Freeform Optical Surfaces Research Articles

Dynamic Interferometry for Freeform Surface Measurement Based on Machine Learning-Configured Deformable Mirror.

Optical freeform surfaces are widely used in imaging and non-imaging systems due to their high design freedom. In freeform surface manufacturing and assembly, dynamic freeform surface measurement that can guide the next operation remains a challenge. To meet this urgent need, we propose a dynamic interferometric method based on a machine learning-configured deformable mirror (DM). In this method, a dynamic interferometric system is developed. By using coaxial structure and polarization interference, transient measurement of the measured surface can be realized to meet dynamic requirements, and at the same time, DM transient monitoring can be realized to reduce the accuracy loss caused by DM surface changes and meet dynamic requirements. A transient phase modulation scheme using machine learning to configure the DM surface is proposed, which keeps the system in a measurable state. Compared with the traditional phase modulation scheme that relies on iteration, the scheme proposed in this paper is more efficient and is conducive to meeting dynamic requirements. The feasibility is verified by practical experiments. The research in this paper has significance for guiding the application of dynamic interferometry in the measurement of dynamic surfaces.

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.

Local slope tolerance model for optical surfaces with distortion as the evaluation criterion.

Ultra-precision imaging systems support cutting-edge scientific exploration and technological innovation. The continuous development of optical freeform and aspheric surface technology offers new possibilities for high-performance optical systems but also presents significant manufacturing challenges. In this paper, we derive and discuss in detail the impact of surface manufacturing errors on the image point positions of optical systems. The analysis reveals that among the manufacturing errors, the surface slope error is the primary factor driving positional changes in image points. Based on these insights, a local slope tolerance model using distortion as the evaluation criterion is proposed. This model specifies the slope error requirements at each point on the surface, ensuring the optical system's distortion meets the acceptable threshold during manufacturing. The model's effectiveness is validated through an off-axis three-mirror freeform optical system and a Cassegrain aspheric optical system.

Quadratic Bézier curve method for continuous freeform optical surface design

A novel approach is introduced for the design of freeform axisymmetric optical surfaces using an optimization technique based on quadratic Bézier curves. Notably, the continuity (or lack thereof) of the freeform surface produced using the proposed technique is largely unaffected by the source-target mapping function. The validity of the proposed methodology is demonstrated through its application to the design of several laser beam shapers. The results show that the proposed technique requires only a small number of structural points to converge to the optimum design solution. The freeform design method presented herein is mathematically straightforward and can be easily implemented in code. Thus, it offers significant advantages for the design and analysis of a diverse range of optical systems.

Absolute testing of rotationally symmetric surfaces with computer-generated holograms.

Extremely high accuracy is demanded for optics working at very short wavelength. Interferometric testing of optical aspheres or freeform surfaces requires null optics, typically computer-generated holograms (CGHs), to balance the wave aberrations. The measurement uncertainty is primarily limited by the accuracy of the test wavefront, which is predominantly influenced by the CGH and the interferometer optics. Absolute testing is fundamental to achieving accuracy much higher than that of the test wavefront through error separation. This paper presents a method for absolute testing of rotationally symmetric surfaces with CGH null optics. The basic assumption is that the off-axis hologram fabricated by raster scanning beam writing has negligible error of rotationally symmetric component due to pattern error of the CGH. Consequently, the wavefront error contributed by the CGH and the transmission flat can be completely separated from the absolute surface shape by combining the N-position method and the shift-rotation method. A theoretical model for absolute testing is proposed under the assumption. Experimental cross test is then presented to validate the method with sub-nanometer uncertainty. The assumption is further confirmed by characterizing the fabrication error of the hologram structures using a white light interferometer. Finally, the effect of noise, translation error, rotation error and eccentricity of rotation on the absolute testing is analyzed.

Results of round robin form measurements of optical aspheres and freeform surfaces

High-quality aspherical and freeform surfaces are in high demand, and the high-accuracy form measurement of such surfaces is a challenging task. To explore the current status of form measurement systems for complex surfaces such as aspheres and freeforms, interlaboratory comparison measurements are performed. This study presents the pseudonymized results obtained using three different surfaces (metal asphere, glass asphere, toroidal surface) in a total of six different round robins. These results were taken from a total of 13 different measurement instruments based on 9 different measurement principles and operated at 12 different laboratories. They were analyzed using a sophisticated procedure that was first developed in 2018 and then refined and tested on simulated data in 2022 to address the challenges of such a comparison at this level of accuracy. In the current study, we applied these refined methods to data acquired from tactile and optical point measurements as well as from optical areal measurements. As there are no absolutely measured and very well characterized reference standard aspherical and freeform surfaces available at the accuracy level of a few tens of nanometers root-mean-square, the approximated true forms of the surfaces were derived from the measurements and indicate the manufacturing accuracy of the surface forms. Then, the measurement’s differences to the approximated true forms were analyzed, which directly indicate the systematic measurement errors of the instruments. By also comparing the approximated true forms from the two different round robins for each surface, additional insights into the reliability and stability of these so-called virtual reference topographies were gained.

Modeling and analysis for material removal and surface roughness in fluid jet polishing of optical glass

Fluid jet polishing (FJP) is a non-contact polishing technology that can fabricate free-form optical surfaces with sub-micron-level form accuracy and nano-level surface roughness, especially for hard and brittle materials. The surface generation model of FJP can be used to guide the determination and optimization of process parameters and is of great significance for understanding the evolution mechanism of surface microtopography. However, predictive models for the microscopic topography of polished surfaces are still lacking. This study established a macroscopic surface profile model for predicting 3D material removal characteristics and surface texture by combining the 3D computer fluid dynamics (CFD) simulation model and single-particle erosion mechanism. A fractal theory-based erosion model has been built to calculate the material removal caused by the erosion of a single abrasive particle on the rough surface; thus, it predicts the micro-topography and surface roughness of the polished samples. A series of polishing experiments were conducted to analyze the feasibility and accuracy of the model quantitatively and study the influence mechanism of process parameters on the material removal characteristics and surface quality. Results indicated that the models could well predict material removal and surface roughness. The prediction accuracy of the surface roughness Ra and maximum removal depth is better than 91.6% and 90%, respectively. It is also found that the material removal rate of FJP could reach 0.517 mm3/min, and the surface roughness convergence rate could reach 62.9%.

Fast, intelligent and high-precision adaptive null interferometry for optical freeform surfaces by backpropagation.

In the past 10 years, adaptive wavefront interferometry (AWI) has been employed for measuring freeform surface profiles. However, existing AWI techniques relying on stepwise and model-free stochastic optimizations have resulted in inefficient tests. To address these issues, deterministic adaptive wavefront interferometry (DAWI) is firstly introduced in this paper based on backpropagation (BP), which employs a loss function to simultaneously reconstruct and sparsify initial incomplete interferometric fringes until they are nulled. Each iteration of BP requires two phase shifts. Through simulations, we have verified that freeform wavefront error with a peak-to-valley (PV) of up to 168 λ can be fully compensated in tens of iterations using a 1024 × 1024 pixel area of a liquid-crystal spatial light modulator. In experiments, we accomplished a null test of a freeform surface with 80% missing interference fringes in 39 iterations, resulting in a surface profile error PV of 66.22 λ and measurement error better than λ/4. The DAWI has at least 20 times fewer iterations in fringe reconstruction than the 3-step AWI methods, and nearly an order of magnitude fewer iterations in the whole process, paving the way for significantly enhanced efficiency, generality and precision in freeform surface adaptive interferometry.

New polishing concepts for optical components in flexible and efficient process chains

The flexible and efficient production of precise optical free-form surfaces requires advanced kinematic operating principles. Due to the complex surface geometries, polishing processes with point or linear contact are used. These generally result in longer polishing times due to the smaller footprint compared to large-area polishing tools. The creation of a high precision, polishable surface in the shaping steps of the process chain is therefore of great importance. This applies in particular to minimising the roughness, but also the depth of SSD (sub-surface damage) and the mid-spatial frequency errors before the polishing process. The article describes selected process chains for the production of free-form optics and presents options for optimising the required polishing steps.

Determinant of Dynamics and Interfacial Forces in Ultraprecision Machining of Optical Freeform Surface through Simulation-Based Analysis.

This study delves into the intricacies of ultraprecision machining, particularly in the context of machining optical freeform surfaces using Diamond Turning Machines (DTMs). It underscores the dynamic relationship between toolpath generation, hydrostatic bearing in DTMs, and the machining process. Central to this research is the innovative introduction of Metal Matrix Composites (MMCs) to replace the traditional materials used in designing linear bearings. This strategic substitution aims to dynamically enhance both the accuracy and the quality of the machined optical freeform surfaces. The study employs simulation-based analysis using ADAMS to investigate the interfacial cutting forces at the tooltip and workpiece surface and their impacts on the machining process. Through simulations of STS mode ultraprecision machining, the interfacial cutting forces and their relationship with changes in surface curvatures are examined. The results demonstrate that the use of MMC material leads to a significant reduction in toolpath pressure, highlighting the potential benefits of employing lightweight materials in improving the dynamic performance of the system. Additionally, the analysis of slideway joints reveals the direct influence of interfacial cutting forces on the linear slideways, emphasising the importance of understanding and controlling these forces for achieving higher-precision positioning and motion control. The comparative analysis between steel and MMC materials provides valuable insights into the effects of material properties on the system's dynamic performance. These findings contribute to the existing body of knowledge and suggest a potential shift towards more advanced precision forms, possibly extending to pico-engineering in future systems. Ultimately, this research establishes a new standard in the field, emphasising the importance of system dynamics and interfacial forces in the evolution of precision manufacturing technologies.

Study on tool wear and optimization of machining parameters in laser-assisted fast tool servo machining of glass-ceramic

Glass-ceramic is difficult to be ultra precision machined due to its high hardness and brittleness. Laser-assisted fast tool servo machining (LAFTSM) of glass-ceramic optical free-form surface was carried out with tool wear as the characteristic value to study the machining quality of glass-ceramic. Orthogonal experiments on LAFTSM were conducted using the Taguchi method (TM). The range of tool wear reduction obtained by comparing laser-assisted machining (LAM) with fast tool servo (FTS) machining is 48.83%–64.12%. The order of contribution of each machining parameter obtained through variance analysis to the reduction of tool wear is: spindle speed > laser power > feed rate > piezoelectric frequency. The optimal combination of machining parameters that can minimize tool wear obtained through signal-to-noise ratio (S/N) analysis is: spindle speed 55 rpm, feed rate 0.01 mm/rev, piezoelectric frequency 8 Hz, laser power 75 W. Artificial neural network (ANN) and genetic algorithm (GA) were used to fit and optimize the machining parameters and experimental results in TM orthogonal experiments. The fitting values of ANN are highly consistent with the orthogonal experimental results. The optimal combination of machining parameters obtained after GA optimization analysis is: spindle speed 50 rpm, feed rate 0.015 mm/rev, piezoelectric frequency 4 Hz, laser power 75 W. Experiments were conducted using the optimal combination of machining parameters of TM and ANN, the results showed that ANN performs better than TM in predicting minimum tool wear and optimizing machining parameters. This study provides a reference for LAFTSM and the research methods of tool wear.

A Toolpath Planning Method for Optical Freeform Surface Ultra-Precision Turning Based on NURBS Surface Curvature

As the applications for freeform optical surfaces continue to grow, the need for high-precision machining methods is becoming more and more of a necessity. Different toolpath strategies for the ultra-high precision turning of freeform surfaces can have a significant impact on the quality of the machined surfaces. This paper presents a novel toolpath planning method for ultra-precision slow tool servo diamond turning based on the curvature of freeform surfaces. The method analyzes the differential geometric properties of freeform surfaces by reconstructing NURBS freeform surfaces. A mathematical model is constructed based on the parameters of different positions of the freeform surface, toolpath parameters, and tool residual height. Appropriate toolpath parameters can be calculated to generate the optical freeform ultra-precision slow tool servo diamond turning toolpath. Compared with the toolpaths generated by the traditional Archimedes spiral method, the ultra-precision slow tool servo diamond turning toolpath planning method proposed in this paper can generate more uniform toolpaths on the freeform surfaces and keep the residual tool height within a small range.

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.

Spatial-frequency-oriented measurement strategy in two-dimensional slope deflectometry systems.

A single-point-probe-based slope profiler is a common measurement scheme for the measurement of freeform optical surfaces, which has been a challenging research direction. Efficiency is a key issue in two-dimensional scanning-based measurement. This study establishes a measurement system simulation model and reveals that the height reconstruction accuracy of different reconstruction algorithms is primarily correlated with the sampling density. The spatial resolution calibrated of the slope measurement device is also identified to be an essential part of the strategy. Based on a kind of slope profiler, this paper applies variable sampling intervals for different spatial frequency characteristics of the surface under test (SUT). The result shows that the reconstruction accuracy can be controlled by selecting sampling parameters and calibrating the slope measurement device. For objects with different spatial characteristics, targeted optimization of the measurement scheme can be achieved. This strategy also has a certain universality for general scanning slope measurement and height reconstruction, providing a reference for device selection and sampling settings for different spatial frequency measurement requirements.

Optical freeform reflective imaging system design method with manufacturing constraints.

With the development of space optics, optical freeform surfaces have gradually been utilized in reflective optical imaging systems in recent years. Freeform surfaces not only bring many benefits to the optical imaging system, but also present many challenges to their manufacture. Regardless of the machining method used, machining errors during the fabrication of freeform surfaces will exist, which limits the accuracy of freeform surface machining. In this paper, the deviation root mean square (RMS) of a freeform surface from the reference aspheric surface is proposed to evaluate the manufacturability of the freeform surface by using single-point diamond turning. Then the deviation RMS of freeform surfaces is added to the design process of the optical system as a manufacturing constraint. Subsequently, an off-axis three-mirror system and an off-axis two-mirror system with and without manufacturing constraints are designed, respectively. Then the imaging quality of these optical systems and the linear interpolation error RMS of freeform mirror are analyzed. It can be concluded that, on the basis of reaching the imaging quality requirements, the machining difficulty of a freeform mirror can be reduced when adding manufacturing constraints to the design process.

FreeformNet: fast and automatic generation of multiple-solution freeform imaging systems enabled by deep learning

Using freeform optical surfaces in lens design can lead to much higher system specifications and performance while significantly reducing volume and weight. However, because of the complexity of freeform surfaces, freeform optical design using traditional methods requires extensive human effort and sufficient design experience, while other design methods have limitations in design efficiency, simplicity, and versatility. Deep learning can solve these issues by summarizing design knowledge and applying it to design tasks with different system and structure parameters. We propose a deep-learning framework for designing freeform imaging systems. We generate the data set automatically using a combined sequential and random system evolution method. We combine supervised learning and unsupervised learning to train the network so that it has good generalization ability for a wide range of system and structure parameter values. The generated network FreeformNet enables fast generation (less than 0.003 s per system) of multiple-solution systems after we input the design requirements, including the system and structure parameters. We can filter and sort solutions based on a given criterion and use them as good starting points for quick final optimization (several seconds for systems with small or moderate field-of-view in general). The proposed framework presents a revolutionary approach to the lens design of freeform or generalized imaging systems, thus significantly reducing the time and effort expended on optical design.

Study on the Performance of laser-assisted fast tool servo machining device for glass-ceramic

As an optical hard brittle material, glass-ceramic is widely used in radome, astronomical telescopes, and laser industries. However, an efficient method for machining optical free-form surface of glass-ceramic still needs to be studied by academia and industry. In this study, a laser-assisted fast tool servo machining device for glass-ceramic is developed. The theoretical stiffness of semicircular flexure hinge in the device is calculated by flexibility matrix method. The displacement output characteristics of the device are verified by simulation and displacement measurement experiment. Static and dynamic temperature measurement experiments of glass-ceramic are carried out respectively. The free-form surface morphology of glass-ceramic is obtained through machining experiment. Laser-assisted fast tool servo machining can reduce surface roughness by 24.4% and tool wear by 35.7% compared to conventional machining, which fully proves that the laser-assisted fast tool servo machining device can obtain higher machining quality of optical free-form surface.

Design of compact off-axis freeform imaging systems based on optical-digital joint optimization.

Using a freeform optical surface can effectively reduce the imaging system weight and volume while maintaining good performance and advanced system specifications. But it is still very difficult for traditional freeform surface design when ultra-small system volume or ultra-few elements are required. Considering the images generated by the system can be recovered by digital image processing, in this paper, we proposed a design method of compact and simplified off-axis freeform imaging systems using optical-digital joint design process, which fully integrates the design of a geometric freeform system and the image recovery neural network. This design method works for off-axis nonsymmetric system structure and multiple freeform surfaces with complicated surface expression. The overall design framework, ray tracing, image simulation and recovery, and loss function establishment are demonstrated. We use two design examples to show the feasibility and effect of the framework. One is a freeform three-mirror system with a much smaller volume than a traditional freeform three-mirror reference design. The other is a freeform two-mirror system whose element number is reduced compared with the three-mirror system. Ultra-compact and/or simplified freeform system structure as well as good output recovered images can be realized.

Study of the surface roughness and optimization of machining parameters during laser-assisted fast tool servo machining of glass-ceramic

Glass-ceramic is a typical hard and brittle material that is difficult to machine. In order to improve the surface quality of laser-assisted fast tool servo machining optical free-form surface of glass-ceramic, the effects of spindle speed, feed speed, piezoelectric frequency and laser power on the surface roughness were investigated. Firstly, the Taguchi method (TM) was used to establish the orthogonal experiment, and the contribution rate of each machining parameter to the surface roughness was obtained through variance and signal-to-noise ratio (S/N) analysis. The order of the influence degree of each parameter on the surface roughness is as follows: laser power > spindle speed > feed speed > piezoelectric frequency. The optimal machining parameter combinations obtained for the TM experiment are as follows: spindle speed 50 rpm, feed speed 0.01 mm rev−1, piezoelectric frequency 8 Hz, laser power 75 W. The range of surface roughness reduction obtained by comparing laser-assisted machining (LAM) with pure fast tool servo (FTS) machining is 38.75%∼58.77%. The Box-Behnken Design (BBD) in response surface methodology (RSM) was used to design experiments and a regression model for surface roughness was established through RSM. The deviation between the surface roughness predicted by the regression equation and the experimental value is less than ±6%. The influence law of various machining parameters on surface roughness was studied through three-dimensional response surface. RSM optimized the minimum surface roughness with a desirability of 99.43%. The optimal combination of machining parameters optimized through RSM is as follows: spindle speed 53.71 rpm, feed speed 0.02 mm rev−1, piezoelectric frequency 6.73 Hz, laser power 72 W. This paper is the first to combine LAM with FTS for machining optical free-form surface of glass-ceramic. This study provides a reference for laser-assisted fast tool servo machining and the research methods of surface quality.

Convex optical freeforms using fringe Zernike overlay approach for two-mirror and three-mirror telescopes for space applications

The challenge in manufacturing and testing of convex optical parts is well known in comparison to its concave counterpart and an optimized imaging system invariably features a combination of both. Of late, freeform mirrors find lot of interest in space applications as the optical systems remain compact within the allocated envelope. As is well known, these freeform mirrors are difficult to manufacture and test due to their lack of rotational or translational symmetry and poses additional challenges if it has convex profile. In the current investigations, two new convex freeform optical surfaces are proposed which is based on fringe Zernike overlay technique. The first convex freeform envisaged is for a two-mirror off-axis telescope where the secondary mirror is an off-axis freeform and the second convex freeform for a three-mirror anastigmat telescope where the secondary mirror is an on-axis convex freeform. Substitution of these convex freeform surfaces in the two-mirror and three-mirror telescope systems aid in the correction of asymmetrical aberrations to a wider view field, thereby enhancing the performances of the de-centred and tilted systems in the respective configurations. The procedure adopted for the manufacturing of these convex freeform surfaces using bonnet polishing methods and the interferometric tests using modified-Hindle null corrector and subaperture-stitching techniques for evaluation are described in detail.