to measure the surface profile of aspheric and freeform optical surfaces. Freeform metrology systems must accurately characterize the full surface under test, which can be difficult with steep surface slopes. Here we present an interferometric surface metrology probe for highly sloped aspheric and freeform optical surfaces. The optical design of this probe allows the measurement of surface slopes up to 50deg without tilting the probe, which simplifies stage design and increases the accuracy of the system. A spectrally controlled light source is used to create a virtual ball in front of the probe tip to measure the surface distance and angle. This system produces a cloud of points, to which Zernike polynomials are fit and used to reconstruct the surface. We will show sensitivity tests and accuracy results.

Creation of One- and Two-Dimensional Copper and Zinc Oxides Semiconductor Structures

The most effective methods for the synthesis of nanostructured copper and zinc oxides, which have unique properties and potential applications in a variety of fields including electronics, photonics, sensorics, and energy conversion, are analyzed. Special attention is paid to laser-based methods for synthesizing oxide nanostructures, with an emphasis on the importance of controlling power density distribution to influence the quality and properties of the nanomaterials. The great significance of wavefront shaping techniques for controlling laser-initiated processes is highlighted, which enable precise control over the phase and amplitude of light waves to achieve desired outcomes in optics and laser-assisted formation of one- and two-dimensional structures of oxide semiconductor materials. Diffractive computer optics is presented as a powerful tool for precise beam control. The significance of laser-induced thermochemical processes for creating and improving the properties of ZnO and CuO-based nanomaterials is discussed. The presented analysis shows that the synthesis of nanocomposites based on ZnO and CuO using pulse-periodic laser treatment, coupled with precise laser beam control using free-form diffractive optics, presents novel opportunities for applications in optoelectronics, sensor technology, electronics and portable energy sources manufacturing, and various other fields.

Laser assisted diamond turning of silicon freeform surface

Freeform optics find wide applications in the field of illumination, imaging, and bio-medical devices. It is difficult to achieve high-quality, high-precision, and high-efficiency freeform machining on hard and brittle material substrate due to its brittle nature and severe diamond tool wear. Laser assisted diamond turning (LADT) method can effectively promote diamond tool life and machining quality. However, it is a difficult for LADT to ensure the stability of the thermal field and the accuracy of freeform surfaces. To overcome the defects, the PID laser power controller is utilized to accurately maintain the laser heating temperature in the ideal range, which is determined by the high-temperature nanoindentation tests. The LADT thermal expansion is also pre-compensated in the tool path according to the finite element thermal analysis results. The experimental results indicate that silicon freeform optics without thermal defects can be achieved with adaptive laser power in-process heating assistance. The effective improvement of form accuracy confirms the feasibility of the proposed tool path thermal pre-compensation method. Challenges and prospects are discussed to guide future studies.

Design of freeform phase diffractive optical elements based on the quadratic assignment problem.

The design of freeform phase diffractive optical elements is a challenging task, typically necessitating the use of complex differential equations or a large number of iterative calculations. This paper proposes what we believe to be a novel approach to address this problem. In this strategy, we introduce overall comparison optimization (OCO) to ensure the fast convergence of the cost function. The quadratic assignment problem (QAP) is used as the mathematical framework for designing freeform phase diffraction optics. Specifically, the ray mapping calculation problem in geometric optics is simplified as a QAP. To solve this problem, we apply the OCO method, which ensures that the cost function rapidly progresses in the "non-negative" direction, thereby facilitating fast convergence in each optimization iteration. In this manner, the proposed approach alleviates the computational burden associated with repeated evaluations of the cost function and accelerates convergence in the design process. We construct holographic masks using the OCO method and perform simulations to demonstrate the potential of the proposed method in swiftly realizing complex illumination patterns. The results show that the design model has good performance when dealing with complex illumination tasks. The conclusions obtained in this paper can be extended to the realization of phase-only holography and the solution of freeform surfaces illumination design.

Gradient descent-based freeform optics design for illumination using algorithmic differentiable non-sequential ray tracing

Algorithmic differentiable ray tracing is a new paradigm that allows one to solve the forward problem of how light propagates through an optical system while obtaining gradients of the simulation results with respect to parameters specifying the optical system. Specifically, the use of algorithmically differentiable non-sequential ray tracing provides an opportunity in the field of illumination engineering to design complex optical system. We demonstrate its potential by designing freeform lenses that project a prescribed irradiance distribution onto a plane. The challenge consists in finding a suitable surface geometry of the lens so that the light emitted by a light source is redistributed into a desired irradiance distribution. We discuss the crucial steps allowing the non-sequential ray tracer to be differentiable. The obtained gradients are used to optimize the geometry of the freeform, and we investigate the effectiveness of adding a multi-layer perceptron neural network to the optimization that outputs parameters defining the freeform lens. Lenses are designed for various sources such as collimated beams or point sources, and finally, a grid of point sources approximating an extended source. The obtained lens designs are finally validated using the commercial non-sequential ray tracer LightTools.

B-spline surface approximation method for achieving optimum dwell time in deterministic polishing

In the computer-controlled optical surfacing (CCOS) process, the accurate calculation of the dwell time map is essential for achieving the desired amount of material removal distribution. However, it remains challenging for current methods to generate a smooth dwell time map that reduces the dynamic requirements of machine tools while maintaining the high finishing capability on freeform optics. This paper proposes a B-spline surface approximation method for obtaining the optimum dwell time in deterministic polishing. The B-spline surface representation allows the dwell time map to be expressed by a small number of control points instead of a large number of discrete dwell points. The dwell time deconvolution then becomes a linear least-squares problem with only a few control points as variables, which significantly reduces the scale of the problem. To achieve a more accurate and smoother dwell time map, a knot position optimization algorithm is proposed to adapt the knots to the geometric features of the target removal surface. Simulation results demonstrate that the proposed B-spline-based dwell time algorithm significantly outperforms common dwell time algorithms in terms of the computational accuracy, efficiency, as well as smoothness of the dwell time map. To validate the effectiveness and practicability of the proposed method, experimental polishing of a bi-sinusoidal optical surface has been carried out. The results show that the developed algorithm has greatly reduced the tracking error of the machine tool caused by dwell time fluctuations, and consequently, the corresponding residual error of material removal in deterministic polishing.

Automatic control method for freeform surface shapes.

Designing freeform optics with high degrees of freedom can improve their optical performances; however, there are high requirements for controlling the surface shapes of such optics. Optical designers need to add constraints to the optimization process and make repeated adjustments to ensure the manufacturability of these shapes; this process is cumbersome and relies heavily on the experience of the designer. In this study, an automatic control method for freeform surface shapes is proposed. By adding an outer loop to the optimization process, the principal curvature and sag departure of the sampling points are gradually controlled during the optimization cycle based on the system requirements and surface evaluation results. The method was implemented in CODE V and successfully applied to a design example in freeform prism optics.

Freeform Optics for Achieving Collimated and Uniform Light Distribution in LCD-Type UV-Curable 3D Printing

Freeform Optics for Achieving Collimated and Uniform Light Distribution in LCD-Type UV-Curable 3D Printing

A novel calibration method for angular misalignment in independently controlled fast tool servo-based diamond turning

With significant technological progress in optics fields, such as VR and 3D sensing technologies, the demand for optical components with complex shapes (e.g., freeform surfaces) has expanded significantly in recent years. Ultra-precision diamond turning is one of the common manufacturing methods used for freeform optics. There are two tool-motion mechanisms for freeform diamond turning: slow tool servo (STS), which moves the entire tool rest, and fast tool servo (FTS), which only drives the diamond tool. In particular, high-frequency and long-stroke FTS units driven by a separate control system from the machine tool controller have recently been developed as a new trend in FTS-based diamond turning. However, this type of independent FTS control system causes a time delay between the machine tool instruction and the FTS tool motion. Even a millisecond-scale time delay can cause a considerable angular misalignment owing to the high rotation rate of the spindle, resulting in a micron-scale form error on the workpiece surface. In this paper, a novel method for precisely measuring the time delay from the machined workpiece surface and compensating for the misalignment based on the measured time delay was proposed. To measure the time delay, spherical dimples were machined on the workpiece surface by using STS and FTS. Subsequently, the angular misalignment and time delay were obtained by comparing the measured surface profiles at specific positions of the spherical dimples. Thus, the time delay can be measured with microsecond-scale accuracy. Based on the measured time delay, the shifted tool position along the spindle axis by the time delay was compensated to the ideal tool position by considering the cutting velocity. Consequently, the angular misalignment was completely eliminated, and submicron-level form accuracy was achieved. This calibration method of angular misalignment for an independent FTS unit is expected to significantly improve the accuracy of ultra-precision machining of freeform optics.

Establishment and analysis of feasibility evaluation system and ultra-precision manufacturing technology for small aperture free-form surface optical element

Free-form optical elements are more and more broadly used in modern optical systems due to their distinctive characteristics. In order to realize the high-precision manufacturing of free-form optical element, the constraints on parameters of manufacture and measurement were established based on the designing parameters of free-form optical element. Meanwhile, the evaluation system for the machinability and detectability of free-form optical element was obtained by means of the corresponding mathematical model. Furthermore, the White Light Interference (WLI) stitching detection technology, coupled with the least square multi-parameter optimization algorithm, was used to solve shape-error measurement of free-form optical element. Additionally, a free-form surface compensation manufacturing mechanism of asymmetric shape error was established. Based on the above methods, the polynomial free-form optics were processed and measured. According to the surface shape measurement results, the same element was processed with compensation manufacturing twice. The surface shape precision was obviously improved from PV = 2553 nm and RMS = 481 nm to PV = 214 nm and RMS = 19.9 nm, which verified the effectiveness of the method. A significant value was unfolded in the engineering application of this method.

Computational-sampling-moiré-based on-machine alignment for freeform optics.

The manufacturing and characterization of freeform optical surfaces are influenced by their high sensitivity to misalignments. In this work, the computational sampling moiré technique combined with phase extraction is developed for the precise alignment of freeform optics during fabrication and in metrology applications. This novel, to the best of our knowledge, technique achieves near-interferometry-level precision in a simple and compact configuration. This robust technology can be applied to industrial manufacturing platforms (such as diamond turning machines, lithography, and other micro-nano-machining techniques) as well as their metrology equipment. In a demonstration of computational data processing and precision alignment using this method, iterative manufacturing of freeform optical surfaces with a final-form accuracy of about 180 nm was accomplished.

Inkjet-printed freeform gradient refractive index Alvarez-Lohmann optics for vision correction in respiratory masks

Inkjet-print additive manufactured freeform gradient refractive index representations of an Alvarez-Lohmann lens were developed and optimized for use in vision-correction inserts for respiratory masks. A series of planar 30-mm by 20-mm Alvarez-Lohmann lens pair were printed and characterized. Select lens pairs were mounted with printed mechanical lens mounts and translation guides optimized for vision correction. Metrology showed accurate reproduction of the cubic refractive phase functions. Tests matching simulated performance showed a large diopter adjustment over a large eyebox and a wide gaze angle. The printed optics were environmentally tested and then mounted in a respiratory mask and demonstrated with glove-accessible control electronics. The performance demonstrates the benefits of using printed three-dimensional freeform gradient index optics for implementing complex refractive optical functions for challenging applications including artificial and virtual reality systems.

Light field displays with computational vision correction for astigmatism and high-order aberrations with real-time implementation.

Vision-correcting near-eye displays are necessary concerning the large population with refractive errors. However, varifocal optics cannot effectively address astigmatism (AST) and high-order aberration (HOAs); freeform optics has little prescription flexibility. Thus, a computational solution is desired to correct AST and HOA with high prescription flexibility and no increase in volume and hardware complexity. In addition, the computational complexity should support real-time rendering. We propose that the light field display can achieve such computational vision correction by manipulating sampling rays so that rays forming a voxel are re-focused on the retina. The ray manipulation merely requires updating the elemental image array (EIA), being a fully computational solution. The correction is first calculated based on an eye's wavefront map and then refined by a simulator performing iterative optimization with a schematic eye model. Using examples of HOA and AST, we demonstrate that corrected EIAs make sampling rays distributed within ±1 arcmin on the retina. Correspondingly, the synthesized image is recovered to nearly as clear as normal vision. We also propose a new voxel-based EIA generation method considering the computational complexity. All voxel positions and the mapping between voxels and their homogeneous pixels are acquired in advance and stored as a lookup table, bringing about an ultra-fast rendering speed of 10 ms per frame with no cost in computing hardware and rendering accuracy. Finally, experimental verification is carried out by introducing the HOA and AST with customized lenses in front of a camera. As a result, significantly recovered images are reported.

Freeform optics characterization with surface registration and fitting algorithms for optical point-based spatial path 3D topography metrology.

Accurate characterization of the form error for freeform optics is critical for controlled manufacturing and evaluation of optical properties. To solve the difficulty of current surface registration and fitting algorithms, and improve characterization accuracy of the form error of freeform optics for optical point-based spatial path 3D topography metrology, in this paper, improved surface registration and fitting algorithms are proposed, including a B-spline surface description of freeform optics, point orthogonal projection, registration parameter optimization, and B-spline fitting. Limited by the angular characteristics of an optical point-based sensor, the slope and reference frame of freeform optics must be flexibly adjusted, and polynomial surfaces are described and fitted as B-spline surfaces based on B-spline geometric invariance. To efficiently determine corresponding points on B-spline surfaces, the point orthogonal projection algorithm without Bezier subdivision is proposed using the first-order Newton method. Then, the iteration procedure of coordinate adjustment in sphere space using Lie algebra registration parameters is proposed to solve the difficulty of the current registration parameter optimization procedure. To fit a spatial path form error, the least squares B-spline fitting method is proposed to improve the Zernike method. Through simulation experiments, the proposed registration algorithm with good convergence can improve accuracy by one to two orders of magnitude compared with current registration algorithms. Through repeated experiments of a freeform prism, the proposed method can significantly improve the peak-to-valley and RMS accuracies compared with the stylus method, and characterize the mid-high frequency form error (about 200nm) of a freeform prism.

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.

Programmable freeform optics with extended white light sources: possibilities and limitations.

Freeform optics can be used in lighting applications to generate accurate prescribed illumination patterns from compact light sources such as LEDs. When targeting dynamic illumination systems, a time-variable optical functionality is needed. Phase-only spatial light modulators (SLMs) have been used in the past for various dynamic beam shaping applications with monochromatic, zero-étendue illumination under paraxial conditions. Such limitations can no longer hold when considering lighting applications. In this paper, a novel algorithm for the calculation of smooth phase shift patterns is presented in order to generate arbitrary target patterns from arbitrary incident wave fronts for non-paraxial conditions. When applying such phase shift patterns to SLMs, these devices can be considered as programmable freeform optics. The experimental performance of the calculated phase patterns is analyzed on a real SLM, with a maximal phase shift of 6π, for collimated laser beams and white LEDs. The possibilities and limitations of generating accurate prescribed target patterns are critically discussed in terms of the angular extent of the target pattern, the consider spectrum of the light source and the étendue of the incident light beam.