在数字全息显微术中, 为了获得非重叠、高质量再现像, 需要设置合理的记录距离。本文结合再现条件与记录条件进行较全面地分析设计, 即在考虑采样定理、频谱分离条件之外, 还研究了光学传递函数离散条件和再现像与放大像之间的尺寸关系, 进而更精确地得到了预放大数字全息系统记录距离的设置方法。以USAF1951分辨率板为样本, 分别以记录距离为50.50, 134.20和140.30 mm进行实验, 结果表明, 当记录距离不考虑放大像与再现像之间尺寸关系时, 利用菲涅尔衍射法获得的再现像模糊; 当记录距离考虑光学传递函数离散条件时, 利用卷积法再现能获得清晰再现像; 当记录距离同时满足再现条件和记录条件时, 数值再现能获得高质量的再现像, 且能分辨分辨率板的7.6组条纹, 即横向分辨力达到2.19 μm, 进一步论证了所提需要考虑再现像与放大像之间的尺寸关系和光学传递函数离散条件来设计记录距离的方法更精确。通过理论推导和实验验证了所提的设计记录距离的方法较全面、给出的记录距离范围较合理, 为数字全息显微术获得高质量的再现像提供了保障。

A reasonable recording distance sets the premise to obtain a reconstructed image with no overlap and high-quality pre-magnification digital holography. Herein, a comprehensive analysis and design of the recording distance were proposed, which combines the conditions of recording and numerical reconstruction. In addition, not only were the sampling theorem and the spectrum separation theorem considered, but the relationship between the sizes of reconstructed and amplified images, and the sampling requirement of the optical transfer function was also studied. Furthermore, a reasonable design method of the recording distance was obtained by theoretical derivation under four conditions. Finally, the resolution test target, 1951 USAF, was used as an example. There were three holograms with recording distances of 50.50, 134.20, and 140.30 mm. The experimental results demonstrate that the reconstructed images, obtained by the Fresnel transform, are indistinct when the relationship between the sizes of the reconstructed and amplified images is not considered; the reconstructed images obtained using the convolution approach are distinct when the sampling requirement of the optical transfer function is considered; the reconstructed images are distinct when two conditions of the numerical reconstruction are considered. The resolution of the reconstructed images reaches 2.19 μm. Moreover, the design combining the relationship between the sizes of the reconstructed and amplified images is quite precise, and it represents the sampling requirement of the optical transfer function. The theoretical derivation and experiments indicate that the design of the recording distance is comprehensive and reasonable. This design can provide a guarantee for obtaining the reconstructed image with no overlap and high quality.