Surface Error Research Articles

Prediction of the Waviness Error in Ultra-Precision Fly Cutting Using the Direct Integration Method

Abstract Fly cutting is widely used in manufacturing of large-scale, high-precision optical components. However, the discontinuity of fly cutting machining leads to significant relative vibrations between the tool and the workpiece. The cutting process generates periodic waves along the cutting direction, which will deteriorate the wavefront characteristics of optical components. Based on the machining dynamics, this paper proposes a direct integration method to predict the waviness error of the machined surface. The cutting force model of fly cutting is established. The multi-mode characteristics of the spindle-tool system are measured by the experimental method. Then, the influence of uncertainties on the calculation results is analyzed by the variance-based sensitivity analysis method. Finally, the plane cutting experiment verifies that the direct integration method effectively predicts the waviness error and its variation trend, and the waviness prediction research is important for optimization of the machining parameters.

Optical structuring and finishing toward mid-spatial-frequency error reduction using femtosecond lasers.

We demonstrate nano-structuring and the reduction of mid-spatial-frequency errors using femtosecond laser figuring and finishing. For the first time, to the best of our knowledge, we have corrected mid-spatial-frequency errors from 17 nm to one nanometer in magnitude. We established a method for creating and predicting periodic nanostructures. This demonstration opens the path of using femtosecond lasers to correct surface errors that inherently result from sub-aperture manufacturing techniques.

Evaluation of surface quality and error compensation for optical aspherical surface grinding

Optical aspherical lenses are widely used in the aerospace, electronics, and optical communication industries. Grinding is the primary processing method used to ensure their precision. It is difficult for traditional evaluation indexes to fully reflect the optical properties of optical surfaces after grinding. This paper presents a novel method for characterizing surface quality of optical aspherical surface oriented to the application of optical properties. The proposed evaluation indicators include the profile error, surface roughness, slope error, and projection-area scale-deviation value, which can be used to comprehensively evaluate the surface quality. Subsequently, a novel grinding compensation method for the optical aspherical surface is proposed, and its compensation precision is evaluated using the abovementioned evaluation indicators. The results show that the maximum surface-shape error decreases to less than 150 nm; additionally, the central cusp point is restrained. The precision and efficiency of error compensation for the optical aspherical surface are significantly better than those of the conventional method. The proposed evaluation indicators can be applied to reflect the features of optical aspheric surface directly. The high efficiency and precision compensation of optical aspherical surface can be achieved with the proposed evaluation method and modified error compensation algorithm.

Back analysis of shear strength parameters of slope based on BP neural network and genetic algorithm

AbstractEfficient and accurate acquisition of slope shear strength parameters is the key to slope stability analysis and landslide prevention engineering design. This paper establishes a back analysis method based on uniform design, artificial neural network, and genetic algorithm. It can obtain the shear strength parameters of slopes based on information such as the radius and center coordinates of the slip surface obtained from on‐site investigations. This method has been applied to engineering practice. The research results indicate that the stability of the waste dump slope is most sensitive to the response of the internal friction angle of the loose body, followed by cohesion, and least sensitive to the response of the soil volume weight. This method can effectively reduce the number of network training samples and efficiently and quickly determine the initial weights of the BP (abbreviation for back‐propagation) neural network. This method can efficiently and quickly conduct back analysis to obtain the shear strength parameters of slopes. Using the obtained shear strength parameters for slope stability calculation, the most dangerous slip surface abscissa error, ordinate error, and slip surface radius error are only 3.59%, 0.95%, and 1.83%. It is recommended to promote the back analysis method of shear strength parameters in engineering practice in the future.

Influence of sunlight on the surface error of a large antenna reflector and its correction method

Influence of sunlight on the surface error of a large antenna reflector and its correction method

Absolute tests of three flats for interferometer with 800 mm aperture.

In this study, absolute tests of three flats were performed by using an 800 mm Fizeau interferometer. The flats were installed by employing double-wedge rubber, and the deformation of the flats, primarily involving power and spherical aberrations, was analyzed by conducting finite element analysis. The measurement results revealed an astigmatism component that did not follow the rotation. The astigmatism was separated from the measurement result, and the remaining aberration was consistent with the simulation results, confirming that the astigmatism deformation did not originate from the rubber installation. Subsequently, an absolute test of an 800 mm flat was completed, and the results were compared with those of the traditional three-flat absolute test and Zygo interferometer. The directions of the vertical diameter lines were consistent. The peak-to-valley difference in the full-surface shape was less than 4 nm, and the root mean square was less than 1 nm. The surface errors of flats A and C were consistent with the result of replacing the reference flat, B, with the fourth flat, D, to perform an absolute test. The difference between flats A and C was similar to Zygo's results, thus eliminating the influence of the transmission flat. These results verified the accuracy of the results.

An error compensation method for single point oblique axis grinding considering the grinding wheel wear

With the increasing amount of high quality optical products, the manufacturing requirement for the high-precision optical glass lenses is on the rise. Grinding is typically the main manufacturing process for the optical mold. The degree of wheel wear has a direct impact on the precision of the grinding process. In this paper, the wear rule of grinding wheel in the grinding process of optical aspheric surface is studied with the in-site wear measurement system. A new image processing method and a wear degree evaluation method are proposed. The wear prediction model for the grinding wheel is established. Then a modified compensation method of optical aspheric surface considering grinding wheel wear is proposed. The optical aspheric surface is then compensated using a modified multinomial equation considering grinding wheel wear. The results demonstrate that the profile error of optical aspheric surface can be reduced to less than 150 nm. The proposed compensation method that takes into account the grinding wheel wear can highly improve the grinding precision and efficiency of optical aspheric surface as compared with the conventional compensation method.

Influence of reference sphere on test accuracy of Ritchey–Common method

AbstractThe authors analyse the influence of reference sphere on the test accuracy of Ritchey–Common method during testing of flat mirror surface. A simulation model is established to simulate the influence of different radii of curvature of reference sphere on system wavefront. Then, the difference between the flat mirror surface result with reference sphere surface error to the actual flat mirror surface is examined by this model. The test accuracy of flat mirror result can be effectively improved by eliminating the influence of the surface error of reference sphere. When the surface accuracy of the reference sphere is better than 0.01 λ, the influence on RMS test accuracy is within 0.01 λ. R–C test path is built to test a 100 mm‐diameter flat mirror surface, and its results are compared with those of the flat mirror surface without surface error of reference sphere and with the test result of the interferometer. When the surface accuracy of the actual used area of reference sphere is better than 0.01 λ, the effect on flat mirror RMS accuracy is within 0.01 λ. The RMS test accuracy can reach 0.01 λ, when the surface error of reference sphere is retained. The experiment verifies the correctness of the simulation results and guarantees the improvement in the test accuracy of R–C method.

Wave aberration corrections in PSF ellipticity measurements of astronomical telescopes using a multi-objective optimization.

The weak gravitational lensing (WGL) produces a shear effect on the observed galactic ellipticity that is much smaller than the endogenous ellipticity of the galaxy itself. Achieving such a high-level astronomical observation requires the superior performance of telescopes. To ensure the optical properties of telescopes to be competent in WGL detections, it is very necessary to measure point spread function (PSF) ellipticity of telescopes in labs. In this paper, a 2m off-axis telescope that would be used to detect WGL in space is analyzed and studied. A collimator whose aperture is 2m has been built to measure PSF ellipticity of the telescope. The wave aberrations of the collimator are roughly equal to those of the telescope, so they are important systematical errors and must be removed. However, it is difficult to precisely measure the wave aberrations of optical systems that have large apertures and long focal lengths. In addition, a 2m flat mirror, which is indispensable to measure wave aberrations of optical systems, has significant surface errors. In this paper, a multi-objective optimization method is proposed to eliminate the effects of wave aberrations on PSF ellipticity measurements of the telescope. By constructing an equivalent model, the wave aberrations from collimators and flat mirrors can be corrected so that PSF ellipticity measurement error is reduced to within 0.01. Measurement accuracy of PSF ellipticity of the telescopes can be improved significantly.

Surface Reconstruction of the Pediatric Larynx via Structure from Motion Photogrammetry: A Pilot Study.

Endoscopy is the gold standard for characterizing pediatric airway disorders, however, it is limited for quantitative analysis due to lack of three-dimensional (3D) vision and poor stereotactic depth perception. We utilize structure from motion (SfM) photogrammetry, to reconstruct 3D surfaces of pathologic and healthy pediatric larynges from monocular two-dimensional (2D) endoscopy. Models of pediatric subglottic stenosis were 3D printed and airway endoscopies were simulated. 3D surfaces were successfully reconstructed from endoscopic videos of all models using an SfM analysis toolkit. Average subglottic surface error between SfM reconstructed surfaces and 3D printed models was 0.65 mm as measured by Modified Hausdorff Distance. Average volumetric similarity between SfM surfaces and printed models was 0.82 as measured by Jaccard Index. SfM can be used to accurately reconstruct 3D surface renderings of the larynx from 2D endoscopy video. This technique has immense potential for use in quantitative analysis of airway geometry and virtual surgical planning.

ACCURACY EVALUATION OF AUTOMATIC SEGMENTATION IN BIOMEDICAL IMAGES: 3D SPATIAL MAPPING OF SEGMENTATION ERRORS

Currently implemented accuracy metrics in open-source libraries for segmentation by supervised machine learning are typically one-dimensional scores [1]. While extremely relevant to evaluate applicability in clinics, anatomical location of segmentation errors is often neglected.This study aims to include the three-dimensional (3D) spatial information in the development of a novel framework for segmentation accuracy evaluation and comparison between different methods.Predicted and ground truth (manually segmented) segmentation masks are meshed into 3D surfaces. A template mesh of the same anatomical structure is then registered to all ground truth 3D surfaces. This ensures all surface points on the ground truth meshes to be in the same anatomically homologous order. Next, point-wise surface deviations between the registered ground truth mesh and the meshed segmentation prediction are calculated and allow for color plotting of point-wise descriptive statistics. Statistical parametric mapping includes point-wise false discovery rate (FDR) adjusted p-values (also referred to as q-values).The framework reads volumetric image data containing the segmentation masks of both ground truth and segmentation prediction. 3D color plots containing descriptive statistics (mean absolute value, maximal value,…) on point-wise segmentation errors are rendered. As an example, we compared segmentation results of nnUNet [2], UNet++ [3] and UNETR [4] by visualizing the mean absolute error (surface deviation from ground truth) as a color plot on the 3D model of bone and cartilage of the mean distal femur.A novel framework to evaluate segmentation accuracy is presented. Output includes anatomical information on the segmentation errors, as well as point-wise comparative statistics on different segmentation algorithms. Clearly, this allows for a better informed decision-making process when selecting the best algorithm for a specific clinical application.

Prediction of machining errors for free-form surfaces based on an improved grey model (1,N)

An improved grey model (GM) for predicting free-form surface machining errors was established to address the low measuring efficiencies of coordinate measuring machines (CMMs) and the low prediction accuracy of the GM(1,1) model. A number of points on a free-form surface are measured with a CMM, and machining errors are obtained. Ideas from metabolic methods and the GM(1,N) prediction model were combined. To reduce the impact of random fluctuations of the machining errors, a Markov prediction model was then used to correct the fitted results for the residuals and obtain the predicted results of the machining errors for free-form surfaces, thus improving the prediction accuracy of the model. The predicted results of the metabolic GM(1,1) and metabolic GM(1,N) models were then compared. The experimental results showed that the combination of metabolic theory, a grey model, and Markov theory effectively improved the prediction accuracy.

A Geometric Digital Twin Modeling Method for Thin-Walled Microstructures Considering Laterally Distributed Error

Precision microstructures are the core devices of electromechanical products, and their accuracy directly affects the product’s overall performance. Laterally thin-walled structures such as precision tooth plates and silicon arms are the most common types of precision microstructures. Due to the characteristics of their tiny size and complex shape, the laterally thin-walled surface is challenging to measure and model, which in turn makes it impossible to realize the accurate prediction and quantitative control of its assembly accuracy. To address this problem, this paper proposes a geometric digital twin modeling method considering the laterally distributed error of thin-walled microstructures. A geometric digital twin model that accurately represents the geometric distributed error of the structure’s lateral surfaces is built by applying an image measuring instrument to measure the point clouds of the upper and lower surface profiles, followed by point cloud filtering and merging based on a common datum, and finally surface reconstruction and integration with an ideal 3D model. The method is effectively validated on the silicon arm, a vital component of the thermal mechanical package. Its geometric modeling error is less than 1/10 of its tolerance, and the relative error between the model-based stiffness simulation calculation results and the experimental data is less than 10%. The method can effectively analyze the influence of the manufacturing errors of thin-walled lateral surfaces on the assembly accuracy and provides an adequate model basis for the control of the geometrical and physical performances of precision microstructures.

Surface Reconstruction and Error Compensation Method Based on NSGA-II Sensing Position Optimization

Surface Reconstruction and Error Compensation Method Based on NSGA-II Sensing Position Optimization

Effects of sinusoidal mid-spatial frequency surface errors on optical transfer function

Effects of sinusoidal mid-spatial frequency surface errors on optical transfer function

Method of Measuring Surface Error Peak to Valley of Micro Lens Based on Far-Field Light Distribution

Method of Measuring Surface Error Peak to Valley of Micro Lens Based on Far-Field Light Distribution

Effect of aerostatic spindle dynamic characteristics on the medium frequency waviness error of silicon wafer surface

Effect of aerostatic spindle dynamic characteristics on the medium frequency waviness error of silicon wafer surface

Conceptual frameworks for creating an automated potato harvester with a digital system for identifying soil lumps and separating them from commercial potato products

FSC VIM has developed the conceptual basis for creating an automated potato harvester with a digital system for identifying soil lumps and separating them from marketable products. Existing machines carry out the technological process in conditions of high soil moisture, which negatively affects the quality of harvesting as a result of a decrease in the completeness of separation. To determine the optimal values of the developed separating system and recommendations for subsequent changes in the design and technological parameters of the machines, a design diagram of an automated harvester is presented, a schematic diagram of modeling a system for identifying soil lumps in the Matlab/Simulink environment, data selection from field studies of the operation quality of the harvesting machine separating system, as well as the work of the neural network system and the neuron error surface for identifying soil lumps while moving along the separating surface are shown.

Optimal self-stress determination for high-accuracy mesh reflectors design considering the pillow distortion

The pillow distortion is a significant barrier to the high-accuracy design of mesh reflector antennas, which is caused by the compatible deformation between the flexible cable network and the metallic mesh, manifested as the pillow-like distortion of the mesh reflecting surface. The pillow effect deviates the mesh surface from the desired paraboloidal shape leading to the surface error. Unfortunately, current researches usually neglect this effect in the mesh reflector design due to its complicated formulation. Focusing on this phenomenon, this paper proposed an optimal self-stress determination method for high-accuracy mesh reflector design. Firstly, a mechanism model of pillow distortion is proposed based on the cable-membrane constitutive models and coupling relations. The integrated equilibrium equation of the mesh reflector is established and solved by the dynamic relaxation (DR) method, which effectively analyses the influence of the pillow distortion on the mesh reflector. Then, considering the pillow distortion, a high-accuracy design method for the mesh reflector is proposed by optimising the geometrical sizes of the cable network and the metallic mesh combining the DR method with optimisation algorithm. Finally, the proposed method is effectively applied to the design of an eighteen-unit mesh reflector antenna, and the feasibility and effectiveness of the proposed method are demonstrated.

Wear characteristics analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission considering assembly error theory

Wear is the main failure form of the gear transmission interface, runs through the whole life cycle of gear service, and the distributed error of the tooth surface due to the introduced assembly error will make the actual meshing state of the tooth surface different from the ideal meshing state, thus affecting the tooth surface wear trajectory and state. Therefore, considering the coupling relationship between assembly error and tooth surface contact analysis, the variation laws of the wear amount of the gear transmission interface of the variable hyperbolic circular-arc-tooth-trace cylindrical gear were studied under the consideration of assembly error in this article. Based on the tooth surface contact analysis method and Hertz contact theory, the transient linear load, the combined radius of curvature, the length axis and short axis of the contact ellipse, and the instantaneous sliding velocity were calculated. Through revising the calculation method of adhesive wear of variable hyperbolic circular-arc-tooth-trace cylindrical gears, the correlations between the tooth surface wear amount and gear parameters of variable hyperbolic circular-arc-tooth-trace cylindrical gears under different assembly errors were analyzed. The results show that the maximum wear occurs at the root of the tooth, and the wear at the indexing circle approaches zero, whether it is standard installation or non-standard installation. The vertical axial error and horizontal axial error have little effect on the wear, while the center distance error will aggravate the wear. The proposed method comprehensively considers the influence of assembly error and gear parameters on tooth surface wear, and this method can provide a theoretical reference for the design and analysis of anti-wear, wear reduction, and life extension of variable hyperbolic circular-arc-tooth-trace cylindrical gear tooth surface.