Freeform Surfaces Research Articles

Review of Patents on Small Grinding Wheel Polishing Technology

Abstract: Grinding disc polishing is an important polishing method that can be used to manufacture various high-precision and high-quality optical components. The smoothing effect of grinding discs is a simple and effective method widely used to suppress MSF errors. Grinding disc technology has good polishing effects on flat, spherical, aspherical, and free form surfaces. The polishing mechanism is to generate chips through the small plastic cutting of abrasive particles, but it only uses a very small amount of abrasive particles to exert force and uses the flow friction between the abrasive particles and the grinding disc and the workpiece to flatten the surface roughness of the workpiece. It can be seen from the relevant literature that the floating tool holder maintains a constant pressure to solve the problem of uneven pressure distribution between optical components. The adjustable tool holder can adjust the amount of spring deformation to adapt to local surface changes of optical parts, ensuring consistent material removal. The force-adaptive tool holder can be adjusted in real time during the machining process to reduce errors generated during machining. The jointed tool holder improves the fit between the grinding wheel and optical components, ensuring a tight fit between the grinding wheel and optical components. This patent paper aims to introduce grinding wheel polishing technology as an essential method for manufacturing high-precision, high-quality optical components. It explores the optimization of abrasive tool design and the improvement of processing efficiency and proposes suggestions and prospects for future research, applications, and development. Through querying literature and patent databases, patent documents related to grinding disc polishing technology were collected and analyzed. The design characteristics of the device structure, technological innovations, as well as the effectiveness and improvements in practical applications were focused. Grinding disc polishing technology effectively removes surface defects and enhances the optical performance of optical components, particularly in suppressing MSF errors. This technology is suitable for flat, spherical, non-spherical, and freeform surfaces, with broad potential applications. Despite the numerous advantages of grinding disc polishing technology, such as simplicity, effectiveness, and wide applicability, critical issues still need to be addressed, including surface morphology control, improving polishing efficiency, and enhancing consistency. Future research should focus on optimizing tool design and developing new polishing materials and processes to improve the manufacturing quality and efficiency of optical components.

Dual Representation of Geometry for Ray Tracing Acceleration in Optical Systems with Freeform Surfaces

Dual Representation of Geometry for Ray Tracing Acceleration in Optical Systems with Freeform Surfaces

Iterative critical ray tracing for local tolerance analysis of freeform imaging systems

Tolerance analysis of the freeform surfaces serves as a critical bridge between design and manufacturing, offering essential guidance for the desensitization design of optical systems and playing a crucial role in the development of advanced imaging systems. Recently, Deng et al. proposed a direct method [Deng et al. Optica 9, 1039 (2022)] for solving tolerances of freeform surfaces, which reveals the local characteristics of the tolerances of freeform surfaces. However, the method requires dense sampling of the fields of view (FOVs) and the entrance pupil (EP) to cover as many optical surface points as possible, thereby achieving more accurate tolerance envelope solutions. Here, we propose an iterative algorithm called "critical ray tracing" to calculate the critical rays at points on the optical surface and utilize this information for surface tolerance analysis. This method involves fitting the coordinate space of the optical system into a 4D polynomial and employing numerical iteration to determine the rays closest to the preset wave aberration boundary at each surface point. Converting the FOVs and EP sampling into optical surface sampling significantly reduces the number of samples required, achieving computational efficiency without compromising accuracy in determining tolerable surface errors. We demonstrate the effectiveness of our method through tolerance analysis of two different freeform imaging systems. Furthermore, a tolerance analysis example of a complete off-axis three-mirror optical system demonstrates the universality of the process.

7-axis synchronization-integrated on-the-fly laser texturing system of freeform surface: design and development

Abstract While laser surface texturing (LST) is a promising manufacturing technique for surface functionalization, simultaneously realizing high precision and high efficiency in the LST of complex curved surface is challenging, due to continuously varied geometries of laser-matter incidence. In the present work, we propose a novel manufacturing system of 7-axis on-the-fly LST for complex curved surface, based on the integrated synchronization of 5-axis linkage motion platform with 2-axis galvanometer. Specifically, the algorithm for decomposing spatial texture trajectory on curved surface into low-frequency and high-frequency parts is established, based on which the kinematic model of synchronized 7-axis system is developed to derive the motion of each axis in both 5-axis linkage motion platform and 2-axis galvanometer simultaneously. Subsequently, the synchronized 7-axis LST system is experimentally realized, including the setup of mechanical stages integrated with optical path, the configuration of numerical control unit, and the development of processing software. Finally, case study of 7-axis on-the-fly LST of freeform aluminum surface is performed, and the advantages in terms of processing efficiency and texturing accuracy over 5-axis linkage LST are demonstrated. The correlation of reduced following errors between mechanical stages with the promoted performance of curved surface texturing by the 7-axis on-the-fly LST is further analyzed. Current work provides a feasible solution for establishing the manufacturing system for high performance LST of complex curved surface.

Development and evaluation of a free-form-based optical antenna with enhanced channel performance

Optical receiving antennas play a pivotal role in enhancing the communication quality of visible light communication (VLC) systems. In this study, we propose an innovative optical receiving antenna based on free-form surfaces. Initially, the layout scheme for the LED array is meticulously optimized to ensure uniform indoor illumination. Subsequently, a three-piece integrated optical receiving antenna is designed using XY polynomial free-form surfaces with the primary objectives of amplifying the optical gain, augmenting the received power, and elevating the signal-to-noise ratio (SNR). To further validate the efficacy of the proposed optical receiving antenna, an indoor VLC channel model is established, and its performance is rigorously analyzed. Experimental outcomes reveal that the mean square error of indoor illumination stands at 113.3 lx, the optical gain of the free-form optical receiving antenna reaches an impressive 11.29, the semiregular field of view spans 35.2°, the average received power amounts to 6.1251 dBm, the average SNR attains 84.7054 dB, and the radius of the optical spot is a mere 1.5 mm. Consequently, the optimized free-form optical receiving antenna can guarantee high-speed and stable communication within indoor VLC systems, thereby furnishing crucial technical support for the advancement of VLC communication technology.

Adaptive Sampling Technique for Free-Form Surface of Aero-Engine Blades Based on Discrete Curvature

Adaptive Sampling Technique for Free-Form Surface of Aero-Engine Blades Based on Discrete Curvature

Research on laser measurement point cloud preprocessing and 3D reconstruction technology for free-form surfaces.

Surface morphology measurement and reconstruction technology based on point cloud data is one of the key technologies for 3D information processing in the digital manufacturing industry and has been widely applied in fields such as reverse engineering, computer vision, and unmanned driving system navigation. A method for 3D modeling of aircraft-engine blade profiles based on laser measurement point cloud data is proposed to address the difficulties in measuring the 3D morphology of aircraft-engine blades and the low modeling accuracy. This method first preprocesses the measured point cloud and then uses Poisson's algorithm to reconstruct the blade surface in three dimensions based on the calculation of the point cloud normal. Through error statistical analysis, the overall reconstruction effect is good. The experimental results further validated the generality and effectiveness of this method.

Machining error compensation of free-form surfaces by combination of ordinary kriging method and mirror compensation method

ABSTRACT Improving the accuracy and efficiency of free-form surface machining is a common goal of modern manufacturing. In this study, a compensation method combining the ordinary kriging method based on sequential quadratic programming method optimization (SQP-OK) and the mirror compensation method for machining errors of free-form workpieces was applied, with the aim of significantly improving the workpiece machining accuracy. Machining errors on the surface of the workpiece were predicted utilizing the SQP-OK after the workpieces were completed with semi-finishing machining based on the on-machine measurement (OMM) results of the workpiece. Based on the prediction result, the mirror compensation method was applied to calculate the compensation points. Free-form workpieces were compensated for by modifying the NC code for semi-finishing. To verify the effectiveness of the proposed method, two free-form workpieces were machined with computer numerical control (CNC) compensation, applying the proposed method and the method modifying the overall machining allowance. The experimental results revealed that the compensation method proposed in this paper reduced the average value of the machining errors decreased by 28.6% in absolute value, 31.1% in maximum undercut, and 28.8% in maximum overcut for the free-form workpiece, respectively, compared with the compensation method of modifying the overall machining allowance.

Desensitization design of freeform off-axis TMA optical systems with configuration selection

The off-axis three-mirror anastigmatic (TMA) optical system has the advantages of eliminating all primary aberrations, having no aperture obscuration, no chromatic aberration, and good environmental adaptability, making it essential in high-performance optical instruments. Freeform surfaces, with their rich degrees of freedom (DOFs) in mathematical representation, positively affect the image quality and sensitivity of optical systems. When applied correctly to off-axis TMA optical systems, they can achieve fast F-numbers, large fields of view (FOVs), and long focal lengths. There are dozens of configurations for off-axis TMA optical systems, and freeform surfaces can be combined in numerous ways within these systems. This paper first analyzes the sensitivity of off-axis TMA optical systems with different configurations, selects the configuration with the lowest sensitivity, and combines it with a low sensitivity freeform surface combination to achieve high-performance freeform off-axis TMA optical systems with low sensitivity.

Calculation of Tool Offset and Tool Radius Errors Based on On-Machine Measurement and Least Squares Method in Ultra-Precision Diamond Turning

Metal mirrors will be widely used in the coming decades. Therefore, as one of the enabling technologies for metal optical freeform surface manufacturing, ultra-precision (UP) diamond turning error compensation has become a research hotspot. However, for the tool offset error and tool radius error, which are the main errors in UP diamond turning, no precise and efficient calculation method has been found in the literature. In this study, a more precise and efficient algorithm was developed and validated in three ways using on-machine measurement data and profilometer measurement data. After one compensation, the tool offset error can be reduced to below 0.1 μm, and the tool radius error can be reduced to below 1 micrometer, which will significantly improve the UP turning accuracy and efficiency of optical parts.

Additive manufacturing of polyamide 12 bulk structures using directed energy deposition with a thulium laser: Effect of process conditions on morphology and mechanical performance

Laser-based directed energy deposition of polymers (DED-LB/P) is a highly flexible additive manufacturing process capable of fabricating three-dimensional structures with a high degree of customization on free-form surfaces. In this article, the manufacturability of polyamide 12 bulk structures using DED-LB/P in combination with a thulium laser operating at a wavelength of 1.94 μm is investigated for the first time. The typical absorption bands at this wavelength eliminate the need for additives such as carbon-based nanoparticles, which would limit the range of applications. The generated structures were analyzed regarding porosity, thermal behavior, and mechanical properties to evaluate the potential of DED-LB/P with a thulium laser. As a consequence of the evaporation of absorbed moisture or ethanol residues resulting from powder preparation, a thermal pretreatment of the polymer powder reduced the porosity of the DED-LB/P structures to 0.9%. Depending on the processing parameters, the crystallinity of the produced structures ranged from 25.6% to 29.9%. For the tensile tests, the required geometries were milled from the DED-LB/P bulk structures. The results show that an ultimate tensile strength of up to 52 MPa, an elongation at break of up to 58%, and Young's modulus of up to 1590 MPa can be achieved. These remarkable mechanical properties are primarily attributed to the complete melting of the powder particles in DED-LB/P and the improved surface quality resulting from the milling process.

Off-axis freeform optical design for large curved field of view imaging

Recording neuron activities is pivotal for elucidating the functionality of the nervous system. However, the curved cortex surface of experimental mice presents a significant challenge for optical systems, particularly when a larger field of view (FOV) is required. To address this challenge, we have designed an off-axis three-mirror system that incorporates freeform surfaces on both the primary and secondary mirrors. This system achieves a large imaging FOV of 18°×9°, delivering near-diffraction-limit imaging quality across a curvature spectrum of −14.7 to −15.3mm. A manufacturability analysis indicates that the freeform surfaces are straightforward to produce, and the overall system demonstrates low sensitivity to tolerance and measurement errors. This study introduces a novel, to the best of our knowledge, solution to the field curvature constraints in optical imaging of cortical activity, providing substantial technical support for in vivo neuronal imaging endeavors.

Hybrid Refractive and Diffractive Testing Method for Free-Form Convex Mirror in High-Resolution Remote-Sensing Cameras

The development of high-resolution and large field of view remote-sensing cameras is inextricably linked to the application of free-form mirrors. The free-form mirror offers higher design of freedom and is more effective at correcting aberrations in optical systems. The surface shape error of a free-form mirror directly affects the imaging quality of remote-sensing cameras. Consequently, a high-precision free-form mirror detection method is of paramount importance. For the convex free-form surface mirror with a large aperture, a hybrid refractive and diffractive testing method combining computer-generated holography (CGH) and spherical mirrors for high-precision null test is proposed in this paper. When comparing the effect of error and the detection sensitivity of different designs, the results showed that the influence of the system error is reduced by about 42% and the sensitivity is increased by more than 2.6 times. The proposed method can achieve higher testing accuracy and represents an effective and feasible approach for the surface shape detection method.

Improving neural-network-based prediction models for misalignment in off-axis three-mirror anastigmat telescopes

The performance of a telescope system heavily relies on the precise alignment of the mirrors. The off-axis three-mirror anastigmat (TMA) telescope presents unique challenges due to its complex optical design. Each optical element within the off-axis TMA telescope is inherently introduced with theoretical eccentricity and tilt. Furthermore, the incorporation of freeform surfaces and other optical elements with intricate surface features typically leads to low initial alignment accuracy of the optical path. With this low initial alignment accuracy and the noise of the measurements, the prediction of the misalignment of the telescope is getting harder. A fully connected neural network architecture is proposed as a misalignment calculation method for an off-axis TMA telescope system with a freeform surface. Random training data is created by using optical design software. The sensitivity of the mirrors to the wavefront error is quantified and incorporated into the loss function of the neural network to improve prediction accuracy. Adding the noisy measurement samples to the training data creates a noise-immune neural network model. Simulation results show that our model can successfully predict misalignment of the mirrors with noisy measurement values.

A Study on the Coarse-to-Fine Error Decomposition and Compensation Method of Free-Form Surface Machining

To improve the machining accuracy of free-form surface parts, a coarse-to-fine free-form surface machining error decomposition and compensation method is proposed in this paper. First, the machining error was coarsely decomposed using variational mode decomposition (VMD), and the correlation coefficients between the intrinsic mode function (IMF) and the machining error were obtained to filter out the IMF components that were larger than the thresholding value of the correlation coefficients, which was the coarse systematic error. Second, the coarse systematic errors were finely decomposed using empirical mode decomposition (EMD), which still filters out the IMF components that are larger than the thresholding value of the set correlation coefficient based on the correlation coefficient. Then, the wavelet thresholding method was utilized to finely decompose all the IMF components whose correlation coefficients in the first two decomposition processes were smaller than the threshold value of the correlation coefficient set. The decomposed residual systematic errors were reconstructed with the IMF components screened in the EMD fine decomposition, which gave the fine systematic error. Finally, the machining surface was reconstructed according to the fine systematic error, and its corresponding toolpath was generated to compensate for the machining error without moving the part. The simulation and analysis results of the design show that the method has a more ideal processing error decomposition ability and can decompose the systematic error contained in the processing error in a more complete way. The results of actual machining experiments show that, after using the method proposed in this paper to compensate for the machining error, the maximum absolute machining error decreased from 0.0580 mm to 0.0159 mm, which was a 72.5% reduction, and the average absolute machining error decreased from 0.0472 mm to 0.0059 mm, which was an 87.5% reduction. It was shown that the method was effective and feasible for free-form surface part machining error compensation.

Effect of tool orientation on surface roughness and dimensional accuracy in ball end milling of thin-walled blades

AbstractIn the aerospace industry, high-precision components like impellers and blisks present considerable challenges in machining due to their intricate geometries and the need for reliable performance. Blades, often classified as thin-walled parts with complex, free-form surfaces, are crucial in ensuring the efficiency and safety of aircraft engines. Their geometries and materials require strict control over cutting parameters, such as tool path and orientation, to avoid deformation and maintain surface integrity. This study investigates the impact of tilt angle variation during ball end milling of Ti6Al4V thin-walled parts. Four different tilt angles (15°, 30°, 45°, and 60°) were analysed to evaluate their effect on dimensional accuracy and surface roughness. The results show that tilt angle significantly influences surface quality and dimensional precision. A tilt angle of 30° achieved the best balance between surface finish and dimensional tolerances, with flatness values ranging from 0.038 mm at 30° to 0.101 mm at 60°, representing a 152.5% increase in flatness. The findings provide practical guidelines for optimizing ball end milling of thin-walled components, emphasizing the importance of tool orientation in reducing deformation and enhancing surface quality.

Grid Optimization of Free-Form Spatial Structures Considering the Mechanical Properties

In recent years, the application of free-form surface spatial grid structures in large public buildings has become increasingly common. The layouts of grids are important factors that affect both the mechanical performance and aesthetic appeal of such structures. To achieve a triangular grid with good mechanical performance and uniformity on free-form surfaces, this study proposes a new method called the “strain energy gradient optimization method”. The grid topology is optimized to maximize the overall stiffness, by analyzing the sensitivity of nodal coordinates to the overall strain energy. The results indicate that the overall strain energy of the optimized grid has decreased, indicating an improvement in the structural stiffness. Specifically, compared to the initial grid, the optimized grid has a 30% decrease in strain energy and a 43.3% decrease in maximum nodal displacement. To optimize the smoothness of the grid, the study further applies the Laplacian grid smoothing method. Compared to the mechanically adjusted grid, the structural mechanical performance does not significantly change after smoothing, while the geometric indicators are noticeably improved, with smoother lines and regular shapes. On the other hand, compared to the initial grid, the smoothed grid has a 21.4% decrease in strain energy and a 28.3% decrease in maximum nodal displacement.

Design of geostationary orbit ultrawide FOV long-wave infrared imaging spectrometer.

The geostationary orbit imaging spectrometer offers distinct advantages for diverse applications in remote sensing. To enhance swath and data richness, there is a growing trend toward spectrometers with broader fields of view (FOV) and extended slit lengths. Optical systems equipped with these features face significant challenges in aberration correction. This paper investigates the parameters of geostationary orbits and designs a spectroscopic system capable of achieving ultrawide FOV without the need for stitching spectrograph subsystems. Additionally, it also designs a front-end telescope system that matches the spectroscopic system. The spectroscopic system features a slit length of 240 mm, employing an enhanced Offner structure for a long slit spectroscopic system, incorporating a freeform surface on the third mirror. To inhibit the effects of radiation stray light, the system's exit pupil is controlled to be positioned in front of the image plane to facilitate matching with the cold shield. The analysis indicates that the spectral resolution of the long-wave infrared imaging spectrometer system is 50 nm, with a total of 90 spectral sampling channels. The system's spatial resolution is 100 m, enabling a swath width of 400 km. Furthermore, the modulation transfer function (MTF) exceeds 0.42 at the Nyquist frequency of 8.35 lp/mm. The maximum RMS radius of the system is less than 27 μm at wavelengths ranging from 8 to 12.5 μm.

New shape optimization method for tree structures based on BP neural network

To realize the intelligent optimization for the tree structures supporting freeform surface roof or bearing uneven load, a new shape optimization method based on the back-propagation (BP) neural network is proposed. This method enables the intelligent positioning of hierarchical nodes through a recursive approach from top-down, with the aim of satisfying the zero bending moment and structural stability. Using three-dimensional tree structures as an example, this study provides a detailed description of the implementation method and steps of intelligent shape optimization, along with a comparative analysis with the reverse-hang recursive approach. Results indicate that the proposed approach effectively addresses the challenge of locating load-bearing centers in tree structures with uneven loads or freeform surface roofs. It not only demonstrates universality for tree structures under complex engineering conditions, but also enhances efficiency and intelligence in the structure optimization design.

Tailored porosity in additive manufacturing of 7075 aluminum alloy for crack suppression and high strength

Laser-directed energy deposition (LDED) additive manufacturing of 7075 aluminum (Al) alloy is highly challenging due to the inherent poor printability and high cracking tendency. Here, we disclose a new approach to suppress cracking in LDED-processed 7075 Al alloy by engineered porosity (about 1.14 %). The crack-free 7075 Al alloy was achieved by slightly sacrificing the densification. Further increasing the density of the material by increasing laser energy input leads to cracking. The mechanisms of minor pores in alleviating cracks are mainly reflected in three aspects: (i) pores disrupt the epitaxial growth of columnar grains; (ii) free-form surfaces surrounding pores could release the accumulated residual stress, and (iii) more dislocations near pore drive nucleation of near equiaxed grains. The LDED-processed crack-free 7075 Al alloy after heat treatment shows an ultimate tensile strength of 464 ± 12 MPa and break elongation of 9.7 ± 1.2 %, attaining a good strength-ductility synergy among many additively manufactured 7075 Al alloys in the current literature. Unlike the mainstream additive manufacturing of metallic materials, which pursues high densification to attain high-performance components, this work demonstrates the positive roles of pores in the additive manufacturing of cracking-sensitive materials. The findings of this work highlight new insights regarding the balance between pores and cracks for better manufacturability and higher mechanical performance of materials.