Optical tweezer is a useful tool to trap and manipulate small dielectric particles with a tightly focusing laser beam [1]. Holographic optical tweezers (HOTs) extend optical trapping into three dimensions (3D) with computer-generated holograms displayed on a spatial light modulator (SLM) [2–4]. With this technique, multiple laser foci can be produced interactively at arbitrary 3D positions at microscale. 3D volume imaging of trapped particles becomes a concern as axial displacement results in a defocused image. Conventional 3D imaging techniques, such as confocal microscopy, usually require scanning that physically moves the samples. Scanning greatly reduces the trapping stability and it is not preferred in a fast interactive process.

Previously, there have been several attempts to combine 3D volume imaging techniques with 3D optical trapping systems. Digital holography [5] could retrieve accurate results but at the expense of computationally involved numerical reconstruction and constraints in the reconstruction quality for large numbers of particles. The methods of engineered point spread functions [6] and stereoscopic imaging [7,8] use precalibrated look-up tables or parallax, respectively, to reconstruct 3D locations. 3D information can also be retrieved by putting two objective lenses in orthogonal observation planes [9]; this configuration results in more complex optical systems, special sample cells, and requires techniques to correlate images obtained from two separate objectives. In addition, none of the techniques mentioned above have demonstrated application in fluorescence imaging mode.

Here we present a 3D HOT integrated in a volume holographic microscope (HOT–VHM) imaging system. VHM is a spatial–spectral imaging system incorporating multiplexed holographic gratings, which capture 3D information in a single measurement [10,11]. Each multiplexed holographic grating is Bragg matched [12,13] to a different depth, and is highly selective to angular and wavelength information. VHM imaging consists of recording and imaging processes. In the recording process, during an exposure the interference pattern of the reference and signal beam form a grating that is Bragg matched to light originating from a given depth. Multiplexed gratings are formed by multiple exposures to capture several depths simultaneously [14]. Figure 1 illustrates the imaging process of a two-multiplexed gratings with volume hologram. Each holographic grating is selective to its corresponding imaging depth, which is projected at laterally separated locations on the CCD plane without overlapping due to $\mathrm{\Delta }\theta$ difference determined in the recording process. Thus, multiple depth-resolved imaging can be achieved in single measurement.

 

Fig. 1. VHM imaging system setup.

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Now consider the imaging condition in each of the multiplexed gratings. When a probe point source that has the same wavelength as the recording wavelength is placed at the focal point of the imaging objective lens, the probe field will be collimated and a replica of the reference beam will be incident on the hologram. This satisfies the Bragg-matching condition, and a replica of the signal beam is diffracted. The lens after the volume holographic gratings then focuses the beam onto a point on the CCD plane so that an image of the probe point source is formed on the camera sensor. When the probe source is moved along the $y$ axis in the focal plane, it creates a Bragg-degeneracy condition in reconstruction [10]. A displacement in the $y$ axis will result in a displacement defined by the system magnification in the image plane. When the probe point source is displaced in the $x$ axis in the focal plane results in Bragg-mismatch, the diffraction efficiency will be reduced in this case according to

In many cases, for example imaging fluorescent beads as shown in experiment later, the illumination source is not monochromatic. Imaging with broadband source is still possible in VHM. Bragg degeneracy allows holographic reconstruction to be done at wavelengths different than the recording laser wavelength provided the reconstruction angle is matched [10]. By using a broadband source or fluorescence emission, the Bragg degeneracy widens the lateral field-of-view. Thus, this method is not restricted to bright-field, or even fluorescence imaging mode.

Figure 2 shows the HOT–VHM experimental arrangement, which consists of two parts: the HOT and the VHM imaging part. The beam from a Verdi-V6 (532 nm) cw laser is collimated with a spatial filter and a collimating lens. To fully utilize the SLM and achieve high efficiency, the beam size is adjusted to fit the height of the SLM (Holoeye PLUTO-VIS). The SLM is controlled by Red Tweezers software [16] to generate holograms in real time. The beam then passes through a 4-f system to fit the size of the back aperture of a high NA microscope objective lens (MO1: Olympus UPLSAPO, 100X, NA 1.4). Fluorescent beads in diluted solution are prepared on a glass slide and mounted on a xyz stage. The emission light is collected by another microscope objective lens (MO2: Olympus ULWD MSPlan, 50X, NA 0.55), and then passes through a relay. A volume hologram grating is placed at the intersection of the focal planes of the two relay systems. Bandpass filters are used between the relay and volume hologram. This volume hologram grating was prefabricated for imaging at two planes 30 μm apart. Another microscope objective (MO3: Mitutoyo Plan Apo, 2X, NA 0.055) is used as the tube lens to project the image to the camera (Andor iXon 3). A 1951 USAF resolution target was used to experimentally test the lateral resolution of the VHM imaging system with a broadband illumination source. A bandpass filter (Thorlab FB550-40) was used in the detection path. The results are shown in Fig. 3. Features of 2 μm can be easily resolved by the system.

 

Fig. 2. Schematic design of the HOT system combined with a volume holographic imaging system. $f_1=125\mathrm{mm}$, $f_2=75\mathrm{mm}$. MO1-3, microscope objective lens. A half-wave plate is used before the SLM to align the polarization with the SLM.

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Fig. 3. (a) Lateral resolution measurement of VHM imaging system. A 1951 USAF resolution target is used. This two-plane multiplexed volume hologram shows two depths information. The resolution target is placed on the focal plane of the second depth. Group 7 Element 6 has 228.0 line pairs/mm and could be easily resolved. (b) and (c) show pixel values along vertical lines indicated by the yellow dash line at in-focus plane and defocus plane, respectively.

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To investigate the axial resolving capability of our system (Fig. 2), a ray-tracing software Zemax was utilized. In this simulation, the arrangement is the same with the volume holographic imaging part in Fig. 2. The volume hologram is represented by a Zemax user defined surface (UDS) developed by our group [17]. The formulation of this UDS is based on the k-sphere theory. In the simulation model, the volume hologram UDS parameters are set to duplicate the experimental setup. The thickness of the volume hologram used in the model is 0.9 mm. The diffraction efficiency is normalized to the peak efficiency. To experimentally measure the angular selectivity, a plane wave is incident onto the volume hologram mounted on a rotation stage (Thorlab NR360S/M). The volume hologram is rotated around the Bragg-matching angle at 0.001 deg step size. The probing wavelength is 488 nm. The diffracted light intensity is measured by an area power meter. The experimental data is compared with simulation and analytical models are plotted in Fig. 4(a). The analytical model is based on Eq. (3). The experimental result shows good agreement with the simulation.

 

Fig. 4. (a) Angular selectivity experimental measurement compared with Zemax simulation result and analytical solutions. The results show an angular selectivity FWHM of 0.03 deg. (b) The depth selectivity experimental measurement shows a FWHM of 14 μm.

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To experimentally measure the depth selectivity of our HOT–VHM system, a point source is created on the imaging plane by another objective lens (Olympus UPLFLN 40X, NA 0.75) mounted on a motorized stage (Thorlab Nanomax 300). The setup is similar to the configuration in the recording process. The point source is moved along the axial direction by moving the objective lens at 1 μm step size. The defocused images are captured on the camera. Figure 4(b) shows normalized total intensity of each defocused plane images versus the defocus distance.

To demonstrate real-time three-dimensional optical trapping and multidepth view microscopy, we trapped two microbeads of 10 μm diameter (Invitrogen F8836). Figure 5 shows the time sequence images of real-time manipulation of fluorescent beads by the HOT–VHM system. Only two trapping points were created on the targeted beads. Each subimage is an image captured in one exposure. Plane A and Plane B are two imaging planes separated by 30 μm. Some defocus images may be resolved on either Plane A or B because depth separation is slightly smaller than the axial resolution of our HOT–VHM, and this can be solved by simply increasing distance between Plane A and Plane B. Holograms generated by the software at video rate are displayed on the SLM, which allows the user to manipulate samples in real time. In this experiment, the HOTs first trapped two beads in focal Plane A, and then lifted up two beads by 30 μm. In a conventional microscope, the beads would become defocused and gradually disappear as they are lifted. In our HOT–VHM imaging system, however, these two beads enter the focus of the second imaging Plane B. On this plane, the beads were rotated along the optical axis.

 

Fig. 5. HOTs system is trapping and manipulating two 10 μm fluorescence microbeads (Media 1). Plane A and Plane B are 30 μm apart. Images at different focal planes are directly shown simultaneously on the camera. The beads are trapped and moved in Plane A first (a and b). The optical tweezers then pushed the two beads along the optical axis, placed them on Plane B (c and d), and then rotated these beads along the optical axis (e and f). The beads tend to fade in the last image due to photobleaching caused by the high power trapping.

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All these processes could be observed even though the beads had been moved by a rather long range along the axial direction. In this demonstration, the optical tweezers could only hold the beads up to about 50 μm range in the axial direction, so a VHM with two multiplexed planes was sufficient to image the beads throughout the entire range of HOT movement. However, in a more complex situation, if active operation with optical tweezers needs to be applied to a large sample, an alternate VHM imaging system with more multiplexed focal planes would be required. As example, in prior work we have previously shown a VHM imaging system with five multiplexing planes separated by 50 μm which yield a total depth of 200 μm [14].

In conclusion, we have demonstrated a 3D HOT system integrated with a volume holographic imaging system for real-time interactive trapping, manipulating, and multidepth view capability. The VHM is a direct imaging method without any computational reconstruction. The system was characterized with ray-tracing software simulation and experimental verification. The ability to work in both bright-field and fluorescence mode makes it a versatile tool for many biological applications. More importantly, to the best of our knowledge, this is the first demonstration to image 3D fluorescence samples trapped by optical tweezers. Future work involves adapting a femtosecond laser or near-infrared laser for better manipulating particles with minimal bleaching effect, and utilizing more multiplexed gratings for single-shot imaging more depth planes, i.e., larger volumes of possible bead manipulation.