分数傅里叶变换的快速算法及计算全息图的研究

Research on Fast Algorithm and Compute-Generated Hologram of Fractional Fourier Transform

通过分析菲涅耳衍射积分的快速算法,依据Lohmann提出的任意阶的分数傅里叶变换的单透镜光学实验装置,详细分析了光场在此单透镜系统中的传播过程,提出了一种基于傅里叶变换的分数傅里叶变换快速算法,并对基于此快速算法的分数傅里叶变换全息图的计算机生成与数字重现进行了研究。实验结果示出了分数傅里叶变换全息图及其在重构过程中分数阶匹配与否的实验结果,验证了分数傅里叶变换分数阶的重要性质和笔者提出算法的可行性。

Proposes a fast simulated algorithm of fractional Fourier transform based on FFT by analysing the fast algorithm of Fresnel diffraction and analyzing the physical process of optical field transmitting through single - lense system by Lohmann. Also realise the computer simulation holographic generation and reconstruction. The experiment shows that the results of the fractional Fourier transform holography and reconstructed image with and without the matched fractional order, supports the availability of the fast algorithm we propose.