Peak-to-valley Research Articles

Cylindrical surface shape measurement method and measurement comparison

Optical elements are used in various fields, in which it is required to measure spherical, aspherical, and free-form surface shapes. We use a nanoprofiler previously developed by our research group to measure a cylindrical surface shape. Unlike spherical or aspherical shapes, the cylindrical surface shape of free-form surface is rotationally asymmetrical and thus difficult to determine the measured position. Therefore, we processed fiducial marks on the measured sample and specified the measurement position by fiducial marks. Then we performed comparative measurements with a Fizeau interferometer using a computer generated hologram (CGH) as a reference plane. The nanoprofiler and interferometer measured to accuracies of 43.7 nm peak-to-valley (PV) and 60.9 nm PV, respectively; the difference between the two was 17.2 nm PV. Furthermore, a spherical shape and an aspherical shape were similarly measured by both devices. The spherical shape had a difference of 8.4 nm PV and that of the aspherical shape was 9.7 nm PV; thus the difference between the measurements of the cylindrical surface shape was larger. Considering that the guaranteed accuracy of CGH for measuring a cylindrical surface shape is ∼30 nm PV, we concluded that this is a reasonable result and fiducial marks are effective to determine the position.

Effect of Robot Motion Accuracy on Surface Form during Computer-Controlled Optical Surfacing Process

Nowadays, large-aperture optical components are increasingly used in high-power laser systems, remote-sensing satellites, and space-based astronomical telescopes. Fabricating these surfaces with submicron-scale shape accuracy and a nanoscale surface finish has been a great challenge for the optical industry, especially for hard and difficult-to-machine materials. Thus, to achieve the high-efficiency and high-precision polishing of large-aperture aspherical optical parts, this study combined robotic machining technology with computer-controlled optical surfacing (CCOS) technology and investigated the effect of robot motion accuracy on the surface topography of workpieces during polishing. First, a material removal model considering the normal error of the polishing tool was developed based on contact mechanics, kinematic theory, and the abrasion mechanism. Next, in combination with the polishing trajectory, the surface morphology and form accuracy after polishing were predicted under different normal-error conditions. Then, preliminary experiments were conducted to verify the model. The experimental data agreed with the simulation results, showing that as the normal error increased from 0° to 0.5° and 1°, the peak-to-valley (PV) values of the surface profile of the optical element decreased from 5.42, 5.28, and 4.68 μm to 3.97, 4.09, and 4.43 μm, respectively. The corresponding convergence rates were 26.8%, 22.5%, and 5.3%. The root mean square (RMS) values decreased from 0.754, 0.895, and 0.678 μm to 0.593, 0.620, and 0.583 μm, with corresponding convergence rates of 21.4%, 30.7% and 14.0%, respectively. Moreover, a higher motion accuracy enabled the polishing robot to reduce the mid- and high-frequency errors of the optical element.

A novel reciprocating cluster magnetorheological polishing device: Design and investigation of removal model

In the traditional magnetorheological polishing of flat planar elements, there have been problems like low efficiency and uneven surface. To improve the surface quality of optical glass and explore the material removal mechanism, a novel reciprocating cluster magnetorheological polishing (MRP) device was designed with a magnetic field consisting of six curved permanent magnets and one static magnetic finite element for analysis. By analyzing the forces and motion behaviors of single abrasive particles during the polishing process, a novel removal model was developed and the effects of the main parameters on the material removal mechanism were investigated. The experiments ware conducted on the K9 glass through the polishing process by this proposed device and traditional cold working separately. The results showed that reciprocating cluster MRP for 120 min was able to achieve a surface roughness of 2.7 nm, a Peak to Valley (PV) value of 0.689 fr (216 nm) and a Root Mean Square (RMS) value of 0.077 fr (24 nm), respectively, which made a significant improvement on the conventional cold working. Therefore, the proposed device and novel polishing process could effectively reduce the surface roughness value and the PV value of K9 glass, while improving both the polishing efficiency and accuracy of optical components.

Rapid polishing process for the x ray reflector.

X ray mirrors are symmetrical workpieces along the length and width and are widely used in various optical systems. Unlike the center-symmetric circular mirror, it is more difficult to suppress the edge effect of the x ray mirror during the polishing process, which greatly limits the polishing accuracy and polishing efficiency. Based on this, the unique edge effect of x ray mirrors is investigated in depth in this paper. First, the causes and distribution laws of the edge effect of the x ray mirror were obtained by analyzing the inherent structure of the computer controlled optical surface (CCOS) and the motion trajectory of the polishing tool. Second, a mathematical model was established based on the material removal states of different regions on the x ray mirror. Finally, a combined polishing process based on the influence function of different shaped tools is proposed and experimentally verified. The results show that the edge effect on the x ray mirror is significantly weakened and its surface errors peak to valley (PV) and RMS are increased by 21.5 times and 47.9 times, respectively. This indicates that the combined polishing process has a good suppression effect on the edge effect of the x ray mirror.

Local tolerance and quality evaluation for optical surfaces

The manufacture of high-precision surfaces is the foundation of building high-performance optical systems. For over 50 years, the tolerance for optical surfaces has been specified by the root-mean-square (rms) or peak-to-valley (PV) value over the entire surface geometry. However, different regions on optical surfaces do not contribute equally to image quality and, thus, can tolerate different levels of errors. A global tolerance described by a single or few parameters cannot precisely provide the manufacturing requirements of each region on the surface, which may result in unnecessary accuracy specifications for surfaces. Furthermore, the components with the same PV or rms figure errors can produce different imaging qualities; however, this difference cannot be distinguished by the conventional figure of merit. To address these problems, a framework that includes a local tolerance model and a quality merit function for optical surfaces is proposed. The local tolerance model can provide an accurate tolerance for each region on the surface so the targeted wave aberration requirements are met during components manufacturing. More importantly, the proposed merit function closely ties the surface figure error to imaging performance, e.g., the findings can explain that the component with lower geometric accuracy may produce better imaging quality. This framework provides new insights into optical design, manufacture, and metrology and especially paves the way for the manufacture of high-precision large-aperture systems.

Precision estimation of large space-borne parabolic antenna support structure

An accuracy analysis approach – mosaic equivalence approach which is based on the principle of approximate structure substitution, to a large complex spatial mechanism with three-dimensional (3D) paired bearings support joint (PBS-joint) clearance is presented to effectively estimate the support structure precision of large parabolic space-borne antenna. The analysis suggests when all the PBS-joints equipped with Metric 628/6 bearings in standard clearance, the surface precision of support structure can obtain relatively high accuracy with a 99.73% probability that root mean square (RMS) was kept in (0.3275, 0.7673) mm and peak-to-valley (PV) was kept in (0.8806, 1.8178) mm. The solution of deviation configuration under a large complex spatial mechanism using the proposed mosaic equivalence approach can be transformed into that under a mosaiced structure of its simple sub-mechanisms. As a result, the high-dimensional coupling between the deviation configuration decision variables can be effectively avoided. Besides, the constraint equations of large complex mechanisms with the PBS-joint 3D clearance can be simplified. This method lays a foundation for reducing the manufacturing cost and risk of large-diameter, high-precision satellite antennas. It has essential engineering value.

In-situ measurement and compensation of complex spatio-temporal couplings in ultra-intense lasers

Diffraction wavefront errors of large-scale Treacy compressors may induce complex spatio-temporal couplings (CSTCs) in chirped pulse amplification and degrade the quality of the pulsed beam in both near and far fields. This problem is particularly pronounced in petawatt laser facilities that require tiled compressor gratings. Here, to the best of our knowledge, we present the first in-situ measurement method named pseudo lateral shearing interferometry (PLSI) for the CSTC wavefront error and manufacture a continuous phase plate (CPP) according to the measurement to reduce the distortion. A Shark-Hartmann wavefront sensor is used to characterize wavefronts of the entire system at two different wavelengths, and the CSTC wavefront error can be reconstructed similarly to lateral shearing interferometry (LSI). Our approach strongly reduces systematic errors and the impact of other optics. The root-mean-square (RMS) value of the resulting error is 40 nm in a single measurement, and the day-to-day repeatability is 55 nm. The employed CPP reduces the peak-to-valley (PV) value of the CSTC wavefront error from 675 to 312 nm, and the focused peak intensity is improved by 51%.

Wheel Setting Error Modeling and Compensation for Arc Envelope Grinding of Large-Aperture Aspherical Optics

Precision grinding is a key process for realizing the use of large-aperture aspherical optical elements in laser nuclear fusion devices, large-aperture astronomical telescopes, and high-resolution space cameras. In this study, the arc envelope grinding process of large-aperture aspherical optics is investigated using a CM1500 precision grinding machine with a maximum machinable diameter of Φ1500 mm. The form error of the aspherical workpiece induced by wheel setting errors is analytically modeled for both parallel and cross grinding. Results show that the form error is more sensitive to the wheel setting error along the feed direction than that along the lateral direction. It is a bilinear function of the feed-direction wheel setting error and the distance to the optical axis. Based on the error function above, a method to determine the wheel setting error is proposed. Subsequently, grinding tests are performed with the wheels aligned accurately. Using a newly proposed partial error compensation method with an appropriate compensation factor, a form error of 3.4 μm peak-to-valley (PV) for a Φ400 mm elliptical K9 glass surface is achieved.

High-aperture low-coherence interferometer with a diffraction reference wave.

A high-aperture low-coherence interferometer with a diffraction reference wave based on a tipped single-mode optical fiber was proposed and investigated. Due to the usage of the central least-aberrated region of the diffracted wavefront, the interferometer comprise record working aperture among known PDIs. The interferometer makes it possible to study samples with a reflectance that varies over a wide range. A demonstration of the use of this interferometer for high-precision measurements of a spherical mirror is presented. Sub-nanometer reproducibility of measurements in terms of the peak to valley (PV) parameter and sub-angstrom reproducibility in terms of the rms are demonstrated.

Mitigation of atmospheric turbulence effect by light beams carrying self-rotating wavefront.

We propose an approach against the turbulence-induced degradation by using laser beam with self-rotating wavefront. Such laser beam, generated by the coherent combination of vortex beams with different helical charges and central angular frequencies, can introduce coupling of its wavefront in spatial and temporal domain, that is, periodic wavefront rotation. When the wavefront rotation is faster than the airflow, the laser beam can travel through the inhomogeneity and anisotropy of air in the azimuthal direction within the time interval of airflow. The wavefront distortion caused by the turbulent atmosphere is therefore rotated and gradually smoothed as the laser beam travels. After the laser propagating through the turbulent atmosphere, the total wavefront distortion becomes centrosymmetric with lower peak-to-valley (PV) value. Such smoothed wavefront distortion can dramatically eliminate the turbulence-induced degradation of laser beams, especially beam centroid drift. We believe that this approach can lead to new trend in remote sensing, free-space optical communication, lidar, etc.

Monoscopic Phase Measuring Deflectometry Simulation and Verification

The three-dimensional (3D) shape of specular surfaces is important in aerospace, precision instrumentation, and automotive manufacturing. The phase measuring deflectometry (PMD) method is an efficient and highly accurate technique to measure specular surfaces. A novel simulation model with simulated fringe patterns for monoscopic PMD is developed in this study. Based on the pre-calibration and the ray-tracing model of the monoscopic PMD system, a comprehensive model from deformed pattern generation to shape reconstruction was constructed. Experimental results showed that this model achieved high levels of measuring accuracy in both planar and concave surfaces measurement. In planar surface measurement, the peak to valley (PV) value and root mean square (RMS) value of the reconstructed shape can reach 26.93 nm and 10.32 nm, respectively. In addition, the accuracy of the reconstructed concave surface can reach a micrometre scale. This work potentially fills critical gaps in monoscopic PMD simulation and provides a cost-effective method of PMD study.

Virtual-real combination Ritchey-Common interferometry.

Large optical flats play a remarkable role in advanced large-aperture optical systems and the testing of the surface shape error is indispensable for the fabrication. The widely adopted Ritchey-Common test for large optical flats will fail without the rigorous test configurations including a large F/# prerequisition and a flat-to-interferometer distance invariance. A virtual-real combination Ritchey-Common interferometry is proposed to avoid the large F/# prerequisition by accurately modelling the optical path in a virtual interferometer. Furthermore, a virtual-real combination iterative algorithm is proposed in this method to break the flat-to-interferometer distance invariance. Measurement experiments for 100 mm and 422 mm aperture flats were performed to demonstrate the feasibility of this method. Compared with a direct testing in a standard Zygo interferometer, the peak to valley (PV) and root mean square (RMS) errors were less than 0.1 λ and 0.01 λ (λ=632.8 nm), respectively, in different Ritchey angles and flat-to-interferometer distances. Further numerical simulations demonstrate that RMS errors for various Zernike aberrations in arbitrary F/# are less than 0.01 λ. This method can break the distance invariance restriction and achieve high accuracy with an arbitrary F/#, thus providing substantial freedom in the design of test configurations to accommodate various test scenarios.

Shape-adaptive magnetic field-assisted batch polishing of three-dimensional surfaces

The increasing demand of the superfinished three-dimensional (3D) surfaces has stimulated the development and upgrade of the precision polishing technology. However, current ultra-precision polishing methods usually polish the workpiece one-by-one, leading to low production efficiency and high polishing cost. Even though some batch polishing methods have been developed for polishing a number of workpieces simultaneously, it is difficult for them to obtain high form accuracy, as well as nanometre scale surface roughness. Hence, this paper presents a shape-adaptive magnetic field-assisted batch polishing (SAMABP) method which not only implements nanometre scale batch polishing of 3D surfaces, but also achieves high form maintainability. Firstly, the effect of surface shape on the material removal in magnetic field-assisted batch polishing (MABP) is revealed. Secondly, the shape-adaptive optimization (SAO) algorithm is developed to cater for the effect of the material removal variation on different kinds of surface shapes, based on the kinematic analysis of the magnetic brush in MABP, as well as modelling of the material removal distribution. At last, a series of verification experiments are designed and conducted on convex, concave and structured surfaces to validate the proposed method. The surface roughness of 3D surface was significantly reduced from larger than 100 nm to less than 10 nm or even less than 5 nm in arithmetic surface roughness (Sa) after 20 min of polishing. Meanwhile, the surface forms were maintained well, and the deviation of them after polishing were all less than 4 μm in peak-to-valley (PV). These results show that the SAMABP method is effective to obtain nanometric surface roughness together with micrometric form accuracy in the batch polishing of 3D surfaces. This study sheds the light for the applications of SAMABP in batch polishing of optical components and moulds, functional structured surfaces, turbine blades, dental crowns, surgical knives, high-end jewelleries, etc.

Robotic Magnetorheological Finishing Technology Based on Constant Polishing Force Control

The normal positioning error hinders the use of magnetorheological finishing (MRF) in robotic polishing. In this paper, the influence of robotic normal positioning error on the MRF removal rate is revealed, and a force-controlled end-effector for the robotic MRF process is presented. The developed end-effector is integrated into a six-axis industrial robot, and the robot positions the end-effector while the end-effector realizes the constant force control. A fused silicon mirror is polished, and the result shows that the proposed device effectively compensates for robotic normal positioning error and simultaneously maintains the stability of the polishing process. After deterministic polishing, the PV (peak to valley) of the figure is reduced from 126.56nm to 56.95nm, and the RMS (root mean square) is reduced from 22.15 nm to 7.59 nm.

Machining control of non-axisymmetric aspheric surface based on piezoelectric fast tool servo system

Non-axisymmetric aspheric machining is increasingly important in photoelectric industry. The machining process requires an external feeding device mounted to a machine tool to achieve fast-tool servo (FTS) function. In this study, a piezoelectric (PZT, Lead zirconate titanate) FTS was used to perform non-axisymmetric aspheric machining by control methods. In the beginning, system identification of the PZT tool holder was conducted to obtain the mathematical model of the system and then the simulations were performed for various controllers, including the PID (Proportional-integral-derivative), sliding mode control (SMC), non-singular terminal sliding mode control (NTSMC), and adaptive NTSMC. The simulation results showed that the NTSMC and the adaptive NTSMC had excellent control performances with the tracking errors of 0.0 and 3.1 nm, respectively. Then, control practices without machining were performed with the PV (Peak-to-valley) tracking errors of 0.96 μm, 0.77 μm, and 0.95 μm obtained by the PID controller, NTSMC, and adaptive NTSMC, correspondingly. The large PV errors were found due to the low sampling rate of position commands. Finally, experiments of non-axisymmetric aspheric machining with the implemented controllers were performed for a workpiece of oxygen-free copper (OFC) having 5 mm diameter. The measured results of the machined surfaces were with the PV form errors of 7.2 μm, 2.8 μm, and 3.8 μm in corresponding to the usual machining, using NTSMC and adaptive NTSMC. The effectiveness of the implemented controllers was demonstrated, and the NTSMC showed the best performance. Future works are to examine the repeatability of various controllers with a large hardware memory size and improved environment.

Prediction of Surface Profile Evolution of Workpiece and Lapping Plate in Lapping Process

Abstract Lapping has a history of hundreds of years, yet it still relies on the experience of workers. To improve the automaticity and controllability of the lapping process, a modeling method of friction and wear is developed to predict the surface profile evolution of the workpiece and lapping plate in the lapping process. In the proposed method, by solving the balance equations of resultant force and moment, the inclination angles of the workpiece can be calculated; thus, a more accurate contact pressure distribution of the workpiece/lapping plate interface can be calculated. Combined with the material removal rate model, the continuous evolution process of the workpiece and lapping plate can be predicted in the lapping process. The modeling method was validated by a lapping test of a flat optical glass workpiece (Φ 100 mm) with a composite copper plate. The results show that the proposed method can predict the evolution of the surface profile of the workpiece and lapping plate with high accuracy. Consequently, the lapping plate can be dressed at the right time point. Benefit from this, in the validation test the Peak to Valley (PV) value of the workpiece (with 5 mm edge exclusion) was reduced from 5.279 µm to 0.267 µm in 30 min. The proposed surface profile evolution modeling method not only improves the lapping efficiency but also provides an opportunity to understand the lapping process.

Hadamard matrix calibration and fuzzy proportional integral differential closed-loop control of adaptive optics system

Conventional adaptive optics algorithms are studied through calibration or closed-loop control point of view. A Hadamard matrix algorithm was used to calculate the interaction matrix from the wavefront slope to the deformable mirror voltage. A fuzzy proportional integral differential (PID) control algorithm was used to adjust the control parameters to complete the closed-loop control of the adaptive optics. The simulation shows that when the atmospheric turbulence intensities D / r0 are 1, 10, and 20, respectively, the mean wavefront peak to valley (PV) values are are 0.38, 0.93, and 3.53 μm, respectively, after wavefront correction by Hadamard + PID algorithm; the wavefront PV mean values are 0.38, 0.93, and 3.48 μm, after wavefront correction by PushPull + FuzzyPID algorithm; and the wavefront PV mean values are 0.36, 0.92, and 3.30 μm after wavefront correction by Hadamard + FuzzyPID algorithm. The experimental results show that: the wavefront PV mean values are 3.84, 3.56, and 3.36 μm for Hadamard + PID algorithm, PushPull + FuzzyPID algorithm, and Hadamard + FuzzyPID algorithm, respectively. The Hadamard algorithm significantly improves the interaction matrix measurement accuracy, and the FuzzyPID control algorithm improves the adaptive ability under strong turbulence conditions. The wavefront correction using two advanced algorithms is better than that of the combination of advanced and conventional algorithms.

Fast reconstruction technology of a laser beam spatial transmission characteristic curve.

The traditional multiposition method of the M2 factor measurement system is a good method, but it is relatively time consuming, so it cannot meet the requirements of the transient test of a Gaussian beam. To solve this problem, a quadriwave lateral shearing interferometer and a wavefront construction method based on a difference Zernike polynomial are analyzed. This interferometer uses a special grating to select four replicas of the wavefront, and the interferogram generated by four replicas includes difference wavefront information. Then the difference Zernike polynomial method is used to analyze quadriwave lateral shearing interferograms. The characteristic parameters are obtained after finding the optimal terms of the Zernike polynomials. As a result, the errors of F-number, beam radius, and radius of curvature are 3.7%, 3.8%, and 0.6%, respectively, which verifies this method to calculate parameters of Gaussian beam. In addition, we also find that the shear amount has influence on the reconstructed wavefront. It is showed that as the amount of shear increases from 20 pixels to 90 pixels, the peak-to-valley (P-V) values and RMS values both gradually decrease with a nonlinear relationship, which could be used to decrease the error of wavefront reconstruction further.

Ultra-precision turning method efficient for optical freeform surfaces with a hybrid slow-fast tool servo.

The machining of freeform surfaces is a current research hotspot: A slow tool servo (STS) has limitations in machining accuracy and efficiency for large steep freeform surfaces. Most fast tool servo (FTS) tools are limited by their stroke and cannot manufacture freeform surfaces with a large sag. We propose a hybrid slow-fast tool servo method that combines STS and FTS to machine large steep freeform surfaces by decomposing the freeform surfaces and simultaneously turning efficiently with STS and FTS. Experimental studies were undertaken to fabricate a saddle surface. Meanwhile, a variable feedrates tool path was designed and applied to further improve the machining efficiency. The results show that this method can improve the processing efficiency by 47.5%. The arithmetic mean of surface roughness (Ra) is 2-4 nm, and the peak-to-valley (PV) value is 0.4780 µm at the hollows and 0.3884 µm at the swells.

An ultra-smooth planarization method for controlling fluid behavior in cluster magnetorheological finishing based on computational fluid dynamics

The machining method for controlling the behavior of Bingham fluids in cluster magnetorheological finishing (MRF) is a novel ultra-smooth planarization method. It is necessary to simulate cluster MRF fluid state during machining to optimize the surface microstructures on the polishing disk. The behavior of MRF fluids in a magnetic field is determined by using a rheometer. On this basis, a simulation model is established for fluids during the machining for controlling the behavior of Bingham fluids in cluster MRF pads using the computational fluid dynamics (CFD). The influences of different surface microstructures on polishing disks on the magnetic flux density modulus, size of polishing pads, fluid velocity, and fluid pressure are studied. Surface microstructures on the polishing disk can increase the magnetic flux density modulus, decrease fluid velocity, and increase fluid pressure, and can enhance the polishing effect of soft abrasives. In addition, these surface microstructures reduce slip between the polishing pads and the polishing disk, thus slowing the wear of the polishing disk. Simulation results show that the polishing disk with micro-holes demonstrates the largest magnetic flux density modulus and forms the most extensive polishing pressure. Polishing tests are conducted using sapphire wafers with a diameter of two inches (50 mm) as workpieces. Compared with using a smooth polishing disk, the material removal rate (MRR) is 68.4% higher, while the roughness Ra and peak-to-valley (PV) values are decreased by 34.1% and 75% when using the polishing disk with micro-holes. The test results match the simulation results arising from the use of the model.