在设计自由曲面光学元件零补偿检测的计算全息图(CGH)时,利用光线追迹可得到散乱分布的离散相位点,需通过插值得到连续的相位分布函数,以计算CGH刻线位置。采用双三次B样条插值法,对散乱分布的离散相位点进行拟合并用较少的采样点满足精度要求。利用双三次B样条的矩阵表达式及CGH加工相位函数在所加载频方向单调递增的性质,简化了求解插值曲面与x-y平行平面精确交线的方法,高精度地求取了相位型CGH的上下沿刻线位置。最后给出了一例用于自由曲面干涉零补偿检测的CGH图样。

Designing methods of null test computer generated hologram (CGH) for freeform surface optical element are researched. Bicubic non-uniform B-spline interpolation is used to fit a continuous phase function from scattered phase compensation data,which is calculated by universal ray tracing numerical method. Matrix representation of bicubic B-spline and monotonicity of CGH phase function are used to calculate the precise intersection lines of planes paralleling to x-y plane and the interpolated B-spline surface,and the positions of fringes of a phase-only CGH are solved with high accuracy. Finally a design example of null test CGH for freeform surface optical element is presented.