Geometrical characterization of fluorescently labelled surfaces from noisy 3D microscopy data

Modern fluorescence microscopy enables fast 3D imaging of biological and inert systems alike. In many studies, it is important to detect the surface of objects and quantitatively characterize its local geometry, including its mean curvature. We present a fully automated algorithm to determine the location and curvatures of an object from 3D fluorescence images, such as those obtained using confocal or light‐sheet microscopy. The algorithm aims at reconstructing surface labelled objects with spherical topology and mild deformations from the spherical geometry with high accuracy, rather than reconstructing arbitrarily deformed objects with lower fidelity. Using both synthetic data with known geometrical characteristics and experimental data of spherical objects, we characterize the algorithm's accuracy over the range of conditions and parameters typically encountered in 3D fluorescence imaging. We show that the algorithm can detect the location of the surface and obtain a map of local mean curvatures with relative errors typically below 2% and 20%, respectively, even in the presence of substantial levels of noise. Finally, we apply this algorithm to analyse the shape and curvature map of fluorescently labelled oil droplets embedded within multicellular aggregates and deformed by cellular forces.     

大导程滚珠螺母磨削砂轮廓形精确设计和干涉消除

针对在加工大导程滚珠螺母时,可能会出现砂轮磨杆与螺母端面发生干涉的问题,从滚珠螺母磨削加工的基本方法出发,依据砂轮回转面与被加工螺母内滚道面包络的接触线是一条空间曲线的原理,建立任意安装角度下砂轮回转曲面的计算模型,并将此计算模型用于解决大导程滚珠螺母加工干涉问题.提出在保证加工时不发生干涉的前提下,选取砂轮最佳安装角和中心间距参数的方法以及在此参数下砂轮廓形的拟合优化方法.该方法计算简单、可以随时根据安装角和中心间距参数值对砂轮廓形进行修整,以保证磨削精度.以某型号大导程滚珠螺母为例,完成在保证不发生干涉的情况下相关工艺参数的选择以及砂轮廓形的优化设计,对结果进行误差分析,验证了方法的有效性.     

Automated detection of surface defects on power transmission belts

Development of a new method for an automated detection of surface defects on synchronous belts is presented and demonstrated on a group of samples with typical surface defects. Three-dimensional shape of the belt teeth is initially measured by a laser scanning system and further processed using a novel approach based on deviation map analysis. A deviation map shows deviations between the measured surface and a predefined reference surface of the tooth. Defects are detected and classified on the base of the deviation parameters calculated from the deviation map. The developed method produces results that correspond well with the results of the visual inspection.     

基于三坐标测量机的大口径球面拟合测量方法

在球面检测中,对大口径球面的测量和评价缺乏有效的手段。本文提出利用三坐标测量机获得被测球面面型的坐标数据,用最小二乘法对这些数据进行拟合,得到被测球面的几何参数。在最小二乘法的拟合过程中,提出通过改变目标函数将拟合计算转化为求解广义特征向量以获得较好的拟合效果并简化计算过程,客观地反映大口径球面的实际参数。借鉴圆度、圆柱度误差的评定建立球度误差以反映被测球面的形状误差。     

Modeling,simulation and manufacturing of drill flutes

The designing of twist drill flutes (as well as that of end mills and of some combined tools) cannot be separated from the way they are manufactured. The aim of this paper is to present an intuitive direct method for modelling, simulation and manufacturing of the drill flutes with different shapes using conical grinding wheels with standardized shapes. The mathematical approach is described, which enables us to determine the flute profile in a section perpendicular to its axis as well as the manufacturing parameters. The grinding wheel has an initial position with respect to the cylindrical work piece, which is described using four parameters (Denavit Hartenberg parameters). We have presented algorithms in pseudocode that produce the flute shape and that compute the optimum parameters of the wheel position in the manufacturing process. Subsequently, a software application based on the aforementioned model is able to create visualizations of the flute shape. The analysis of the flute shape has enabled us to understand the influence of the geometrical parameters and the position of the grinding wheel on the resulting product in the grinding process. The order in which these parameters are to be set is also specified. We have built atlases of maps presenting the influence of the geometrical parameters and the position of the grinding wheel in the grinding process upon the shape of the flute. The validity of the method is proven by the agreement of the computed values with the input and output data produced by experiment. The proposed method allows helical flutes to be generated solely by using cylindrical and conical grinding wheels of standard shapes.     

New data‐driven method from 3D confocal microscopy for calculating phytoplankton cell biovolume

Confocal laser scanner microscopy coupled with an image analysis system was used to directly determine the shape and calculate the biovolume of phytoplankton organisms by constructing 3D models of cells. The study was performed on Biceratium furca (Ehrenberg) Vanhoeffen, which is one of the most complex‐shaped phytoplankton. Traditionally, biovolume is obtained from a standardized set of geometric models based on linear dimensions measured by light microscopy. However, especially in the case of complex‐shaped cells, biovolume is affected by very large errors associated with the numerous manual measurements that this entails. We evaluate the accuracy of these traditional methods by comparing the results obtained using geometric models with direct biovolume measurement by image analysis. Our results show cell biovolume measurement based on decomposition into simple geometrical shapes can be highly inaccurate. Although we assume that the most accurate cell shape is obtained by 3D direct biovolume measurement, which is based on voxel counting, the intrinsic uncertainty of this method is explored and assessed. Finally, we implement a data‐driven formula‐based approach to the calculation of biovolume of this complex‐shaped organism. On one hand, the model is obtained from 3D direct calculation. On the other hand, it is based on just two linear dimensions which can easily be measured by hand. This approach has already been used for investigating the complexities of morphology and for determining the 3D structure of cells. It could also represent a novel way to generalize scaling laws for biovolume calculation.     

High-precision detection of focal position on a curved surface for laser processing

A new technique for detecting the focal position of a curved surface provides several advantages both in research and industrial applications. The quality of patterns lasered on a roll surface is determined by the precision of the focus detection, and surfaces of the massive rolls used in laser fabrication can be difficult to adjust properly using conventional technologies. Here, a unique method for detecting the focal position of a curved surface based on the reflected profile of a laser beam is presented. The versatility of the proposed technique results from being able to adjust the laser beam based on changes in the shape and diameter of the beam spot when the specimen surface deviates from the focal plane. A theoretical model based on three-axis movement is proposed, and experimental setups are developed based on the model. Analysis of the obtained results enables high precision positioning of the specimen and identification of the focal point. Furthermore, the presented technique can be used to locate the focal point on any curved surface. Therefore, the theoretical model, analysis results, and focal detection method can be combined in an algorithm for a novel auto-focusing system that can be applied to laser processing of curved surfaces, such as fabricating microgrooves, or engraving roll surfaces in printed electronics.     

Digital in-line holography for the analysis of Bénard-convection

Digital in-line holography (Skarman et al., Flow Measurement and Instrumentation 7 (1) (1996) 1–6) represents a novel optical method for flow and temperature measurements of transparent liquid media. A CCD-camera is used to record digital holograms of tracer particles in a fluid volume. The procedure is based on the phase-shift method. Algorithms for computational focusing on individual particles in three dimensions have been developed. As an additional benefit the holographic recording contains interferometric information about the optical path length which in turn enables the calculation of the density and temperature profile of the flow.     

Optical 3D profilometer for in-process measurement of microsurface based on phase retrieval technique

We have proposed an optical method that can be applied to in-process or in situ measurement of the microsurface profile. The present method is based on optically performed spectral analysis and the phase retrieval technique. Spectral information of a surface profile is obtained by measuring the Fraunhofer diffraction intensity. The phase retrieval technique is used to reconstruct the surface profile from the measured spectrum. We have developed an instrument on the basis of the general principles of the present method, and measured the surface of a reference standard having rectangular pockets 44 nm deep at intervals of 10 μm. The measured surface profile was in good agreement with the nominal dimensions of the specimen as well as the surface profile obtained by atomic force microscopy (AFM).     

Complexity analysis and calculation for sculptured surface in multi-axis CNC machining based on surface subdivision

Complexity of sculptured surfaces has a great influence on multi-axis computer numerical control (CNC) machining performances such as processing efficiency, surface quality, and energy consumption. A term called surface machining complexity (SMC) is first presented to describe the complexity level of surface geometrical shape features, and its influence on CNC machining performance. Shape features of sculptured surfaces are classified into seven categories based on surface curvature. An innovative method for quantifying SMC using surface subdivision is proposed. Firstly, representation of sculptured surfaces is introduced. Then, three processes of surface subdivision are presented, which are surface discretization based on iso-parameter line sampling, rough partitioning based on surface shape categories, and region grouping based on two criteria. After that calculation, formulas of SMC including formulas of local SMC and global SMC are developed. The proposed formulas utilize three correction factors to describe the influences of surface size, cutter diameter, grouping order, and mode of different surface shape categories. Finally, the proposed method is applied to calculate SMC for a typical sculptured surface and multi-axis CNC machining experiments to demonstrate the ability of our method, which can form a foundation for further research.     

评定二次曲面轮廓度误差的角度分割逼近法

提出一种基于角度分割逼近算法和粒子群算法计算二次曲面轮廓度误差的最小区域评定方法来准确评定任意位姿的二次曲面轮廓度误差。首先,给出了能够实现角度分割逼近算法的两条前提假设;基于假设,给出了更合理的算法网格布局递推公式。根据曲面轮廓度误差的定义建立了误差评定的精确模型。然后,采用角度分割逼近法求取测点到拟合二次曲面轮廓的距离;通过粒子群算法,以所有的点与二次曲面距离中的最大值为适应度值拟合出二次曲面一般方程,并实现被测轮廓与理论轮廓位置的匹配。最后,采用上述方法对某抛物面天线进行了评定,并与参数分割法、SMX-Insight和最小二乘法进行比较。实验结果显示：该方法测得的天线轮廓度误差为0.659 8 mm,比其它方法准确。结论表明：基于角度分割算法能够更有效地评定任意位姿二次曲面轮廓度误差,计算准确、迅速,而且无需确定待分割区域。     

Modelling of tolerances and manufacturing dimensions

To obtain imposed dimensional and geometrical specifications for any mechanical piece, production tolerances must be calculated. So a simulation of workpiece behavior when it is machined, has permitted calculations of deviations on machined surfaces.The method of deviation calculation is based on a comparison between imposed functional tolerance and the tolerance calculated in relation to deviations on two machined surfaces or between a machined surface and the operational datum.The one direction modelling of deviations inquires practical inputs such as the planning process, the operational datum, the deviations on rough surfaces, and deviations on surface datum for any stage of machining. The developed method allows determining the deviations on machined surfaces. Then, tolerances on production dimensions were calculated in three directions. These results have permitted to define average production dimensions, which may be used for NC machine programming and to prepare an optimal rough piece configuration.The developed method has been applied for the machining of a fixing screw.     

基于激光三角法的汽车同步带齿形轮廓参数测量

针对目前汽车同步带齿形轮廓参数测量过程中存在的测量效率低和人为因素影响大等问题,提出了一种基于激光三角法的汽车同步带齿形轮廓参数非接触式测量方案,并设计了相应的汽车同步带齿形测量装置。该装置通过激光位移传感器与汽车同步带传动速度的配合,对汽车同步带齿形轮廓数据进行采集,并提出一种改进后的分割算法对采集到的齿形截面轮廓数据进行特征分割。通过对分割后齿形数据的拟合,实现了齿形轮廓曲线特征的分段重构并获得被测带齿的轮廓参数。基于激光三角法对汽车同步带齿形轮廓参数进行测量,实现了对齿形轮廓参数自动测量提高了测量效率避免了人为因素的影响,保证了测量精度,有望在汽车同步带实际生产中得到应用。     

螺杆压缩机转子成形砂轮刃形计算

针对给出任意转子型线时转子齿面加工的成形砂轮刃形设计,利用螺杆转子加工过程中转子和砂轮的相对位置关系,通过对转子型线坐标系的旋转变换,建立空间转子坐标系和成形砂轮坐标系之间的几何映射关系;基于啮合原理,建立转子齿面与成形砂轮的接触线方程,并给出解析和离散两种转子型线表达方式的刃形求解方法。在此基础上,根据转子砂轮之间的设计间隙,通过对接触线沿转子齿面法向进行偏置,获得了修整后的砂轮等距齿面刃形,避免了传统修整方法导致的法向齿间间隙不均等问题。加工结果表明,该方法能够满足螺杆转子的加工精度要求,是一种有效的螺杆转子齿面成形砂轮的刃形设计方法,并可推广应用于其他螺旋面成形砂轮或盘形铣刀的刃形设计。     

基于等距曲面的弧面凸轮单侧面数控加工刀位优化算法

针对弧面凸轮廓面的多轴数控加工,在分析现有各种加工工艺方法,尤其是分析单侧面加工方法存在的不足的基础上,围绕减小加工得到的实际廓面与理论设计廓面的极差,提出一种以刀轴轨迹面与凸轮廓面等距曲面的极差最小为优化目标的弧面凸轮单侧面数控加工刀位数据计算的优化算法。所建立的刀位优化算法综合了不可展直纹面侧铣加工的两点偏置算法和三点偏置算法的优点。通过实例对各种单侧面刀轨规划算法进行加工误差综合对比分析,结果表明所建立的刀位计算优化算法正确有效,可显著减小编程误差,为进一步提高弧面凸轮单侧面加工精度和完善加工工艺奠定了扎实的理论基础。     

最大内接圆法内孔截面圆度误差评价与实现

针对内孔圆度误差的最大内接圆法评价,提出了一种基于最大弦线截交对称关系的评价模式。利用最大内接圆评价法的几何特征关系,在确定虚拟中心位置的基础上弦线截交模式可以快速搜索到最大内接圆圆心的位置,并且在评价中避免了计算搜索步长和搜索方向。分析表明:利用几何关系的弦线截交评价模式,达到了高效、精确评价内孔截面圆度误差的目的。可实现三坐标测量机及其它测量仪器利用坐标采样数据对内孔圆周截面形状进行最大内接圆法误差评价。     

机械加工表面形貌分形特征的计算方法

提出应用小波变换计算表面形貌分形特征参数，基于Weierstrass-Mandelbrot函数（W-M函数）和Majumdar-Bhushan函数（M－B函数）这2种常用于表征和模拟机械加工表面轮廓曲线的标准分形函数，验证了小波变换计算分形维数具有很高的精度。与其它计算表面形貌分形维数的方法进行了比较，结果表明小波变换方法的稳定性和准确性好。应用小波变换计算了不锈钢和铜2种材料的机械加工表面的分形维数。     

A simple method for AFM tip characterization by polystyrene spheres

An AFM image would not be the true topography of a surface because of the limitation of a finite size of the tip. The true topography of the surface can be deduced if we can know the tip shape. In this paper a simple method has been established to determine the profile of an AFM tip. A geometrical model for the tip and a spherical object has been proposed to show the procedure for deducing the tip shape from AFM images. Isolated spheres and closely packed spheres with different diameters have been observed to confirm the tip shape by this method. It is a non-destructive method to determine the tip shape and the results can be used for future reconstruction of an AFM image.     

An improved tolerance charting technique using an analysis of setup capability

The tolerance charting method enables the calculation of working tolerances in machining process planning. The method has been used as a basic tool for analysing process plans for many decades. Process capability in tolerance charting is modelled using the tolerances of the working dimensions. The literature shows that machining process capability can be analysed from the point of view of surface position errors. During setups, it is possible to perform decomposition into two surface position tolerances: a datum surface position tolerance and a machining surface position tolerance. This type of analysis has the advantage of producing simplified tolerance chains. This paper provides an adaptation of the tolerance charting technique that uses a capability model based on datum and machining surface position tolerance. The results show an improvement in the working tolerance stackup that reduces the capability required for productive resources. As a result, reductions in manufacturing costs can be achieved. The proposal is valid for manual or computer-assisted techniques.     

On the development of airfoil section inspection and analysis technique

In blade inspection, the measurement and analysis of airfoil section parameters and geometric tolerance are very important but complicated. The aim of this study was to apply coordinate measurement techniques to blade sections measurement and to develop methods for the evaluation of dimensions and geometric tolerance. Due to significant variation in the blade shape, especially near the upper sections, the leading edge and the trailing edge, the measurement paths based on the CAD model may lead to incorrect results. Thus, a two-step measurement procedure, including a rough measurement and a fine measurement, along with the calculation of the back-off directions was proposed to improve the measurement accuracy. In blade profiles analysis, several algorithms, including a best-fit algorithm, blade parameters computation and profile and tolerance zone analysis, were used to evaluate section parameters and geometric tolerance. Successful experimental results have demonstrated the feasibility of the proposed method.