计算全息检测离轴非球面的离散相位拟合

为了计算补偿用计算全息图的刻线位置，需要对光线追迹得到的离散相位数据进行拟合。为此详细推导了均匀三次B样条和非均匀三次B样条的基函数，介绍了各自对应的曲面拟合方法。以一块抛物型离轴非球面数据为例，对其非对称的离散相位分布进行了三次B样条曲面拟合。拟合结果表明，三次B样条曲面拟合能使拟合面经过所有数据点，保证拟合精度，且得到的连续的相位补偿函数表达式结构简单（最高次数只有3次）, 还能根据实际情况优化采样点数量，控制计算量。

Fitting of discrete phase of computer generated hologram for off-axis aspheric test

The discrete phase data should be fitted to calculate the reticle position of computer generated holograms (CGHs) for off-axis aspheric surfaces. The basis functions of uniform B-spline and non-uniform B-spline were deduced in detail, and the corresponding fitting methods were introduced. With an off-axis paraboloid as an example, its discrete phase data was got and fitted by uniform B-spline and non-uniform B-spline. The results show that all the data points are on the fitting surface and the fitting accuracy can meet the requirement. Meanwhile, the expression of the phase function is very simple (the highest order is only three). Moreover, the sample points can be optimized to control the amount of calculation.