用于分数傅里叶域滤波位相元件设计新算法

Novel algorithm for designing of phase filters used in fractional Fourier domain

基于部分相干成像和分数傅里叶变换理论,建立成像系统的分数傅里叶域滤波模型,提出了可快速设计分数域位相型滤波片的 FrPI 算法。此算法将逆向设计预设初位相与分数傅里叶迭代技术相结合,针对成像系统中不同的设计要求可快速设计出所需的分数域滤波片结构。模拟结果表明,对数值孔径有限的部分相干成像系统,使用新算法设计的分数域滤波片,可有效补偿由于高频损失带来的图像失真,从而使局部线宽偏差和面积偏差分别由滤波前的 36.548nm 和 39.09%下降到了 15.234nm 和 7.72%,明显减少了空间像畸变。

A fractional Fourier filtering model for an imaging system is established on the basis of partially coherent imaging and fractional Fourier transform theory and a corresponding fractional-Fourier domain preset-phase iteration (FrPi) algorithm that can quickly design fractional domain phase filters is proposed. The algorithm through inverse design of preset-phase and fractional Fourier iteration, can quickly design the required fractional domain filter structure according to the design demands of the imaging system. The simulation results show that for the partially coherent imaging system with limited numerical aperture, the image distortion induced by high-frequency loss can be effectively compensated by using the fractional domain filter, thus local line width and area deviation can be reduced from 36.548 nm and 39.09% before filtering to 15.234 nm and 7.72%, respectively. It is demonstrated that FrPI algorithm is a new speedy tool for filter structure design applied in the fractional Fourier domain.