Exploiting a holographic polarization microscope for rapid autofocusing and 3D tracking.

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.