形状因子测试的点计数和交点计数法

Form factor test methods with the point count and intersection count

本文探讨了ＦｏｒｍＰＥ、ＦｏｒｍＡＲ、规化形状因子（ＲＦＦ）和形状不规则指数（ＦＩ）４种形状因子不依赖仪器测试的点计数和交点计数测试法。根据Ｂｕｆｏｎ原理，推导出相应的适于网格测试系统的测算公式，即：ＦｏｒｍＰＥ＝１６αＰｘ／（πＩｘ２ｄ２）；ＦｏｒｍＡＲ＝４αＰｘ／（πｄｍａｊｄｍｉｎ）；ＲＦＦ＝ｄＰｘ［６（ｄｍａｊ＋ｄｍｉｎ）－４（ｄｍａｊｄｍｉｎ）１／２］／（πＩｘｄｍａｊｄｍｉｎ）；ＦＩ＝０４３３ｌＩｘｄ／（αＰｘ）１／２。式中α为直线型网格测试系统中每一测试点所代表的面积，Ｐｘ为击中待测结构的测试点数，Ｉｘ为测试线与待测结构的交点数，ｄ为测试线间距，ｄｍａｊ和ｄｍｉｎ分别为待测结构的长轴和短轴。在上式基础上进一步推导出适于不同网格类型和纵横双向交点计数时有关形状因子的测算公式。对本法形状因子的测试误差进行了分析并与图像分析仪的测试结果进行了比较。

The aim of this study was to set up a kind of method to measure form factor without instruments but based on the counts of point and intersection.Four kinds of form factors such as i.e, Form PE,Form AR,regular form factor(RFF) and form irregular index(FII) were chosen for study.According to the principle of Buffon,formulas of Form PE,Form AR,RFF and FII for grid test system of straight lines were deduced,i.e.:Form PE=16αPx/(π Ix 2d 2);Form AR=4αPx/(π dmaj dmin);RFF=dPx[6(dmaj+dmin)-4(dmaj dmin) 1/2 ]/(π Ix dmaj dmin) and FII=0.433l Ix d/(αPx) 1/2 .In the formulas,α means the area per test point,d the distance between two adjacent test lines,Px numbers of points which hit the profile structures X,Ix number of intersections of test line with profile boundary X,dmaj and dmin the major and minor axes of the profile separately.Based on the above deduced formulas,the advance formulas for the sum of intersection counts at horizontal and vertical test lines were also deduced.Comparison of the relative errors of test between our methods and image analysis system of Leica Q500MC was made.The results indicate that the tests of Form PE,Form AR,RFF and FII by the method of point and intersection counts with straight lines test grid system are accurate and practical.