We report on a compact twin-beam interferometer that can be adopted as a flexible diagnostic tool in microfluidic platforms with twofold functionality. The novel configuration allows 3D tracking of micro-particles and, at same time, can simultaneously furnish Quantitative Phase-contrast maps of tracked micro-objects by interference microscopy, without changing the configuration. Experimental demonstration is given on for in vitro cells in a microfluidic environment.
© 2011 OSA
Nowadays the incredible development of bio-microfluidic technology [1,2] highly demands for substantial advancements in multifunctional tools for characterization, monitoring, and manipulation in microfluidic environments. In recent years, the number of proposed and implemented techniques for diagnostic purposes is greatly grown. Single approaches have been demonstrated for imaging, phase-contrast quantitative analysis [3–13], manipulation and trapping [14–16], tracking of micro-objects (i.e. nano-drops, carbon nanotubes, bio-cells, quantum dots, dielectric spheres and for metallic spheres , nano- and micro-particles ), tracking of both non-fluorescent  and fluorescent particles [20,21]. Many techniques accomplish the tracking with high detection accuracy of a single particle [22–24] and others in which a statistical localization algorithms have been proposed [25,26]. Tracking objects in three-dimensional space using digital multiplexing holography have been presented recently . Also a three-dimensional tracking of Brownian motion of a particle trapped in optical tweezers was reported .
Elective approaches to be adopted in microfluidic environments are optical/photonics ones that have the remarkable advantage to be non-contact, full-field, non-invasive and can be packaged thanks to the integrated optics and optofluidic modalities [2,29]. Various microfluidic platforms have been developed for manipulating droplets, handling micro-nano-objects, visualize and quantify processes occurring in-loco and for direct application for lab-on-a chip configurations. In fact, phase-contrast approaches, adapted to a lab-on-a-chip configurations, have given the possibility to get quantitative information with remarkable lateral and vertical resolution directly in situ. Moreover, techniques for tracking of micro-objects needs to be developed for measuring velocity fields, trajectories patterns, motility of cancer cell and so on [3,30]. In ref . the video stream captured by an in-line holographic microscope can be analyzed on a frame-by-frame basis to track individual colloidal particles experiencing three-dimensional motions with nanometer resolution. In  is introduced optical fiber illumination for real-time tracking of optically trapped micrometer-sized particles with microsecond time resolution. Digital shearing method was adopted in  to extract three-component velocity in particle image velocimetry.
Several particle-tracking and imaging methods have achieved three-dimensional sensitivity through the introduction of angled micromirrors into the observation volume of an optical microscope [18,33]. In ref . the authors developed a theoretical model of the imaging response of such devices and show how the direct and reflected images of a fluorescent particle are affected. In particle-tracking applications, asymmetric image degradation manifests itself as systematic tracking errors. Recently some experiments have been performed to get simultaneous trapping and tracking, but, in order to achieve this double function, they used two coupled lasers systems [31,35,36]. In this paper, we show a completely new concept of a compact holographic microscope that can ensure the multi-functionality, accomplishing, by the same configuration and simultaneously, accurate 3D tracking and quantitative phase-contrast analysis. Experimental results are presented and discussed for in vitro cells in microfluidic environment. The system is very simple and compact and is based on twins-laser-beams coming from a single laser source. Through this simple conceptual design we show how two different functionalities can be accomplished by the same optical setup, i.e. 3D tracking of micro-object and quantitative phase contrast imaging. It is important to note that by same system it is possible accomplish other two different functionalities, i.e. for driving particles along appropriate paths, performing simultaneously their interferometric analysis .
2. Working principle
2.1 Optical configuration
The optical configuration is illustrated in Fig. 1 . The particles/cells are loaded in a chamber of about 5x5x0.3mm, assembled by using two cover glasses (0.15 mm thick) with a double-sided tape spacer (0.3 mm thick). Two beams, coming from the same DPSS laser (532nm, 250mW), enter into the microscope objective (oil immersion Nikon 100x, 1.2 NA). The two beams are sent slightly off-axis through the same microscope objective. The angle between the beams is about 4 degrees. Since the two beams passes through the same microscope objective, in principle they are in focus in the same image plane. Nevertheless the twin beams can experience aberrations giving rise to some focus-shift too. A 20x microscope objective is used to obtain an image on a CCD plane. The tracking is performed by evaluating the double out-of-focus projections of the particles due to the twin-beams onto the array detector plane. The principle is simple and allows tracking in 3D. In fact as shown in Fig. 1 each particle forms two shadows on the CCD array, The separation between the two shadows is a function of the longitudinal position of the particle. By the very same configuration also digital holograms can be directly recorded with the aim to obtain quantitative phase contrast images of the micro-objects as depicted in Fig. 1.
2.2 Modeling for 3D tracking
In our model, we have two plane beams sent through an objective microscope. The experimental configuration is depicted in Fig. 2 . The lens makes a Fourier transformation thus focusing the two beams, in ideal condition without considering the aberrations, in its back focal plane. An additional lens is used to image the microfluidic volume. Essentially we can sketch the imaged volume as composed by two cones, transmitted into the microfluidic sample. The two cones (see Fig. 2) are partially superimposed in the image space. On the CCD digital sensor, the intersection between the beam and the sensor plane of each cone is a circle ellipse with radius , where dc is the distance between the digital sensor and the vertex of cone. Supposing that the principal axes of cones are parallel, we consider a reference system of coordinates Oxyz where the plane xy is on the digital sensor with O in the center. In this reference system, we define the vertex of both cones and where and are given by the center of two circles in the sensor plane and . Then we suppose that a microscopic object, that can be considered a point with coordinates , is in the volume defined by the union of the two cones, that is , where are the cones solid angles. In this scenario, we have three possible situations. , in this case we will have a projection of the point P on the sensor plane in the circle relative to the cone 1. If we have a projection of the point P on the sensor plane in the circle relative to the cone 2. Finally if , in this case we have two projections of the point P on the sensor plane (see Fig. 1), i.e. each twin laser beam makes a projection (or shadow) of the particle on the CCD array detector. This latter situation is interesting because we demonstrate that it is possible to find the path of a point using the information on the projections coordinates, by the knowledge of the position of the two vertices C1, C2. Supposing that the projections of P in the two circles are the points and respectively, the estimation of P is given by
The hypothesis assure that one and only one intersection's point exists.
2.2 Modeling for 3D tracking
To demonstrate how the tracking functionality works we firstly present here some numerical simulations to validate the reliability of the working principle of the proposed method. In our numerical simulations, we set , with , and the unit are in pixels. Using these parameters it is possible to find the aperture angles of cones:
We report here simulations of two different paths of particle P. A linear path and helix paths, respectively. The following equations give the math formulation of the two simulated trajectories. The linear path with , , .
Elliptical helix given by the following equation:
For both simulated paths, we compute the mean error and the standard deviation error on the difference between the real path and the path estimated with the proposed method.
Media 1 shows the results of these two simulation (frames on the left). From the simulated images we evaluate the corresponding points P1 and P2 in the sensor plane for both paths. By the knowledge of the P1 and P2 coordinates of and through Eq. (1) we reconstructed the paths. Figure 3 shows the comparison between the simulated and reconstructed paths for the linear and the coil path, respectively. The results show very good agreement between the simulated values and the retrieved paths.
Here we report two experiments to demonstrate the capability and usefulness of the proposed method. First, to show the reliability of the method, we performed the system calibration by using a spherical particle (latex) displaced along the optical axis with known steps, simulating a simple linear path. In a second experiment we show how the method can be applied in real situation by tracking 3D paths of multiple motile in-vitro cells.
3.1 System calibration displacing a particle along the optical axis with known steps
In Fig. 4 are shown the images recorded at different distances. The experimental path is given by , , , with acquisition step equal to 20μm. The CCD pixels dimension are px = py = 6.7µm.
We reconstructed the path by estimating the centroid of two images of micro-spheres for each frame of the recorded sequence, by applying the above equations. The centroids are computed using the classical algorithm for detecting regions of interest  and their center of mass. The result are shown in Fig. 5 (and fully visualized in the supplementary Media 2) for this experiment. We calculate the average value and standard deviation value of difference between the estimated positions and real position having 1.07µm and 2.02µm, respectively. Since the ratio between the standard deviation computed and the acquisition step is approximately 10%, we have the similar accuracy show in the z-localization proposed in .
3.2 Tracking 3D paths of multiple cells
The method was finally applied to a real experimental situation in which we had various particles (cells) floating into a microfluidic environment chamber. In the considered case we did not have a priori information on those floating in-vitro cells, while they are subject to a displacement field in the microfluidic sample. We simply recorded, with the experimental configuration in Fig. 1 a sequence of images. The digital sensor was a CCD array as in the same setup of previous experiment. In Fig. 6 are shown three frames corresponding to the passage of three different cells across the imaged volume. Also in this case, we estimated the centroids of cell by an image processing algorithm for each frame of the recorded movie.
The results of the retrieved 3D paths of the cells were easily estimated by the proposed method. The results, i.e. the 3D plot of the paths, are shown in Fig. 7 . The dynamic evolutions can be seen in full in the supplementary Media 3.
From the last result, it is clear that all the three cells follow paths along the same streamlines in the microfluidic flux. However, can be noted that cells experience a displacement mainly along the longitudinal axis. This is due to the twins beams that have surely a role in influencing and/or determining the paths followed by the particles, because of both scattering (radiation pressure) and the attractive force (similar to optical tweezers). Nevertheless the optical configuration can be designed to cancel the effect of the light on the paths. In fact by using a trivial stroboscopic illumination, depending also on the velocity fields of the particles, the influence of the light on the paths can be drastically reduced up to become completely negligible, making this method a full non-invasive 3D tracking approach.
4. Quantitative phase – contrast microscopy of tracked particles
In addition to the tracking functionality we show here that the same set-up can be adopted as quantitative phase contrast microscope. In fact due to the coherence properties of the adopted laser source we can see that the twin-beams interfere to produce nice interference fringe patterns at the CCD sensor plane. Indeed the interference patterns, as those in Figs. 4 and 6, are really digital holograms. Such digital holograms contain quantitative information about the cells. In fact optical path length variations due to the presence of the cells along can be retrieved easily. Digital holograms (i.e., each frames of the recorded movies) can be numerically reconstructed by well known diffraction propagation methods to get the quantitative phase contrast maps of the cells (QPMs). We adopted the holographic reconstruction by the convolution method [8,37–41]. In Fig. 8 , we show an example of the phase-contrast map of the cell A.
It is important to note that digital holography method could also give the 3D tracking of the particles in the imaged volume. In fact the numerical reconstruction of the whole complex optical wavefront would allow to have reconstructions at different depths (i.e. at various distances from the CCD array, on the hologram plane). However it is well known that have accurate information of the axial position of a particles it would be necessary to assess with high accuracy of the in-focus position . Various method have been investigated and demonstrated for this aim and the topic is still matter of intensive investigation. Different strategies have been proposed and often quite heavy computational efforts are necessary to get the good in-focus images and sometimes high uncertainties still remain. The method proposed here, on the contrary, allows quite easy calculation of the depth coordinate of the particles.
We developed a simple and compact digital holographic microscope in off-axis configuration by using two twins laser beams passing through the same microscope objective. We demonstrate the effectiveness of this novel configuration that can be especially suitable for phase contrast analysis and 3D imaging of biological sample and microfluidic devices. We implemented experimental the set-up, validated the model either numerically and from the experimental point of view. Demonstration of the 3D tracking and the capability to perform Quantitative Phase-Contrast microscopic analysis, on multiple moving in-vitro cells in a microfluidic environment, was finally performed and we believe can be useful in lab-on-a-chip devices. The optical configuration is very simple as it is made by only two beams. The beams can be produced by various configurations such a diffraction grating at the input pupil of the microscope objective, or even by using a spatial light modulator . Furthermore, to make the optical configuration very compact, specialized laser devices can be used for generating the twin-beams simultaneously. For example, in the visible spectral region, the second harmonic generation in PPLN crystals can be used for the simultaneous generation of twins beams at 532 nm , while in mid-IR (10 μm) multibeams generation can be achieved by quantum cascade lasers  in a region of the spectrum in which digital holography has been demonstrated too [41,44].
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