一种基于Abel变换的温度场重建方法

光学干涉测量通常以干涉条纹的形式显示被测对像的信息，如何从干涉条纹中获得被测流场的投影数据是重建流场的首要问题；本文提出获取流场折射率投影数据的一种方法，该方法是根据干涉条纹位移量和折射率的Abel变换关系式，将被测流场分割成不等间距的若干个圆环，使得在每一个分割间距内恰出现一条条纹，则条纹密集处获得数据点多，保证了重建的精度；通过计算机模拟验证了该方法不仅简单易行，而且获取的折射率分布的精度高；最后将该方法应用到轴对称温度场中，由折射率重建了三维温度分布。

A method of reconstructing temperature field based on abel transform

The result of optical measurement is displayed through the interference fringes. While, how to obtain the measurement data from interference fringes becomes the first question. A new method of obtaining the refractive index distribution from interference fringes was proposed. Based on the Abel transform relation between the fringe displacement and the refractive index distribution, the flow field was zoned by a series of varying space concentric circles and so as to exist only one fringe in every space concentric circle to assure the measurement accuracy. So there are mere data points in the great change distribution of the refractive index. The simulated result indicates that this method is not only simple but also higher accurate in obtaining the refractive index distribution. Finally this method has been applied in the axis symmetry temperature field and reconstructed the temperature distribution.