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用于非球面光学元件检测的计算全息图的设计与制作精度对实现非球面的高精度检测是至关重要的。为了提高计算全息图的设计精度,采用Householder变换把矛盾方程组的系数矩阵正交三角化,直接求解波面拟合系数,避免了法方程组的构造。全息图的设计是直接利用MATLAB的内部函数编程来实现的。对具有旋转对称性和非旋转对称性的物波进行了波面拟合,并设计了相应的计算全息图。结果表明,物波函数的拟合精度和全息图的绘制精度均有明显的提高,且计算速度快。
The design and fabrication accuracy of computational holograms for the detection of aspheric optics are crucial to achieving high-precision detection of aspheric surfaces. In order to improve the design accuracy of the computed hologram, the Householder transform is used to orthogonalize the coefficient matrix of the contradictory equations. The coefficient of wavefront fitting is solved directly, avoiding the construction of the normal equations. Hologram design is the direct use of MATLAB’s internal function programming to achieve. The wavefront fitting of rotational waves with symmetry and non-rotational symmetry is carried out and the corresponding computed hologram is designed. The results show that both the fitting accuracy of the wave function and the rendering accuracy of the hologram are obviously improved and the calculation speed is fast.