数字全息显微再现像横纵向尺寸与放大倍数的关系

Analysis on the relationship between the lateral and longitudinal dimension of the reconstructed image and the magnification in digital holographic microscopy

数字全息显微再现像是物体经过显微物镜之后放大像的再现,因此,再现像和放大像的纵向尺寸易被混淆,认为再现像与放大像的纵向尺寸相等。为了辨识再现像的纵向尺寸,本文分析了数字全息显微再现像的横纵向尺寸与放大倍数的关系。首先根据光学衍射理论,对再现像的横向尺寸与放大倍数的关系和纵向尺寸与放大倍数的关系进行了理论分析,得到了数字全息显微再现像的横向尺寸与放大像相同,都被放大Mβ倍,而再现像的纵向尺寸未被放大。其次,以测量石英玻璃上刻蚀的圆孔为样本,调整样本与显微物镜的距离,以Mβ1=20.29,Mβ2=17.51和Mβ3=15.3三种横向放大倍数进行了数字全息显微实验。实验结果表明,三个再现像的纵向尺寸近似为570nm,与被测物纵向尺寸相等,未受放大倍数的影响。并且相应再现像和放大像的横向尺寸近似相等,最大差值约为0.58μm。因此,本文从理论和实验两方面证明了再现像的横向尺寸被放大了Mβ,而再现像的纵向尺寸等于被测物的纵向尺寸,不受放大倍数的影响,且可由被测物引入的光程差计算得到。本文的分析对比为准确计算数字全息显微再现像的横纵向尺寸提供技术支撑。

The reconstructed image is simply seen as the magnified image of an object in digital holographic microscopy(DHM),and hence resulting in the thought that the longitudinal dimension of the reconstructed image is misunderstood as that of the magnified image.For correctly calculating the longitudinal dimension of the reconstructed image,the relationship between the lateral and longitudinal dimension of the reconstructed images is presented in this paper.According to the optical diffraction theory,the theoretical analysis based on the lateral and longitudinal dimension of the reconstructed image is performed to obtain the relationship.The results demonstrated that the longitudinal dimension of the reconstructed image is not magnified.the lateral dimension of the reconstructed image is identical with the magnified image,which is magnified by Mβ-fold.Then,aphase micro-hole arrays etched in quartz glass is used as a sample.The experiments of measuring the micro-hole arrays in different lateral magnifications(Mβ1=20.29,Mβ2=17.51 and Mβ3=15.3)are performed to compare the dimension of the reconstructed images.The experimental results demonstrated that the longitudinal dimensions of the three reconstructed images are approximately equal to 570 nm,which are not affected by magnification.Whereas,the lateral dimensions of the corresponding reconstructed and magnified images are equal approximately,the max lateral different value is 0.58μm.Moreover,the lateral dimension of the reconstructed image is magnified by Mβ-fold,the longitudinal dimension of the reconstructed image is equal to the longitudinal dimension of the sample,and which can be calculated by the optical path difference between the object and its surrounding medium.This analysis can provide guarantee for correctly calculating the dimension of the reconstructed image in DHM.