显微数字全息中物光波前重建方法研究和比较

根据全息理论和线性系统理论,采用离轴无透镜傅里叶变换全息记录光路,对利用菲涅耳近似法、基于瑞利—索末菲衍射积分的卷积法以及角谱理论方法数值重建全息图进行了比较研究,并做了计算机模拟验证.结果表明：菲涅耳近似法和角谱方法重建像质比较好,且菲涅耳方法重建速度快；在记录距离极小的情况下,尽管记录距离不满足通常的菲涅耳近似条件,菲涅耳近似公式仍然成立；自由空间脉冲响应的快速傅里叶变换的性质与距离有关,由卷积方法得到的再现像只在某一特定距离下比较理想；对于极小物场、大孔径显微数字全息来说,菲涅耳近似重建方法是较为有效的方法.

Comparative Studies for Reconstruction Algorithms of Object Wave Front in Microscopic Digital Holography

Based on the theorems of holography and linear system,the numerical reconstructing methods of the off-axis lensless Fourier transform hologram by Fresnel diffraction formula and by the convolution method based on Rayleigh-Sommerfeld diffraction integral and by angular spectrum theorem are studied.Both results of the theoretical analysis and the computer simulation show that the quality of the images acquired by Fresnel approximation and by angular spectrum method are better than by convolution,and the reconstructing rate by Fresnel method is fastest.Although the Fresnel approximate condition isn′t fulfilled in the condition of very short recording distance,Fresnel diffraction formula is still correct.The characters of the fast Fourier transform of the free space impulse response are related to reconstructing distance,so the quality of the reconstructed image by convolution is idea only in a special condition. For the minimal object field and large-aperture hologram,Fresnel approximation method is ideal.