Shape Error Measurement Using Ray-tracing and Fringe Scanning Method

自由形式用于制造工业产品，以改善其自身的功能。自由曲面的测量对于获得高质量的产品非常重要。由于测量所需的精度变高，因此需要在加工中和加工机器上进行测量。本文提出了一种改进的光栅投影法来精确测量自由曲面。并开发了相应的测量系统和软件，使该方法更适合于实际应用。主要研究成果如下：1）自由曲面测量机的研制：根据所提出的原理研制了自由曲面测量机。由于所开发的机器包括液晶面板，因此投影的网格图案的间隔和相位是电可变的。2）用于分析形状的基本程序的开发：开发了网格的设计程序和修改的网格的分析程序。用所开发的程序对样品的电导率进行了测量。3）开发了一种高速分析算法：以被测形状的倾斜度为数据源，采用该方法得到的数据为被测形状的倾斜度。形式整合倾向。因此，提出了一种适用于求积的高精度积分方法。我们提供的系数条件，使积分误差小于辛普森的3/8规则，这是一个典型的积分方法。通过仿真实验验证了该方法的优越性，并对该方法的实用化进行了前景展望。

A free-form is used for manufacturing industrial products to improve on their own function. Measurements of the free-form are important to obtain the products of quality. Since accuracy required for measurements becomes high, it is necessary to measure in a processing and on a processing machine. In this report, a grating projection method modified from the Hartmann test is proposed to measure the free-form precisely. And furthermore, measuring systems and software are developed to make the proposed method fit for practical use. Results are follows.1) Development of a free-form measurement machine:The measurement machine was developed based on the proposed principle. Since the developed machine include a liquid crystal panel, an interval and a phase of projected grid patterns are electrically variable.2) Development of basic program to analyze a shape:A design program of grids and an analyzing program of modified grids are developed. Shapes of samples were measured with the developed programs. And the results was compared with results measured by general measurement machine.3) Development of an algorithm for analyzing at high speed:Data obtained by the proposed method were inclination of form under test. The form integrates the inclination. Therefore a highly precise integration method appropriate for quadrature is proposed. We provide the coefficient conditions for rendering the integration error smaller than that of Simpson's 3/8 rule ; this is a typical integration method. In addition, the advantage of this method is demonstrated by simulation experiments.A prospect to make practicable was obtained from the results.