Complex Optical Surfaces Research Articles

Development of a Novel Type of Modularized Fast Tool Servo Devices for Manufacturing Complex Optical Surfaces

Development of a Novel Type of Modularized Fast Tool Servo Devices for Manufacturing Complex Optical Surfaces

Unified framework for geometric error compensation and shape-adaptive scanning in five-axis metrology systems

In response to the escalating demand for precise shape metrology of complex optical surfaces, this study unveils a unified geometric error compensation and trajectory planning framework tailored for high-accuracy five-axis scanning metrology systems, which remains a notably underexplored field compared to error compensation in machine tools. Founded on a unified geometric model, the proposed framework seamlessly integrates a versatile shape-adaptive trajectory planning strategy, a thorough global error sensitivity analysis approach, and an exhaustive geometric error compensation scheme. Leveraging inverse kinematics, an innovative shape-adaptive scanning trajectory generation strategy is mathematically formulated, thereby facilitating adaptable measurement trajectory generation for diverse surface geometries. Employing forward kinematics, an exhaustive geometric error model is established to extensively address the 53 distinct geometric errors in the metrology system. This proposed error model fundamentally augments conventional geometric error models in machine tool by managing not only the geometric errors from the motion system, but also those from the probe and workpiece. To streamline the error compensation procedure, a novel global error sensitivity analysis approach is introduced, identifying both system-oriented and process-oriented sensitive geometric errors for targeted compensation. Experimental validation using a standard ball, which achieved an exceptional 89.35% reduction in the root mean square of the measurement errors, further confirms the feasibility and effectiveness of the proposed framework. By offering an universal trajectory planning, sensitivity analysis and error compensation trinity for five-axis scanning metrology systems, this study sets the stage for precision advancements and design optimization across diverse configurations of metrology systems.

Stitching interferometry using alternating calibration of positioning and systematic errors

Stitching interferometry is an essential technique for the non-contact, high-precision measurement of large apertures or complex optical surfaces. However, the accuracy of full-aperture surface reconstruction is significantly compromised by subaperture positioning and systematic errors. To address this challenge, this study introduces a novel stitching interferometry method utilizing alternating calibration of positioning and systematic errors (SIAC). This method calibrates one type of error while maintaining the other constant, and alternates between these processes to effectively decouple the two errors, facilitating accurate phase stitching. Within this calibration framework, an iterative weighted phase stitching model employing vertical projection for estimating overlapping areas was developed to calibrate positioning errors. Additionally, the rotation measurements of a single subaperture, in conjunction with a global fitting approach, were employed to correct reference errors. Numerical simulations have confirmed the efficacy of SIAC in calibrating these errors. Moreover, experimental measurements were performed on both a plane mirror and gullwing aspheres, with the resulting stitched full-aperture phase distributions and cross-testing outcomes affirming the method's accuracy and practicality. This research provides a novel solution for stitching interferometry, enhancing the precision of optical surface measurements.

Single femtosecond pulse writing of a bifocal lens.

In this Letter, a method for the fabrication of bifocal lenses is presented by combining surface ablation and bulk modification in a single laser exposure followed by the wet etching processing step. The intensity of a single femtosecond laser pulse was modulated axially into two foci with a designed computer-generated hologram (CGH). Such pulse simultaneously induced an ablation region on the surface and a modified volume inside the fused silica. After etching in hydrofluoric acid (HF), the two exposed regions evolved into a bifocal lens. The area ratio (diameter) of the two lenses can be flexibly adjusted via control of the pulse energy distribution through the CGH. Besides, bifocal lenses with a center offset as well as convex lenses were obtained by a replication technique. This method simplifies the fabrication of micro-optical elements and opens a highly efficient and simple pathway for complex optical surfaces and integrated imaging systems.

Exploring the Potential of Chalcogenide Lens Designs for Cost-effective LWIR Systems

The high cost of optical raw materials in the long wavelength infrared (LWIR) region necessitates the development of cost-effective solutions without compromising resolution. Chalcogenide glasses offer a faster and easier production process compared to growing single crystals of Germanium (Ge). Additionally, they can be molded into complex optical surfaces, reducing processing costs further for serial production. In this study, we explore the potential of chalcogenide lenses. Our comprehensive design study demonstrates that chalcogenide lens designs can achieve comparable or even superior optical performance with reasonable system complexity when compared to a wide-angle benchmark Ge design.

Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing.

Complex optical elements have the advantages of improving image quality and optical performance and expanding the field of view. Therefore, it is widely used in X-ray scientific devices, adaptive optical elements, high-energy laser systems, and other fields and is a hot research direction in precision optics. Especially for precision machining, there is a greater need for high-precision testing technology. However, how to measure complex surfaces efficiently and accurately is still an important research topic in optical metrology technology. In order to verify the ability of optical metrology for complex optical surfaces with wavefront sensing based on image information of the focal plane, some experiment platforms in different types of optical surfaces were set up. In order to validate the feasibility and validity of wavefront-sensing technology based on image information of focal planes, a large number of repetitive experiments were carried out. The measurement results with wavefront sensing based on image information of the focal plane were compared with the measurement results with the ZYGO interferometer. The experimental results demonstrate that good agreement is obtained among the error distribution, PV value, and RMS value of the ZYGO interferometer, which shows the feasibility and validity of wavefront sensing based on image information of focal plane technology in optical metrology for the complex optical surface.

Mathematical Description and Design Methods of Complex Optical Surfaces

Mathematical Description and Design Methods of Complex Optical Surfaces

Wavefront-coded phase measuring deflectometry for the all-focused measurement.

Phase measuring deflectometry is a powerful measuring method for complex optical surfaces, which captures the reflected fringe images encoded on the screen under the premise of focusing the measured specular surface. Due to the limited depth of field of the camera, the captured images and the measured surface cannot be focused at the same time. To solve the position-angle uncertainty issue, in this Letter, the wavefront coding technology is used to modulate the imaging wavefront of the deflectometry, thereby making the measuring system insensitive to the defocus and other low-order aberration including astigmatism, field curvature, and so on. To obtain the accurate phase, the captured fringe images are deconvoluted using the modulated point spread function to reduce the phase error. Demonstrated with a highly curved spherical surface, the measurement accuracy can be improved by four times. Experiments demonstrate that the proposed method can successfully reconstruct the complex surfaces defocusing the captured images, which can greatly release the focusing requirement and improve measurement accuracy.

Three-dimensional stitching of stereo-deflectometry based on marker points.

As a non-contact and three-dimensional (3D) mirror surface measurement method, stereo-deflectometry has been developing rapidly in recent years. For solving the problem of the measurement of large surface inclination with traditional stereo-deflectometry, 3D stitching of stereo-deflectometry based on marker points is proposed. In this method, the 3D points in the subregions under different perspectives were measured. Meanwhile, the 3D coordinates of the marker points on the sample table, which were calculated by binocular stereo vision, were used for coarse stitching, and the ICP algorithm was used for fine stitching. In order to verify the 3D stitching algorithm, we built a measurement system for the freeform surface of an ultra-short lens with a diameter of about 100 mm and a steepness of 52.6°. The spherical fitting error of the reflective bowl after stitching is within 60 mm. The experimental results verify the feasibility of the method, leading to potential mass application of stereo-deflectometry in 3D measurement of complex optical surfaces with a large aperture and high steepness.

Sub-regional polishing and machining trajectory selection of complex surface based on K9 optical glass

With the rapid progress of science and technology, complex optical surfaces have been widely used in various devices. Due to the complexity of their geometric features, machining with a single trajectory inevitably has an impact on the accuracy of the machined surface. Sub-regional milling has been studied intensively by researchers worldwide. However, few studies have focused on sub-region polishing. Therefore, sub-regional polishing is not widely used in the machining field. This paper investigates the method of sub-regional polishing of complex surfaces and focuses on the selection of polishing trajectories for different processing areas. The method takes into account the curvature characteristics of each point on the surface and combines the Freeman code method to divide the surface into multiple processing regions. The selection of polishing trajectories for each processing area is analyzed from the viewpoint of surface roughness and power spectrum density analysis. The correctness of the trajectory selection is verified by polishing experiments on K9 optical glass. The results show that all three trajectories used in the experiments can reduce the surface roughness of the workpiece by more than 90%. Using the Hilbert trajectory can effectively reduce the medium-frequency and high-frequency errors of the machined surface and improve the optical properties of the surface. This work is expected to provide significant guidance for efficient and high-quality processing of complex optical surfaces compared with traditional machining methods using a single trajectory.

Correction of aberration-induced phase errors in phase measuring deflectometry.

Phase measuring deflectometry is a powerful measuring method of complex optical surfaces that captures the reflected fringe images associated with a displaying screen and calculates the normal vectors of the surface under test (SUT) accordingly. The captured images are usually set conjugate to the SUT, which in turn makes the screen defocused. As a result, the blurring effect caused by the defocus and aberrations of the off-axis catadioptric imaging system can severely degrade the phases solved from the blurred images. In order to correct the phase errors, the space-variant point spread functions (PSFs) are modeled using a skew-normal function. The phase bias is estimated by forward convolution between the captured images and the PSF models. Demonstrated with a highly curved aspheric surface, the measurement accuracy can be improved by three times.

Curvature effect on surface topography and uniform scallop height control in normal grinding of optical curved surface considering wheel vibration.

High-precision optical components with complex shapes or microstructures have been extensively used in numerous fields such as biomedicine, energy and aerospace. In order to accurately achieve the specific functions of the components, the form accuracy and uniform surface quality need to reach an ever-high level. To achieve this, ultra-precision normal grinding is used for machining various types of complex optical surfaces. However, the intricate variation of the workpiece curvature and grinding wheel vibration gives rise to great challenges to obtain higher precision and uniform surface conditions. In this study, the influence of curvature on surface topography generation has been investigated and a novel model of scallop height has been developed for surface topography generation in the normal grinding of the curved surface. In addition, the relative influence of the curvature is analyzed experimentally, in which the micro-waviness generation as a consequence of the unbalanced vibration of the grinding wheel is modeled and validated by experiments. Finally, the micro sinusoidal array with the setting value for scallop height is achieved by controlling the feed speed, which is determined by the local curvature of surface profile. The results indicated that the curvature variation posed a significant effect on surface uniformity and the model is valid to achieve surface scallop height control in the normal grinding effectively.

Adaptive Phase Correction for Phase Measuring Deflectometry Based on Light Field Modulation

The phase measuring deflectometry is a powerful measuring method for complex optical surfaces, which captures the reflected fringe images associated with a displaying screen and calculates the normal vectors of the surface under test (SUT) accordingly. The captured images are usually set conjugate to the SUT, which in turn makes the screen defocused. As a result, the blurring effect caused by the point spread function (PSF) of the off-axis catadioptric imaging system can bias the solved phases. In order to correct the phase errors, a light field is constructed based on the Fourier compressive sensing method to describe the light transmission between the screen and camera pixels. Fringe modulation is conducted to enhance the robustness against noise, and then, space-variant PSFs can be extracted from the light field. The true phases are obtained by solving a Wiener deconvolution problem, with the merit function adaptively regularized by adjusting the damping parameter. The proposed method can correct adaptively the phase errors induced by the complex aberrations. Compared to the reference measurements, the form accuracy can be improved by four times.

In-situ deflectometric measurement of optical surfaces for precision manufacturing

The in-situ measurement of complex optical surfaces is a challenging task in precision engineering. The phase measuring deflectometry is a powerful measuring method for complex specular surfaces, and it has higher measuring efficiency, stability and dynamic range compared to interferometry. Consequently it is promising to widespread applications in various fields. Deflectometry is essentially a calibration problem, and the measuring accuracy is directly determined by the quality of geometrical calibration. An in-situ deflectometric measuring system is designed based on the single point diamond turning machine. A self-calibration method is developed to specify the relative positions of the camera and screen. Ray tracing is conducted at two positions of an auxiliary reflecting mirror, which is mounted on an air bearing spindle. The accuracy of the geometrical positions can be improved by an order of magnitude by minimizing the deviations of the traced points with respect to the true correspondences. According to the statistical properties of the deviations in reverse ray tracing, the form errors and the position errors can be separated, and the positioning error of the workpiece can be corrected accordingly. Henceforth, the nominal shape of the fabricated workpiece can be fully utilized, and the conventional one-way position-form mapping can be converted into a two-way mapping problem. As for the complex shapes, the whole surface can be covered by sub-aperture measurement. Precise localization of a local region under test is achieved by multi-position imaging, so that correct convergence of the iterative reconstruction process can be guaranteed. Several typical optical surfaces including an off-axis paraboloid mirror are measured, and the measuring accuracy of the proposed method is proved better than 150 nm RMS.

Stitching sub-aperture in digital holography based on machine learning.

Sub-aperture stitching in digital holography (DH) is a very important issue both for the spatial resolution improvement as well as for measuring larger aperture through synthetic enlargement of numerical aperture. In fact, sub-apertures stitching permits to greatly expand the capabilities of optical metrology thus allowing to accurately measure complex optical surfaces such as large spherical and aspheric. Stitching operations can be difficult and cumbersome depending on geometric parameters of specific objects under test. However, here we show that machine learning can definitively aid this process. In fact, here we propose for the first time, to the best of our knowledge, a novel sub-aperture stitching approach based on machine learning applied to an array of different phase-maps sub-apertures recorded by an off-axis digital holographic systems. Essentially, we construct a network according to computation model of sub-aperture stitching and remove the alignment errors and system aberration of sub-aperture maps by training the network. Correct measurement of the surface topography of hemisphere surface is demonstrated thus validating the proposed learning approach. Reported results demonstrate that machine learning can be a useful tool for simplifying the process and for making it a reliable and accurate tool in optical metrology.

Representation of complex optical surfaces with adaptive radial basis functions.

For state-of-the-art optical elements in laser fusion applications, optical surfaces, especially those with residual fabrication error, are generally complex in symmetry, shape of aperture, and spatial frequency distribution. It is critical to represent the optical surface with high accuracy, efficiency, and flexibility during the stages of design, fabrication, and testing. For this purpose, in this paper, we propose that adaptive radial basis functions (ARBF) can be applied to represent the complex optical surface. As more degrees of freedom are harnessed by an adaptive algorithm, the proposed approach presents better accuracy and needs fewer basis functions than that of the classical radial basis functions. Both surfaces, with global and local variation, can be well represented by the proposed method. Furthermore, the fitting ability of ARBF is verified with the measured data from an element polished by magnetorheological finishing technology. Optimization frameworks of the shape parameters for practical use are also discussed. For good measure, spatial relevance between surface height and nodes location shows that ARBF is fairly flexible in representing complex optical surfaces.

Self-calibration of in situ monoscopic deflectometric measurement in precision optical manufacturing.

Accurate in situ measurement of complex optical surfaces is desired for precision manufacturing, and deflectometry is a promising measuring method. However, deflectometry's measurement accuracy depends heavily on the geometric calibration's reliability. Existing calibration methods suffer from the limitations of low efficiency, complicated operations, and expensive equipment. Therefore, a self-calibration method is proposed for the monoscopic deflectometry in order to determine the the camera and screen positions. A flat mirror without markers, rather than high-precision metrological instruments, is employed to assist with the self-calibration work, and a re-projection model is adopted in order to trace the rays from the screen to the camera. Numerical optimization is performed on the global parameters-including the camera intrinsic parameters, the screen intrinsic parameters, and the geometric transformations-in order to improve the geometric calibration's reliability. This self-calibration method only requires that four images be captured, hereby reducing the operating complexity and improving the measuring efficiency. Experiments demonstrate that the re-projection error can be significantly decreased, and also that the measuring accuracy of specular surfaces is comparable to high-precision interferometry.

Development of a novel type of elliptical vibration cutting approaches with varying phase difference

The traditional elliptical vibration cutting (EVC) approaches have been widely employed in cost-effectively machining various complex optical surfaces on many difficult-to-cut materials, but the stiff usages of fixed phase difference and constant vibration frequency will have great limitations on improving performances and extending applications. Therefore, this paper will firstly concentrate on the innovations of a novel type of elliptical vibration cutting with a different frequency (DF-EVC) for several significant benefits, such as improving finish quality, extending tool life, and suppressing scattering effect. As modifications of DF-EVC, another novel type of elliptical vibration cutting with a varying phase difference (VPD-EVC) will be further developed, which can effectively enhance the machining capacities of DF-EVC processes by changing their unfixed phase differences within an available angle range. Beyond the conventional applications, like machining the microstructure and freeform surfaces, the improved VPD-EVC approaches can be elaborately adopted to fabricate two different microgrooves with U-shaped and V-shaped cross-sections, which integrate the high-frequency elliptical vibrations into the cross-feed motions instead of the up-feed motions of traditional EVC. In addition, the mechanism of how the VPD-EVC extends tool life will be discussed in detail, and the dependences of machining capacities to the phase difference amplitudes will be investigated by introducing a dimensionless relative cutting ratio (RCR). Subsequently, the toolpath generations and surface topography simulations of VPD-EVC will be performed and compared to traditional EVC; the suppressing capacity of the scattering effect will be further investigated based on the power spectral density (PSD). Finally, a series of cutting experiments will be practically conducted on the copper materials (T2) with poor machinability, the obtained results can well demonstrate the feasibility and effectiveness of the developed DF-EVC and VPD-EVC approaches for achieving various expected benefits, and several crucial conclusions on current research can be briefly summarized in the end.

Self-assembled nanoparticle antireflection coatings on geometrically complex optical surfaces.

Here we report a simple and scalable electrostatics-assisted colloidal self-assembly technology for fabricating monolayer nanoparticle antireflection coatings on geometrically complex optical surfaces. By using a surface-modified glass volumetric flask with a long neck as a proof-of-concept demonstration, negatively charged silica nanoparticles with 110nm diameter are electrostatically adsorbed on both the interior and exterior surfaces of the flask possessing positive surface charges. The self-assembled monolayer nanoparticle antireflection coatings can significantly improve light transmission through different regions of the flask with varied curvatures, as revealed by optical transmission measurements and numerical simulations using a simplified thin-film multilayer model.

A novel ultrasonic cavitation assisted fluid jet polishing system

Fluid jet polishing is a versatile process used for super-fine finishing of small and complex optical and prosthetic surfaces. Advantages of this process include highly controllable sub-millimetre polishing footprints and absence of tool wear, though the main drawback is very low material removal rate. To address this issue, a novel system was developed in which ultrasonic cavitation causes micro-bubble generation directly upstream of the nozzle outlet. Experimental data shows that these micro-bubbles boost removal rate by up-to 380%, without causing any degradation of the surface finish. This paper reports on the modelling, implementation, and testing of this new polishing system.