Tracking systems that maintain an in-focus state for moving objects have been extensively studied for a wide range of applications [1-3]. For example, the cells floating in a fluid are easily affected by Brownian motion, which causes the cells to drift in the depth direction and makes long-term cell imaging difficult. Various optical and numerical localization algorithms have been widely applied because they have advantages of automation, are non-labor intensive, and have high accuracy. The in-focus object tracking, or autofocusing, system is generally composed of two steps. First, a depth scanning process is performed to estimate the location of the object relative to the focal plane of the imaging system. The second step is to adjust the imaging optics so that the focal plane is relocated to the object plane where the object is placed.

In a conventional focus tracking system, estimating the defocusing distance of an object is usually done by moving the object along the depth direction [2]. However, the object scanning process is relatively slow because it involves mechanical movement such as the motion of a linear stage. Further, it can adversely affect the imaging quality due to the vibration caused by the movement of the stage. In order to minimize this problem, variable focusing methods have been studied, in which the depth scanning is performed by moving the focal plane of the imaging optics [4-7]. This method has a merit of minimizing the mechanical movement, but it also encounters the problem of how to scan the focal plane accurately and smoothly.

In this paper, we propose an autofocus tracking system based on digital holographic microscopy (DHM) and an electrically tunable lens (ETL). The estimation of the defocusing distance is made by taking a digital hologram (DH) of an object and numerically refocusing the image of the object [8-11], and the focal plane adjustment is made by the fast and precise focal length change of an ETL. Recently, great attention has been focused on the field combining DHM and ETL [12-19]. ETL has been used to modulate the phase of illumination or the reference wave [12-14], or to compensate the phase distortion happened in the sample arm of a DHM system [15-17]. On the other hand, the ETL itself was used as a pure phase sample of a DHM system [15, 18], or used to obtain a defocused hologram for the phase retrieval experiment [19]. To the best of our knowledge, however, a study on the autofocus tracking system based on DHM and ETL has not been reported yet. In addition, to get a more accurate and coincident measurement, the DH capturing and the bright field image taking are made simultaneously with a single camera. The different RGB color pixels of a color camera are used as different imaging channels. In our experiment, the red channel is used for getting the DH of an object under imaging and the blue channel for taking the optical image of the same object at the same time.

This proposed method has the advantage of continuous imaging without any physical scanning. It allows us to track an object like a floating cell that is drifting even along the depth direction, without using any physical scanning.

We have implemented the autofocus tracking process by two steps: the defocusing distance estimation by DHM and the focal plane shifting by ETL.

To get a DH, a Mach-Zehnder interferometry setup is configured as shown in Fig. 1. A He-Ne laser beam (Laser; HNLS008L, Thorlabs, λ = 632.8 nm) is divided into an object wave and a reference wave by a beam splitter (BS1). The reference wave is slightly tilted with a reference mirror (M2) to make an off-axis geometry and then recombined with the object wave through the second beam splitter (BS2). The interference image, or the DH, is recorded by the red channel of a color camera (CM; MQ003CG-CM, XIMEA). By illuminating a blue light-emitting diode (LED, M470L3, Thorlabs, λ = 470 nm, bandwidth = 25 nm) from the opposite side of the system, the optical image of the object can be obtained simultaneously by the blue channel of the same camera. The recorded DH is converted into the spectral domain by using Fourier transform to obtain its angular spectrum. Then, Fourier-domain filtering is applied to the angular spectrum to select the region of interest corresponding only to the object spectrum [20, 21].

In Fig. 1, it was assumed that the object S located at the focal plane d₀ was well imaged at the hologram plane denoted by h₀, the same one as the camera plane. When the object is moved to another object plane d for some reason, the image plane is shifted to h away from the original hologram plane at h₀. However, since the camera plane is placed at h₀, the image of the object at d is defocused in general. It means the camera captures a defocused image.