分数域滤波的分数傅里叶变换光学成像性能分析

Performance Analysis of Fractional Fourier Transform Optical Imaging Based on Fractional Fourier-Domain Filtering

将分数域滤波同光学成像相结合,提出了一种基于Lohmann I型的带有滤波孔径的两级联分数傅里叶变换光学成像系统。根据分数傅里叶变换和菲涅耳衍射之间的关系以及分数傅里叶变换的分数阶可加性,结合分数域滤波分析了分数傅里叶变换光学成像的基本理论。以点扩散函数和调制传递函数作为评价成像质量的准则,详细分析了不同分数阶光学系统对遥远物体的成像性能以及滤波孔径和光瞳的相对大小对成像质量的影响,并将其同传统的傅里叶光学成像进行比较。结果表明,某些分数域滤波的分数傅里叶变换光学成像系统成像性能优于传统的傅里叶光学成像,可以获得更高的分辨率。

Combining fractional Fourier-domain filtering with optical imaging, a two cascade fractional Fourier transform （FRFT） optical imaging system with filtering aperture is proposed, which is based on Lohmann I single- lens system. Firstly, the basic theory of the FRFT optical imaging combined with the fractional Fourier-domain filtering is discussed according to the relation between FRFT and Fresnel diffraction as well as fractional additivity of FRFT. Then, imaging performance for distant objects is discussed in terms of different orders, the relative sizes of filtering aperture and pupil, based on the point spread function （PSF） and modulation transfer function （MTF）. The results show that, compared with the traditional Fourier optical imaging, some FRFT optical imaging systems based on fractional Fourier-domain filtering have better imaging performance and higher resolution.