We report a fast autofocusing and accurate 3D tracking scheme for a digital hologram (DH) that intrinsically exploits a polarization microscope setup with two off-axis illumination beams having different polarization. This configuration forms twin-object images that are recorded in a digital hologram by angular and polarization multiplexing technique. We show that the separation of the two images on the recording plane follows a linear relationship with the defocus distance and indicates the defocus direction. Thus, in the entire field of view (FOV), the best focus distance of each object can be directly retrieved by identifying the respective separation distance with a cross-correlation algorithm, at the same time, 3D tracking can be performed by calculating the transverse coordinates of the two images. Moreover, we estimate this linear relationship by utilizing the numerical propagation calculation based on a single hologram, in which the focus distance of one of the objects in the FOV is known. We proved the proposed approach in accurate 3D tracking through multiple completely different experimental cases, i.e., recovering the swimming path of a marine alga (tetraselmis) in water and fast refocusing of ovarian cancer cells under micro-vibration stimulation. The reported experimental results validate the proposed strategy’s effectiveness in dynamic measurement and 3D tracking without multiple diffraction calculations and any precise knowledge about the setup. We claim that it is the first time that a holographic polarization multiplexing setup is exploited intrinsically for 3D tracking and/or fast and accurate refocusing. This means that almost any polarization DH setup, thanks to our results, can guarantee accurate focusing along the optical axis in addition to polarization analysis of the sample, thus overcoming the limitation of the poor axial resolution.

中文翻译：

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利用全息偏振显微镜进行快速自动聚焦和3D跟踪

我们报告了一种数字全息图（DH）的快速自动对焦和准确的3D跟踪方案，该方案本质上利用了具有两个偏振方向不同的偏轴照明光束的偏振显微镜设置。该配置形成通过角度和偏振复用技术记录在数字全息图中的双物体图像。我们表明，记录面上的两个图像的分离与散焦距离呈线性关系，并指示散焦方向。因此，在整个视场（FOV）中，通过使用互相关算法识别各自的分离距离，可以直接获取每个对象的最佳聚焦距离，同时，可以通过计算横向距离来执行3D跟踪两个图像的坐标。此外，我们通过利用基于单个全息图的数值传播计算来估算这种线性关系，其中已知FOV中一个物体的聚焦距离。我们在多个完全不同的实验案例中证明了所提出的方法可进行精确的3D跟踪，即在水中恢复海藻（tetraselmis）的游泳路径并在微振动刺激下快速重新聚焦卵巢癌细胞。报告的实验结果验证了所提出策略在动态测量和3D跟踪中的有效性，而无需进行多次衍射计算，也无需任何精确的设置知识。我们声称这是首次将全息偏振复用设置用于3D跟踪和/或快速准确的重新聚焦。